Search for Third Generation Squarks in the Missing ... - C.I.E.M.A.T
Search for Third Generation Squarks in the Missing ... - C.I.E.M.A.T
Search for Third Generation Squarks in the Missing ... - C.I.E.M.A.T
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<strong>Search</strong> <strong>for</strong> <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong> <strong>in</strong> <strong>the</strong>Miss<strong>in</strong>g Transverse Energy plus Jet Sampleat CDF Run IIBúsquedas de squarks de la tercera familia en sucesoscon jets y momento transverso neto en el experimentoCDF run IICIEMATandDepartamento de Física Atómica, Molecular y Nuclear(Universidad Complutense de Madrid)PhD DissertationMiguel Vidal Maroñoto apply <strong>for</strong> <strong>the</strong> degree of Doctor of Philosophy <strong>in</strong> Physics.Supervised byDr. Oscar González LópezMarch 2010
Dr. Oscar González López, <strong>in</strong>vestigador titular del Departamento de Investigación Básica, delCentro de Investigaciones Energéticas, Medioambientales y Tecnológicas (CIEMAT),Certifica:Que la presente memoria: “<strong>Search</strong> <strong>for</strong> <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong> <strong>in</strong> <strong>the</strong> Miss<strong>in</strong>g TransverseEnergy plus Jet Sample at CDF Run II”, ha sido realizada bajo mi dirección en elDepartamento de Física Atómica, Molecular y Nuclear de la Facultad de Ciencias Físicas de laUniversidad Complutense de Madrid por Miguel Vidal Maroño, para optar al grado de Doctoren Ciencias Físicas.Y para que así conste, en cumplimiento de la legislación vigente, presento ante la UniversidadComplutense de Madrid esta memoria, firmando el presente certificado:Madrid, a 23 de noviembre de 2009
ContentsList of Figures 7List of Tables 111 Introduction 12 Theory Introduction 32.1 Standard Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32.1.1 Quantum Electrodynamics . . . . . . . . . . . . . . . . . . . . . . . . 52.1.2 Quantum Chromodynamics . . . . . . . . . . . . . . . . . . . . . . . 62.1.3 Parton Distribution Functions . . . . . . . . . . . . . . . . . . . . . . 82.1.4 Electroweak Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . 102.1.5 The Higgs Mechanism . . . . . . . . . . . . . . . . . . . . . . . . . . 122.1.6 Standard Model Limitations . . . . . . . . . . . . . . . . . . . . . . . 152.2 M<strong>in</strong>imal Supersymmetric Extension of <strong>the</strong> Standard Model . . . . . . . . . . . 172.2.1 Supersymmetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172.2.2 Supersymmetry and <strong>the</strong> Hierarchy Problem . . . . . . . . . . . . . . . 172.2.3 O<strong>the</strong>r Benefits from <strong>the</strong> Introduction of SUSY . . . . . . . . . . . . . 182.2.4 The M<strong>in</strong>imal Supersymmetric Standard Model . . . . . . . . . . . . . 202.2.5 MSSM Lagrangian and R-parity . . . . . . . . . . . . . . . . . . . . . 232.2.6 SUSY Break<strong>in</strong>g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252.3 <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong> . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
4 Contents2.3.1 Scalar Bottom from Glu<strong>in</strong>o Decay . . . . . . . . . . . . . . . . . . . . 272.3.2 Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o . . . . . . . . . . . . 313 Experimental Setup 353.1 The Tevatron Collider . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 CDF Run II Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.1 Track<strong>in</strong>g and Time of Flight Systems . . . . . . . . . . . . . . . . . . 403.2.2 Calorimeter System . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.3 Central Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . 433.2.4 Plug Calorimeters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 453.2.5 Muons System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 463.3 Lum<strong>in</strong>osity Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.1 CLC detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.3.2 Measurement of <strong>the</strong> Lum<strong>in</strong>osity . . . . . . . . . . . . . . . . . . . . . 483.4 Trigger and Data Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . 493.4.1 Level 1 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513.4.2 Level 2 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 523.4.3 Level 3 Trigger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 543.5 Level 2 Trigger Upgrade <strong>for</strong> High Lum<strong>in</strong>osity . . . . . . . . . . . . . . . . . . 543.5.1 Level 2 XFT Stereo Upgrade . . . . . . . . . . . . . . . . . . . . . . . 553.5.2 Level 2 Calorimeter Upgrade . . . . . . . . . . . . . . . . . . . . . . . 554 Event Reconstruction 574.1 Track and Primary Vertex Reconstruction . . . . . . . . . . . . . . . . . . . . 574.2 Lepton Identification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.1 Electron Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . 584.2.2 Isolated Tracks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604.3 Jet Reconstruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.4 Miss<strong>in</strong>g Transverse Energy Reconstruction . . . . . . . . . . . . . . . . . . . 62
Contents 54.5 Quality Selection Cuts <strong>in</strong> / E T Analysis . . . . . . . . . . . . . . . . . . . . . . 635 Heavy Flavor Tagg<strong>in</strong>g 655.1 Secondary Vertex algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.2 Mistag Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.3 Charm Hadron Analysis Oriented Separator . . . . . . . . . . . . . . . . . . . 715.4 CHAOS Efficiency and Scale Factors . . . . . . . . . . . . . . . . . . . . . . . 746 <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 776.1 Dataset and Basic Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776.2 Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 786.3 Monte Carlo Signal Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.4 Background Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 816.4.1 Top Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 826.4.2 W/Z and Diboson Production . . . . . . . . . . . . . . . . . . . . . . 826.4.3 Mistags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.4.4 Heavy-Flavor Multijet Production . . . . . . . . . . . . . . . . . . . . 836.4.5 MUTARE Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 836.5 Control Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 856.6 Signal Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896.6.1 Neural Networks Architecture . . . . . . . . . . . . . . . . . . . . . . 906.6.2 Multijet Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . 906.6.3 Top Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . 916.7 Systematic Uncerta<strong>in</strong>ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 946.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957 <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 997.1 Dataset and Basic Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.2 Trigger Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1007.3 Monte Carlo Signal Samples . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6 Contents7.4 Background Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.4.1 Top Production . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1047.4.2 W/Z and Diboson Production . . . . . . . . . . . . . . . . . . . . . . 1057.4.3 Mistags . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.4.4 Heavy-Flavor Multijet Production . . . . . . . . . . . . . . . . . . . . 1067.5 Control Regions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1067.6 Signal Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1127.6.1 Heavy-Flavor Multijet Removal Cuts . . . . . . . . . . . . . . . . . . 1127.6.2 Heavy-Flavor Multijet Neural Network . . . . . . . . . . . . . . . . . 1127.6.3 Neural Network Results . . . . . . . . . . . . . . . . . . . . . . . . . 1137.6.4 Charm-jet Selection with CHAOS . . . . . . . . . . . . . . . . . . . . 1157.7 Systematic Uncerta<strong>in</strong>ties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1197.8 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1208 Conclusions 127A Per<strong>for</strong>mance of <strong>the</strong> NN <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong> Sbottom 129A.1 Multijet Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129A.2 Top Neural Network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132B Per<strong>for</strong>mance of <strong>the</strong> NN <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong> Stop 135C Alpgen vs Pythia Comparison <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong> Stop 137D Resumen en castellano 143Bibliography 163
List of Figures2.1 Basic components of <strong>the</strong> Standard Model . . . . . . . . . . . . . . . . . . . . 42.2 The value of <strong>the</strong> runn<strong>in</strong>g coupl<strong>in</strong>g constant, α S . . . . . . . . . . . . . . . . . 72.3 Uncerta<strong>in</strong>ty on gluon and u-quark PDFs . . . . . . . . . . . . . . . . . . . . . 92.4 The m<strong>in</strong>imum of <strong>the</strong> Higgs potential occurs at −µ 2 /(2λ), not at zero . . . . . . 132.5 M W as a function of m t as predicted by <strong>the</strong> SM. . . . . . . . . . . . . . . . . . 192.6 Lead<strong>in</strong>g order glu<strong>in</strong>o pair production mechanisms . . . . . . . . . . . . . . . . 282.7 Glu<strong>in</strong>o decay <strong>in</strong>to bottom quark and sbottom . . . . . . . . . . . . . . . . . . . 282.8 LO and NLO cross section of glu<strong>in</strong>o-pair production . . . . . . . . . . . . . . 292.9 LO and NLO cross sections of glu<strong>in</strong>o-pair and sbottom-pair productions . . . . 302.10 Acceptance efficiency as a function of <strong>the</strong> glu<strong>in</strong>o mass . . . . . . . . . . . . . 312.11 Lead<strong>in</strong>g order stop pair production mechanisms . . . . . . . . . . . . . . . . . 322.12 Stop decay <strong>in</strong>to charm and neutral<strong>in</strong>o . . . . . . . . . . . . . . . . . . . . . . 322.13 LO and NLO cross sections of stop-pair production . . . . . . . . . . . . . . . 333.1 The Tevatron Collider Cha<strong>in</strong> at Fermilab . . . . . . . . . . . . . . . . . . . . . 363.2 Tevatron Collider Run II Integrated Lum<strong>in</strong>osity . . . . . . . . . . . . . . . . . 383.3 Tevatron Collider Run II Peak Lum<strong>in</strong>osity . . . . . . . . . . . . . . . . . . . . 383.4 Isometric view of <strong>the</strong> CDF Run II detector . . . . . . . . . . . . . . . . . . . . 393.5 r × η side view of <strong>the</strong> CDF Run II detector . . . . . . . . . . . . . . . . . . . 403.6 Layout of wire planes on a COT endplate . . . . . . . . . . . . . . . . . . . . 413.7 Layout of wires <strong>in</strong> a COT supercell . . . . . . . . . . . . . . . . . . . . . . . . 423.8 The CDF II tracker layout show<strong>in</strong>g <strong>the</strong> different subdetector systems . . . . . . 437
8 List of Figures3.9 CDF calorimeter system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 443.10 CDF muon system . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473.11 CLC tube schematic view . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483.12 Block diagram show<strong>in</strong>g <strong>the</strong> global trigger and DAQ systems at CDF II . . . . . 503.13 Block diagram show<strong>in</strong>g <strong>the</strong> Level 1 and Level 2 trigger system . . . . . . . . . 535.1 Schematic diagram of <strong>the</strong> secondary vertex tagg<strong>in</strong>g . . . . . . . . . . . . . . . 665.2 Tagg<strong>in</strong>g efficiency of SecVtx as function of <strong>the</strong> tagged jet E T . . . . . . . . . . 675.3 Tagg<strong>in</strong>g efficiency of SecVtx as function of <strong>the</strong> tagged jet η . . . . . . . . . . . 685.4 Mistag rate of SecVtx as function of <strong>the</strong> tagged jet E T . . . . . . . . . . . . . 695.5 Mistag rate of SecVtx as function of <strong>the</strong> tagged jet η . . . . . . . . . . . . . . 705.6 Chaos outputs <strong>in</strong> 2-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.7 Chaos outputs <strong>in</strong> 1-D . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 735.8 Sum of <strong>the</strong> CHAOS outputs <strong>in</strong> 1D . . . . . . . . . . . . . . . . . . . . . . . . 735.9 Vertex mass distributions be<strong>for</strong>e and after <strong>the</strong> cut on CHAOS . . . . . . . . . . 756.1 Total efficiency <strong>for</strong> <strong>the</strong> MET45 Trigger Path . . . . . . . . . . . . . . . . . . . 806.2 SUSY po<strong>in</strong>ts generated with PYTHIA . . . . . . . . . . . . . . . . . . . . . . 816.3 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> control regions with s<strong>in</strong>gle b-tagged events . . . . 876.4 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> control regions with double b-tagged events . . . 886.5 Neural Network’s architecture used <strong>for</strong> tra<strong>in</strong><strong>in</strong>g . . . . . . . . . . . . . . . . . 906.6 Multijet-NN output plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 926.7 Top-NN output plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 936.8 Observed and expected 95% C.L. upper limit on <strong>the</strong> glu<strong>in</strong>o cross section . . . . 976.9 Excluded region at 95% C.L. <strong>in</strong> <strong>the</strong> m(˜g)-m(˜b) plane . . . . . . . . . . . . . . 987.1 Total efficiency <strong>for</strong> <strong>the</strong> MET+JETS Trigger Path . . . . . . . . . . . . . . . . . 1027.2 SUSY po<strong>in</strong>ts generated with PYTHIA . . . . . . . . . . . . . . . . . . . . . . 1037.3 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> HF multijet control region . . . . . . . . . . . . . 1087.4 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> lepton control region . . . . . . . . . . . . . . . . 109
List of Figures 97.5 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> pre-optimization control region . . . . . . . . . . 1107.6 HF multijet removal cuts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137.7 HF multijet-NN architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . 1137.8 Output of <strong>the</strong> multijet-NN to reject HF multijet background . . . . . . . . . . . 1147.9 Sum of <strong>the</strong> CHAOS outputs <strong>in</strong> 1D . . . . . . . . . . . . . . . . . . . . . . . . 1167.10 Mass of <strong>the</strong> vertex after multijet-NN cut . . . . . . . . . . . . . . . . . . . . . 1177.11 Light template from MC and negative tags from data . . . . . . . . . . . . . . 1187.12 Observed f<strong>in</strong>al discrim<strong>in</strong>ant . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1227.13 K<strong>in</strong>ematic distributions <strong>in</strong> <strong>the</strong> f<strong>in</strong>al region . . . . . . . . . . . . . . . . . . . . 1237.14 Observed and expected 95% C.L. upper limit on <strong>the</strong> stop cross section . . . . . 1247.15 Excluded region at 95% C.L. <strong>in</strong> <strong>the</strong> m(˜χ 0 )-m(˜t) plane . . . . . . . . . . . . . 125A.1 Multijet-NN <strong>in</strong>put variables <strong>in</strong> <strong>the</strong> large ∆m optimization . . . . . . . . . . . . 130A.2 Multijet-NN <strong>in</strong>put variables <strong>in</strong> <strong>the</strong> small ∆m optimization . . . . . . . . . . . 131A.3 Multijet-NN tra<strong>in</strong><strong>in</strong>g and test outputs . . . . . . . . . . . . . . . . . . . . . . . 131A.4 Top-NN <strong>in</strong>put variables <strong>in</strong> <strong>the</strong> large ∆m optimization . . . . . . . . . . . . . . 132A.5 Top-NN <strong>in</strong>put variables <strong>in</strong> <strong>the</strong> small ∆m optimization . . . . . . . . . . . . . . 133A.6 Top-NN tra<strong>in</strong><strong>in</strong>g and test outputs . . . . . . . . . . . . . . . . . . . . . . . . . 133B.1 Multijet-NN tra<strong>in</strong><strong>in</strong>g and test output . . . . . . . . . . . . . . . . . . . . . . . 135B.2 Multijet-NN <strong>in</strong>put variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136C.1 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> HF multijet control region . . . . . . . . . . . . . 138C.2 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> lepton control region . . . . . . . . . . . . . . . . 139C.3 Lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> pre-optimization control region . . . . . . . . . . 140C.4 Output of <strong>the</strong> NN to reject HF multijet background . . . . . . . . . . . . . . . 141C.5 F<strong>in</strong>al discrim<strong>in</strong>ant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141D.1 Mecanismos de producción de glu<strong>in</strong>os a primer orden. . . . . . . . . . . . . . 146D.2 Des<strong>in</strong>tegración del glu<strong>in</strong>o en quark bottom y sbottom . . . . . . . . . . . . . . 147
10 List of FiguresD.3 Mecanismos de producción de stop a primer orden. . . . . . . . . . . . . . . . 147D.4 Des<strong>in</strong>tegración de stop en charm y neutral<strong>in</strong>o . . . . . . . . . . . . . . . . . . 148D.5 Vista de CDF Run II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149D.6 Figuras de salida del CHAOS en 1-D. . . . . . . . . . . . . . . . . . . . . . . 155D.7 Límites con un 95% de nivel de confianza en la sección eficaz de producción. . 157D.8 Límites observados con un 95% de nivel de confianza. . . . . . . . . . . . . . 159
List of Tables2.1 Fermionic sector of <strong>the</strong> SM. . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.2 The gauge bosons of <strong>the</strong> SM and <strong>the</strong>ir <strong>in</strong>teractions. . . . . . . . . . . . . . . . 52.3 Superfields and particle content of <strong>the</strong> MSSM. . . . . . . . . . . . . . . . . . . 222.4 The particle content of <strong>the</strong> MSSM. . . . . . . . . . . . . . . . . . . . . . . . . 233.1 Tevatron parameters <strong>for</strong> Run II configuration . . . . . . . . . . . . . . . . . . 373.2 CDF II Calorimeter subsystems and characteristics . . . . . . . . . . . . . . . 454.1 Central electrons identification cuts . . . . . . . . . . . . . . . . . . . . . . . . 594.2 Stubless muons identification cuts . . . . . . . . . . . . . . . . . . . . . . . . 615.1 List of CHAOS <strong>in</strong>put variables . . . . . . . . . . . . . . . . . . . . . . . . . . 715.2 Required muon cuts to def<strong>in</strong>e a “muon jet” . . . . . . . . . . . . . . . . . . . . 745.3 CHAOS efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756.1 Basic selection <strong>for</strong> sbottom from glu<strong>in</strong>o decay search . . . . . . . . . . . . . . 786.2 Samples used <strong>for</strong> trigger studies . . . . . . . . . . . . . . . . . . . . . . . . . 796.3 Number of s<strong>in</strong>gle b-tagged events <strong>in</strong> <strong>the</strong> control regions . . . . . . . . . . . . . 866.4 Number of double b-tagged events <strong>in</strong> <strong>the</strong> control regions . . . . . . . . . . . . 866.5 List of <strong>in</strong>put variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 916.6 Number of expected and observed events <strong>in</strong> <strong>the</strong> signal regions . . . . . . . . . 967.1 Basic selection <strong>for</strong> stop search . . . . . . . . . . . . . . . . . . . . . . . . . . 1007.2 Samples used <strong>for</strong> trigger studies . . . . . . . . . . . . . . . . . . . . . . . . . 10111
12 List of Tables7.3 K<strong>in</strong>ematic regions used <strong>in</strong> <strong>the</strong> trigger parameterizations . . . . . . . . . . . . . 1027.4 Number of s<strong>in</strong>gle tagged events <strong>in</strong> <strong>the</strong> control regions . . . . . . . . . . . . . . 1117.5 List of <strong>in</strong>put variables used <strong>in</strong> <strong>the</strong> HF multijet-NN . . . . . . . . . . . . . . . . 1147.6 MUTARE and mistags prediction right be<strong>for</strong>e CHAOS . . . . . . . . . . . . . 1157.7 Number of expected and observed events <strong>in</strong> <strong>the</strong> signal region . . . . . . . . . . 121D.1 Sector fermiónico del ME. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 144D.2 Los bosones de gauge del Modelo Estándar y sus <strong>in</strong>teracciones. . . . . . . . . . 145D.3 Lista de variables usadas en el CHAOS . . . . . . . . . . . . . . . . . . . . . . 154D.4 Eficiencia del CHAOS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
Chapter 1IntroductionThe twentieth century leaves beh<strong>in</strong>d one of <strong>the</strong> most impressive legacies, <strong>in</strong> terms of humanknowledge, ever achieved. In particular <strong>the</strong> Standard Model (SM) of particle physics has provento be one of <strong>the</strong> most accurate descriptions of Nature. The level of accuracy of some <strong>the</strong>oreticalpredictions has never been atta<strong>in</strong>ed be<strong>for</strong>e. It <strong>in</strong>cludes <strong>the</strong> electromagnetic <strong>in</strong>teraction, and <strong>the</strong>weak and strong <strong>for</strong>ce, develop<strong>in</strong>g <strong>the</strong> Lagrangian from symmetry pr<strong>in</strong>ciples.There are two different types of fundamental constituents of Nature, <strong>in</strong> <strong>the</strong> framework of<strong>the</strong> Standard Model: bosons and fermions. Bosons are those particles responsible <strong>for</strong> carry<strong>in</strong>g<strong>the</strong> <strong>in</strong>teractions among <strong>the</strong> fermions, which constitute matter. Fermions are divide <strong>in</strong>to sixquarks and six leptons, <strong>for</strong>m<strong>in</strong>g a three-folded structure. All <strong>the</strong>se fermions and bosons have anantimatter partner.However, several difficulties po<strong>in</strong>t along with <strong>the</strong> idea that <strong>the</strong> Standard Model is only an effectivelow energy <strong>the</strong>ory. These limitations <strong>in</strong>clude <strong>the</strong> difficulty to <strong>in</strong>corporate gravity and <strong>the</strong>lack of justification to f<strong>in</strong>e tun<strong>in</strong>g of some perturbative corrections. Moreover, some regions of<strong>the</strong> <strong>the</strong>ory are not understood, like <strong>the</strong> mass spectrum of <strong>the</strong> Standard Model or <strong>the</strong> mechanism<strong>for</strong> electroweak symmetry break<strong>in</strong>g.Supersymmetry is a newer <strong>the</strong>oretical framework, thought to adress <strong>the</strong> problems found <strong>in</strong><strong>the</strong> Standard Model, while preserv<strong>in</strong>g all its predictive power. It <strong>in</strong>troduces a new symmetrythat relates a new boson to each SM fermion and a new fermion to each SM boson. In thisway, <strong>for</strong> every exist<strong>in</strong>g boson <strong>in</strong> <strong>the</strong> SM it must exist a fermionic super-partner (named witha sufix <strong>in</strong>o), and likewise, <strong>for</strong> every fermion a bosonic super-partner (named with a prefix s)must also exist. Moreover, ano<strong>the</strong>r symmetry called R-parity is <strong>in</strong>troduced to prevent baryonand lepton number violat<strong>in</strong>g <strong>in</strong>teractions. If R-parity is conserved, super-particles can only be1
2pair-produced and <strong>the</strong>y cannot decay completely <strong>in</strong> SM particles. This implies <strong>the</strong> existenceof a lightest SUSY particle (LSP) which would provide a candidate <strong>for</strong> cold dark matter, thataccount <strong>for</strong> 23% of <strong>the</strong> universe content, as strongly suggested by recent astrophysical data [1].The Tevatron is a hadron collider operat<strong>in</strong>g at Fermilab, USA. This accelerator providesproton-antiproton (p¯p) collisions with a center of mass energy of √ s =1.96 TeV. CDF and DØare <strong>the</strong> detectors built to analyse <strong>the</strong> products of <strong>the</strong> collisions provided by <strong>the</strong> Tevatron. Bo<strong>the</strong>xperiments have produced a very significant scientific output <strong>in</strong> <strong>the</strong> last few years, like <strong>the</strong>discovery of <strong>the</strong> top quark or <strong>the</strong> measurement of <strong>the</strong> B s mix<strong>in</strong>g. The Tevatron experiments arealso reach<strong>in</strong>g sensitivity to <strong>the</strong> SM Higgs boson.The scientific program of CDF <strong>in</strong>cludes a broad spectrum on searches <strong>for</strong> physics signaturesbeyond <strong>the</strong> Standard Model. Tevatron is still <strong>the</strong> energy frontier, what means an uniqueopportunity to produce a discovery <strong>in</strong> physic beyond <strong>the</strong> Standard Model.The analyses presented <strong>in</strong> this <strong>the</strong>sis focus on <strong>the</strong> search <strong>for</strong> third generation squarks <strong>in</strong> <strong>the</strong>miss<strong>in</strong>g transverse energy plus jets f<strong>in</strong>al state. The production of sbottom (˜b) and stop (˜t) quarkscould be highly enhanced at <strong>the</strong> Tevatron, giv<strong>in</strong>g <strong>the</strong> possibility of discover<strong>in</strong>g new physics orlimit<strong>in</strong>g <strong>the</strong> parameter space available <strong>in</strong> <strong>the</strong> <strong>the</strong>ory.No signal is found over <strong>the</strong> predicted Standard Model background <strong>in</strong> both searches. Instead,95% confidence level limits are set on <strong>the</strong> production cross section, and <strong>the</strong>n translated <strong>in</strong>to <strong>the</strong>mass plane of <strong>the</strong> hypo<strong>the</strong>tical particles.This <strong>the</strong>sis sketches <strong>the</strong> basic <strong>the</strong>ory concepts of <strong>the</strong> Standard Model and <strong>the</strong> M<strong>in</strong>imal SupersymmetricExtension <strong>in</strong> Chapter 2. Chapter 3, describes <strong>the</strong> Tevatron and CDF. Based on<strong>the</strong> CDF subsystems <strong>in</strong><strong>for</strong>mation, Chapter 4 and 5 describe <strong>the</strong> analysis objet reconstructionand <strong>the</strong> heavy flavor tagg<strong>in</strong>g tools. The development of <strong>the</strong> analyses is shown <strong>in</strong> Chapter 6 andChapter 7. F<strong>in</strong>ally, Chapter 8 is devoted to discuss <strong>the</strong> results and conclusions of this work, andfuture prospects.
Chapter 2Theory IntroductionThe present chapter describes <strong>the</strong> <strong>the</strong>oretical framework that motivates this <strong>the</strong>sis. It conta<strong>in</strong>sa brief <strong>in</strong>troduction to <strong>the</strong> SM, and one of its most famous extensions, <strong>the</strong> M<strong>in</strong>imal Supersymmetricextension of <strong>the</strong> Standard Model (MSSM). The description of <strong>the</strong> particular signaturessearched <strong>for</strong> as part of this <strong>the</strong>sis is also <strong>in</strong>cluded.2.1 Standard ModelThe Standard Model is a quantum field <strong>the</strong>ory that has proven to describe to an unprecedentedlevel of precision many experimental results [2]. A complete description of <strong>the</strong> <strong>the</strong>ory can beeasily found <strong>in</strong> <strong>the</strong> scientific literature [3, 4].Based on several group symmetries, <strong>the</strong> SM <strong>in</strong>cludes <strong>the</strong> electromagnetic, weak and strong<strong>in</strong>teraction. The build<strong>in</strong>g blocks of Nature, accord<strong>in</strong>g to <strong>the</strong> SM, are a close set of fermions andbosons. The fermions are responsible <strong>for</strong> matter, while <strong>the</strong> bosons mediate <strong>in</strong>teractions.The fermionic sector ensembles six quarks and six leptons and <strong>the</strong>ir antiparticles, divided<strong>in</strong> three parallel families, presented <strong>in</strong> figure 2.1. The members of <strong>the</strong>se families are identical<strong>in</strong> every observable, except <strong>for</strong> <strong>the</strong> mass. Our most immediate world is made with <strong>the</strong> particlesof <strong>the</strong> first family: <strong>the</strong> up quark (u) and down quark (d) that <strong>for</strong>m <strong>the</strong> protons and neutrons <strong>in</strong>nuclei and <strong>the</strong> electrons (e − ) and its associated neutr<strong>in</strong>o (ν e ), as listed <strong>in</strong> Table 2.1. The particles<strong>in</strong> <strong>the</strong> o<strong>the</strong>r two families are more massive and decay rapidly to <strong>the</strong> ones of <strong>the</strong> first family.The <strong>in</strong>teractions of <strong>the</strong> fermions <strong>in</strong> Table 2.1 are mediated by <strong>the</strong> bosonic constituents of <strong>the</strong>SM. These bosons carry <strong>the</strong> fundamental <strong>for</strong>ces derived from <strong>the</strong> symmetries, as summarized3
4 2.1. Standard ModelFigure 2.1: Elementary particles <strong>in</strong> <strong>the</strong> Standard Model.(Image courtesy of Fermilab Visual Media Services)quarksleptons1 st <strong>Generation</strong> 2 nd <strong>Generation</strong> 3 rd <strong>Generation</strong>Up (u) Charm (c) Top (t)1.5-3.0 MeV/c 2 1.25±0.09 GeV/c 2 173.1±1.3 GeV/c 2Down (d) Strange (s) Bottom (b)3.0-7.0 MeV/c 2 95±25 MeV/c 2 4.20±0.07 GeV/c 2Electron neutr<strong>in</strong>o (ν e ) Muon neutr<strong>in</strong>o (ν µ ) Tau neutr<strong>in</strong>o (ν τ )< 2 eV/c 2 < 0.19 MeV/c 2 < 18.2 MeV/c 2Electron (e) Muon (µ) Tau (τ)0.511 MeV/c 2 105.66 MeV/c 2 1776.99 +0.29−0.26 MeV/c2Table 2.1: The fermion sector of <strong>the</strong> SM. All masses are taken from <strong>the</strong> Particle Data Group (PDG) [5], except<strong>for</strong> <strong>the</strong> top quark mass, where <strong>the</strong> last Tevatron comb<strong>in</strong>ation is quoted <strong>in</strong> [6].
Chapter 2. Theory Introduction 5<strong>in</strong> Table 2.2. The overall symmetry of <strong>the</strong> SM is <strong>the</strong> comb<strong>in</strong>ation of <strong>the</strong> color symmetry group<strong>for</strong> <strong>the</strong> strong <strong>for</strong>ce SU(3) C, weak-isosp<strong>in</strong> symmetry <strong>for</strong> <strong>the</strong> weak <strong>in</strong>teraction of left handedparticles SU(2) Land hypercharge symmetry U(1) Y, expressed as SU(3) C⊗SU(2) L⊗U(1) Y.However, <strong>the</strong> orig<strong>in</strong>al symmetry is broken <strong>in</strong> our universe, as it will be detailed latter.Even if gravity is <strong>the</strong> <strong>in</strong>teraction that has been known <strong>for</strong> <strong>the</strong> longest time and is <strong>the</strong> closest toour every day life experience, it still has not been successfully <strong>in</strong>cluded <strong>in</strong> <strong>the</strong> SM framework.This is one of <strong>the</strong> ma<strong>in</strong> arguments aga<strong>in</strong>st <strong>the</strong> SM be<strong>in</strong>g <strong>the</strong> <strong>the</strong>ory of everyth<strong>in</strong>g, <strong>the</strong>re<strong>for</strong>esuggest<strong>in</strong>g that <strong>the</strong>re needs to be a somewhat more general <strong>the</strong>ory. This new <strong>the</strong>ory would haveto <strong>in</strong>clude all <strong>the</strong> symmetries of <strong>the</strong> SM, and, simultaneously accept that <strong>for</strong>th <strong>in</strong>teraction.In <strong>the</strong> follow<strong>in</strong>g sections, an <strong>in</strong>troduction to <strong>the</strong> different parts of <strong>the</strong> SM is presented.After a brief explanation of <strong>the</strong> symmetry orig<strong>in</strong>at<strong>in</strong>g each <strong>in</strong>teraction, a short discussion of <strong>the</strong>coupl<strong>in</strong>gs and eigenstates will be shown.Interaction Particle Masselectromagnetic photon, γ 0strong gluon, g 0W ± 80.403±0.029 GeV/c 2weakZ 0 91.188±0.002 GeV/c 2Table 2.2: The gauge bosons of <strong>the</strong> SM and <strong>the</strong>ir associated <strong>in</strong>teractions [6].2.1.1 Quantum ElectrodynamicsQuantum Electrodynamics (QED) was developed <strong>in</strong> <strong>the</strong> late 1940s and early 1950s chiefly byFeynman, Schw<strong>in</strong>ger and Tomonaga [7], describ<strong>in</strong>g electromagnetic <strong>in</strong>teractions of electronsand photons. This is a quantum relativistic renormalizable <strong>the</strong>ory which is <strong>in</strong>variant under achange of phase or gauge, θ:ψ → ψ ′ = e iQθ ψ , (2.1)where Q represents <strong>the</strong> charge and ψ is <strong>the</strong> Dirac field (sp<strong>in</strong> 1/2). In order to promote <strong>the</strong> globalsymmetry under U(1) trans<strong>for</strong>mations, responsible <strong>for</strong> <strong>the</strong> conservation of <strong>the</strong> charge, to a localone (θ = θ(x)), <strong>the</strong> covariant derivative needs to be <strong>in</strong>troduced:D µ ≡ ∂ µ − ieQA µ , (2.2)
6 2.1. Standard Modelwhere A µ is a field that satisfies:There<strong>for</strong>e, <strong>the</strong> Lagrangian describ<strong>in</strong>g <strong>the</strong> <strong>the</strong>ory becomes:A µ → A ′ µ ≡ A µ + 1 e ∂ µθ . (2.3)L = ¯ψ(iγ µ D µ − m)ψ = ¯ψ(iγ µ ∂ µ − m)ψ + L I (2.4)where <strong>the</strong> last term corresponds to <strong>the</strong> <strong>in</strong>teraction with <strong>the</strong> new field, A µ :L I = eQA µ ( ¯ψγ µ ψ) (2.5)In addition, <strong>the</strong> k<strong>in</strong>etic energy of <strong>the</strong> new field needs to be <strong>in</strong>troduced. From Maxwell’s equations,<strong>the</strong> k<strong>in</strong>etic term must be of <strong>the</strong> <strong>for</strong>m:where F µν ≡ ∂ µ A ν − ∂ ν A µ .L K = − 1 4 F µνF µν (2.6)Thus, <strong>in</strong> this <strong>the</strong>ory <strong>the</strong> electromagnetic <strong>in</strong>teraction is described by two quantum fields: one<strong>for</strong> <strong>the</strong> charged particles and one <strong>for</strong> <strong>the</strong> photon. The strength of <strong>the</strong> <strong>in</strong>teraction is usuallydescribed by <strong>the</strong> coupl<strong>in</strong>g constant α em whose value depends on <strong>the</strong> momentum transfer q 2<strong>in</strong> an <strong>in</strong>teraction. At q 2 → 0 (or low energies) <strong>the</strong> coupl<strong>in</strong>g constant value is that of <strong>the</strong> f<strong>in</strong>estructure constant, α em =be<strong>in</strong>g α em (m Z ) ≈ 1128e2= 1 . At larger scales (short distances) its value <strong>in</strong>creases,4π/hc 137at <strong>the</strong> scale given by <strong>the</strong> mass of <strong>the</strong> Z boson.2.1.2 Quantum ChromodynamicsOne of <strong>the</strong> cornerstones of <strong>the</strong> Standard Model is Quantum Chromodynamics (QCD) that describes<strong>the</strong> strong <strong>in</strong>teraction. Follow<strong>in</strong>g <strong>the</strong> way opened by QED and Yang-Mills <strong>the</strong>ories,QCD was developed <strong>in</strong> 1973 [8] <strong>in</strong> <strong>the</strong> context of Quantum Field Theory based <strong>in</strong> SU(3) symmetrygroup [9]. It is a non-abelian <strong>the</strong>ory and <strong>the</strong> Lagrangian, that describes <strong>the</strong> strong <strong>in</strong>teractionof colored quarks and gluons 1 , is given by:L QCD = ∑flavor¯q a (iγ µ D µ − m q ) ab q b − 1 4 F A αβ F αβA , (2.7)1 The charge associated with <strong>the</strong> strong <strong>in</strong>teraction is <strong>the</strong> color charge. The color property was <strong>in</strong>troduced <strong>for</strong>quarks to satisfy <strong>the</strong> requirement of Pauli exclusion pr<strong>in</strong>ciple [3]. Posterior experiment results proved <strong>the</strong> validityof color hypo<strong>the</strong>sis
Chapter 2. Theory Introduction 7where <strong>the</strong> sum runs over <strong>the</strong> six different flavors of <strong>the</strong> quarks. F A αβderived from <strong>the</strong> gluon field A A α as,is <strong>the</strong> field strength tensorF A αβ = [∂ α A A β − ∂ β A A α − gf ABC A B αA C β ], (2.8)and <strong>the</strong> <strong>in</strong>dices A,B,C run over <strong>the</strong> eight color degrees of freedom of gluon field, g is <strong>the</strong>coupl<strong>in</strong>g constant, which determ<strong>in</strong>es <strong>the</strong> strength of <strong>the</strong> <strong>in</strong>teraction between colored quanta, andf ABC are <strong>the</strong> structure constants of <strong>the</strong> SU(3) color group. The third term <strong>in</strong> equation 2.8 shows<strong>the</strong> non-abelian nature of QCD. This term describes <strong>the</strong> property of <strong>in</strong>teraction between gluons,result<strong>in</strong>g <strong>in</strong> <strong>the</strong> very different behavior of <strong>the</strong> strong <strong>in</strong>teraction compared to <strong>the</strong> electromagnetic<strong>in</strong>teraction. This self-coupl<strong>in</strong>g is <strong>the</strong> reason <strong>for</strong> <strong>the</strong> strong coupl<strong>in</strong>g constant, α s = g2, is large4πat small energies (large distances) and decreases at high energies (small distance) as is shown<strong>in</strong> figure 2.2.Figure 2.2: The value of <strong>the</strong> runn<strong>in</strong>g coupl<strong>in</strong>g constant, α S , as a function of <strong>the</strong> energy scale E.This characteristic runn<strong>in</strong>g of α S is used to expla<strong>in</strong> <strong>the</strong> observed behavior of <strong>the</strong> strong<strong>in</strong>teraction:• Asymptotic freedom: At high energies (small distance) <strong>the</strong> strong <strong>in</strong>teraction proceedsvia color field of reduced strength and <strong>the</strong> quarks and gluons behave as essentially free,non-<strong>in</strong>teract<strong>in</strong>g particles.• Conf<strong>in</strong>ement: At low energies (or large distance) <strong>the</strong> strength of <strong>the</strong> color field is <strong>in</strong>creas<strong>in</strong>g,s<strong>in</strong>ce <strong>the</strong> potential behaves as V (r) ∼ λr, and <strong>in</strong> this way <strong>the</strong> quarks and gluons can
8 2.1. Standard Modelnever be observed as free particles. If two <strong>in</strong>teract<strong>in</strong>g partons are separated, <strong>the</strong> energy of<strong>the</strong> field <strong>in</strong>creases so much that it creates new <strong>in</strong>teract<strong>in</strong>g particles and at <strong>the</strong> end it is leftwith colorless hadrons conta<strong>in</strong><strong>in</strong>g <strong>the</strong> partons. There<strong>for</strong>e partons are not observed as freeparticles.It is important to note that <strong>the</strong> asymptotic freedom property allows <strong>the</strong> application of perturbation<strong>the</strong>ory to calculate cross section measurements <strong>in</strong> scatter<strong>in</strong>g processes where quarksand gluons are <strong>in</strong>volved. Moreover, this property expla<strong>in</strong>s <strong>the</strong> partial success of <strong>the</strong> naïve QuarkParton Model approach, which is go<strong>in</strong>g to be presented below.2.1.3 Parton Distribution FunctionsThe partonic structure of hadrons plays a fundamental rôle <strong>in</strong> elementary particle physics.The comparison of data with SM predictions, precision measurements of SM parameters, andsearches <strong>for</strong> signals of physics beyond <strong>the</strong> SM, all rely on <strong>the</strong> parton picture of hadronic beamparticles.Perturbative QCD is not able to predict <strong>the</strong> x-dependence of <strong>the</strong> PDFs. PDFs at a givenscale Q 2 0 are extracted from fits to data and DGLAP equations are used to predict PDFs to ahigher scale Q 2 . The PDFs are parametrized and <strong>the</strong> parameters are determ<strong>in</strong>ed by a χ 2 m<strong>in</strong>imizationover data from different type of measurements: structure functions <strong>in</strong> deep-<strong>in</strong>elastice, µ or ν scatter<strong>in</strong>g, measurements of Drell-Yan production, W -asymmetry <strong>in</strong> p¯p collisionsand <strong>in</strong>clusive jet cross sections. Different groups provide parameterizations of parton densities.Among o<strong>the</strong>rs, PDFs come from Mart<strong>in</strong>, Roberts, Stirl<strong>in</strong>g and Thorne (MRST) group [10] and<strong>the</strong> “Coord<strong>in</strong>ated Theoretical-Experimental Project on QCD”( CTEQ Collaboration) [11].A Hessian method is used to evaluate <strong>the</strong> PDFs uncerta<strong>in</strong>ties. A brief description of <strong>the</strong>method is given below, <strong>for</strong> more details see [12, 13].In <strong>the</strong> Hessian method, a large matrix (20×20 <strong>for</strong> CTEQ, 15×15 <strong>for</strong> MRST), with dimensionsequal to <strong>the</strong> number of free parameters <strong>in</strong> <strong>the</strong> fit, has to be diagonalized. The result is 20(15) orthogonal eigenvectors <strong>for</strong> CTEQ (MRST), denoted as a i , which provides <strong>the</strong> basis <strong>for</strong><strong>the</strong> determ<strong>in</strong>ation of <strong>the</strong> PDFs uncerta<strong>in</strong>ties <strong>for</strong> any cross section. The Hessian matrix can beexpressed as:H ij = 1 ∂ 2 ˆχ 2. (2.9)2 ∂a i ∂a jThis matrix determ<strong>in</strong>es <strong>the</strong> behavior of ˆχ 2 (a) <strong>in</strong> <strong>the</strong> neighborhood of <strong>the</strong> m<strong>in</strong>imum. The
Chapter 2. Theory Introduction 9po<strong>in</strong>t a 0 <strong>in</strong> <strong>the</strong> n-dimensional parameter space, where ˆχ 2 (a) is m<strong>in</strong>imum, is <strong>the</strong> best fit to <strong>the</strong>global data set. Po<strong>in</strong>ts <strong>in</strong> some small neighborhood of a 0 are also acceptable fits. For eacheigenvector two displacements from a 0 , <strong>in</strong> <strong>the</strong> + and - directions along <strong>the</strong> vector, denoteda + i and a − i <strong>for</strong> <strong>the</strong> i th eigenvector are considered. At <strong>the</strong>se po<strong>in</strong>ts, ˆχ 2 = ˆχ 2 0 + T 2 whereˆχ 2 0= ˆχ 2 (a 0 ) is <strong>the</strong> m<strong>in</strong>imum, and T is a parameter called tolerance. Any PDFs set withˆχ 2 − ˆχ 2 0 < T 2 is considered to be an acceptable fit to <strong>the</strong> global data set. In particular, <strong>the</strong>2n PDFs sets a ± i span <strong>the</strong> parameter space <strong>in</strong> <strong>the</strong> neighborhood of <strong>the</strong> m<strong>in</strong>imum. CTEQ groupchooses T 2 ∼100 and MRST group uses T 2 ∼50.Any quantity Γ that depends on PDFs has a predicted value Γ 0 = Γ(a 0 ) and an associated,a priori asymmetric, uncerta<strong>in</strong>ty δΓ. The + (-) uncerta<strong>in</strong>ties are calculated as:( n∑) 1/2δΓ + = [max(Γ(a + i ), Γ(a− i ), Γ(a 0)) − Γ(a 0 )] 2 (2.10)k=1andδΓ − =( n∑) 1/2[m<strong>in</strong>(Γ(a + i ), Γ(a− i ), Γ(a 0)) − Γ(a 0 )] 2 . (2.11)k=1In figure 2.3 <strong>the</strong> uncerta<strong>in</strong>ties on gluon and u-quark distributions are shown. The u-quarkdistribution is tightly constra<strong>in</strong>ed <strong>for</strong> x≤ 0.8, whereas <strong>the</strong> uncerta<strong>in</strong>ty on <strong>the</strong> gluon distributioncan be larger than a factor of 2 at high x.Figure 2.3: Uncerta<strong>in</strong>ty on gluon and u-quark PDFs. The yellow bands represent <strong>the</strong> global uncerta<strong>in</strong>ty. Thecurves are <strong>the</strong> ratios of <strong>the</strong> 40 eigenvector basis sets to <strong>the</strong> standard set, CTEQ6.1M.
10 2.1. Standard Model2.1.4 Electroweak TheoryThe weak <strong>the</strong>ory was proposed by Enrico Fermi <strong>in</strong> 1934 <strong>in</strong> order to expla<strong>in</strong> <strong>the</strong> proton β-decay[14]. In this <strong>the</strong>ory four fermions directly <strong>in</strong>teracted with one ano<strong>the</strong>r <strong>in</strong> such a way that aneutron (or a down-quark) could be directly split <strong>in</strong>to an electron, an ant<strong>in</strong>eutr<strong>in</strong>o and a proton(an up-quark). The strength of <strong>the</strong> Fermi’s <strong>in</strong>teraction was given by <strong>the</strong> Fermi constant, G F .Feynman diagrams described <strong>the</strong> <strong>in</strong>teraction remarkably well at tree level but loop diagramscould not be calculated reliably because Fermi’s <strong>in</strong>teraction was not renormalizable. The solutioncame <strong>in</strong> 1967 when <strong>the</strong> electromagnetic and weak <strong>in</strong>teractions were successfully unifiedby Glashow, Salam and We<strong>in</strong>berg [15, 16, 17]. This unification constituted <strong>the</strong> Standard ElectroweakModel which is <strong>the</strong> core of <strong>the</strong> SM. The idea of <strong>the</strong> unification is to comb<strong>in</strong>e both<strong>in</strong>teractions <strong>in</strong>to one s<strong>in</strong>gle <strong>the</strong>oretical framework <strong>in</strong> which <strong>the</strong>y would appear as two manifestationsof <strong>the</strong> same fundamental <strong>in</strong>teraction. These <strong>in</strong>teractions are unified under <strong>the</strong> groupSU(2) L⊗U(1) Y . The first part of <strong>the</strong> group has dimension three and <strong>the</strong>re<strong>for</strong>e, three generatorsare needed: t i = σ i2 (i = 1, 2, 3) where σ i are <strong>the</strong> Pauli matrices. These generators, due to <strong>the</strong>global gauge <strong>in</strong>variance under SU(2), <strong>in</strong>troduce a new quantum number called <strong>the</strong> weak isosp<strong>in</strong>(T ). This number is associated to <strong>the</strong> different sp<strong>in</strong>-like multiplets. S<strong>in</strong>ce weak <strong>for</strong>ce only <strong>in</strong>teractswith left-handed particles (right-handed antiparticles), <strong>the</strong> left-handed fermions trans<strong>for</strong>mas doublets while <strong>the</strong> right handed ones trans<strong>for</strong>m as s<strong>in</strong>glets:( ) ( )νifLi = L ui, LlLi d i L(2.12)f i R = li R , ui R , di R (2.13)where i = 1, 2, 3 corresponds to <strong>the</strong> family <strong>in</strong>dex. Hence, <strong>the</strong> weak <strong>in</strong>teraction is divided <strong>in</strong>to a“charged part” (that is, exchang<strong>in</strong>g <strong>the</strong> components of <strong>the</strong> doublet) and a “neutral part” (that is,leav<strong>in</strong>g <strong>the</strong> doublets as <strong>the</strong>y are). S<strong>in</strong>ce SU(2) is a non-Abelian group, it allows self-<strong>in</strong>teractionsof <strong>the</strong>se gauge fields.S<strong>in</strong>ce <strong>the</strong> group U(1) Y has only one dimension, its structure is more simple hav<strong>in</strong>g onlyone generator called <strong>the</strong> hypercharge Ŷ . Once <strong>the</strong> SU(2) L ⊗ U(1) Y group is def<strong>in</strong>ed, <strong>the</strong> SMelectroweak Lagrangian is obta<strong>in</strong>ed by requir<strong>in</strong>g <strong>in</strong>variance under local gauge trans<strong>for</strong>mationsto obta<strong>in</strong> an <strong>in</strong>teract<strong>in</strong>g field <strong>the</strong>ory, follow<strong>in</strong>g <strong>the</strong> analogy with QED. This is achieved byreplac<strong>in</strong>g <strong>the</strong> derivatives of <strong>the</strong> fields by <strong>the</strong> correspond<strong>in</strong>g covariant derivative, which now has<strong>the</strong> <strong>for</strong>m:D µ ≡ ∂ µ − ig ⃗ T ⃗ W µ − ig ′Y 2 B µ , (2.14)
Chapter 2. Theory Introduction 11where g and g’ are <strong>the</strong> coupl<strong>in</strong>g constants correspond<strong>in</strong>g to SU(2) L and U(1) Y , respectively.The first term corresponds to <strong>the</strong> fermion Lagrangian:L EW = L f + L G + L SSB + L Y W . (2.15)L f = ∑ f=l,q¯fi/Df . (2.16)The second term is <strong>the</strong> contribution from <strong>the</strong> gauge fields:L G = − 1 4 W i µνW µνi − 1 4 B µνB µν + L GF + L FP , (2.17)where W i µν (with i = 1, 2, 3) and B µν are, respectively, <strong>the</strong> field strength tensors <strong>for</strong> SU(2) Land U(1) Y def<strong>in</strong>ed as:W i µν ≡ ∂ µ W i ν − ∂ νW i µ + gǫijk W j µ W k ν (2.18)B µν ≡ ∂ µ B ν − ∂ ν B µ (2.19)and L GF and L FP are <strong>the</strong> gauge fix<strong>in</strong>g and Faddeev-Popov Lagrangians that are needed <strong>in</strong> anyYM <strong>the</strong>ory [18].The last two terms of <strong>the</strong> electroweak Lagrangian (equation 2.15) are <strong>the</strong> symmetry break<strong>in</strong>gsector and <strong>the</strong> Yukawa Lagrangian, respectively, which will be described <strong>in</strong> next subsection.The gauge fields presented at equation 2.18 can be rewritten as:W ± µ = 1 √2(W 1 µ ∓ iW 2 µ)Z µ = cosθ W Wµ 3 − s<strong>in</strong> θ (2.20)WB µA µ = s<strong>in</strong> θ W Wµ 3 + cosθ WB µgwhere, A µ represents <strong>the</strong> photon field and cosθ W = is <strong>the</strong> weak mix<strong>in</strong>g angle, which√g′ 2 +g2 relates both coupl<strong>in</strong>gs by <strong>the</strong> simple relation tanθ W = g ′ /g. In addition, W µ ± and Z µ fields areassociated to <strong>the</strong> physical W ± and Z 0 boson particles. In this framework, <strong>the</strong> electron chargeand <strong>the</strong> Fermi constant can be written <strong>in</strong> terms of <strong>the</strong> coupl<strong>in</strong>gs through <strong>the</strong> follow<strong>in</strong>g relations:e = g s<strong>in</strong> θ W√2 g 2G F =8m 2 W.(2.21)
12 2.1. Standard ModelThe electric charge ˆQ, <strong>the</strong> third component of <strong>the</strong> weak isosp<strong>in</strong> ˆT 3 , and <strong>the</strong> weakhyperchargeŶ are l<strong>in</strong>early related by <strong>the</strong> Gell-Mann-Nishijima <strong>for</strong>mula:ˆQ = ˆT 3 + Ŷ /2 . (2.22)Hence, <strong>the</strong> global and local conservation of weak-isosp<strong>in</strong> and hypercharge naturally impliescharge conservation, as required by QED, and <strong>the</strong> electromagnetic and weak <strong>in</strong>teractions areunified under <strong>the</strong> same <strong>the</strong>oretical framework.2.1.5 The Higgs MechanismAs shown, <strong>the</strong> Standard Model <strong>for</strong>malism allows <strong>the</strong> unification of electromagnetic and weak<strong>in</strong>teractions through <strong>the</strong> exploitation of a local gauge symmetry. Never<strong>the</strong>less, this gauge symmetryrequires massless W ± and Z bosons. This requirement is <strong>in</strong> contradiction with <strong>the</strong> observationand one needs to <strong>in</strong>troduce a mechanism <strong>for</strong> generat<strong>in</strong>g non-zero masses while preserv<strong>in</strong>g<strong>the</strong> renormalizability of <strong>the</strong> <strong>the</strong>ory. In <strong>the</strong> SM, <strong>the</strong> Higgs mechanism of Spontaneous SymmetryBreak<strong>in</strong>g (SSB) is proposed.In this mechanisim a new field, <strong>the</strong> Higgs field, is <strong>in</strong>troduced such as:( )φ+Φ ≡ . (2.23)φ 0The correspondent k<strong>in</strong>etic and potential term <strong>in</strong> <strong>the</strong> Lagrangian has <strong>the</strong> <strong>for</strong>m:L Φ = (D µ Φ) † D µ Φ − V (Φ) , (2.24)whereV (Φ) = µ 2 Φ † Φ + λ(Φ † Φ) 2 . (2.25)If λ > 0 and µ 2 < 0 <strong>the</strong> potential V (Φ) has a m<strong>in</strong>imum <strong>for</strong>:Φ † Φ = − µ22λ ≡ v22 . (2.26)Thus, <strong>the</strong> field Φ has a non-zero vacuum expectation value (VEV):〈0|Φ|0〉 = v √2≠ 0 . (2.27)Choos<strong>in</strong>g one of a set of degenerate states of m<strong>in</strong>imum energy breaks <strong>the</strong> gauge symmetry.
Chapter 2. Theory Introduction 13As stated by <strong>the</strong> Goldstone <strong>the</strong>orem, fields that acquire a VEV will have an associatedmassless Goldstone boson which will disappear trans<strong>for</strong>med <strong>in</strong>to <strong>the</strong> longitud<strong>in</strong>al componentof a massive gauge boson. S<strong>in</strong>ce <strong>the</strong> photon is known to be massless, <strong>the</strong> symmetry is chosento be broken so that only <strong>the</strong> fields with zero electric charge (<strong>the</strong> ones that cannot couple to<strong>the</strong> electromagnetic <strong>in</strong>teraction) acquire a VEV. In such a way, <strong>the</strong> symmetry of <strong>the</strong> photonassociatedoperator, ˆQ is preserved:(0v)Φ 0 ≡ 〈0|Φ|0〉 ≡QΦ 0 = 0 . (2.28)4]V(φ) [GeV200φ+0[GeV]-200-2000φ0[GeV]200Figure 2.4: The m<strong>in</strong>imum of <strong>the</strong> Higgs potential occurs at −µ 2 /(2λ), not at zeroExpand<strong>in</strong>g around <strong>the</strong> true m<strong>in</strong>imum of <strong>the</strong> <strong>the</strong>ory, <strong>the</strong> complex field φ becomes:( )Φ(x) = e i ⃗τ ξ(x) ⃗ 1 02 √2 . (2.29)v + H(x)where <strong>the</strong> three parameters ξ(x) ⃗ correspond to <strong>the</strong> motion through <strong>the</strong> degenerated m<strong>in</strong>ima <strong>in</strong><strong>the</strong> SU(2) space. S<strong>in</strong>ce <strong>the</strong> Lagrangian is locally gauge <strong>in</strong>variant, one can choose ξ(x) ⃗ = 0.Hence, <strong>in</strong>troduc<strong>in</strong>g this expansion <strong>in</strong>to <strong>the</strong> SM Lagrangian (equation 2.15), one obta<strong>in</strong>s <strong>the</strong>tree level predictions <strong>for</strong> massive fermions (com<strong>in</strong>g from <strong>the</strong> L Y W part), massive gauge bosons
14 2.1. Standard Model(com<strong>in</strong>g from <strong>the</strong> k<strong>in</strong>etic part of L SSB ) and a new Higgs boson. These relations are:M W = vg(2.30)2√g2 + gM Z = v′2(2.31)2M H = √ −2µ 2 = √ 2λv (2.32)m f = λ fv √2 (2.33)m 2 γ = 0 (2.34)where f stands <strong>for</strong> <strong>the</strong> fermions <strong>in</strong> <strong>the</strong> <strong>the</strong>ory. These relations can also be expressed as a functionof <strong>the</strong> weak mix<strong>in</strong>g angle,which leads to <strong>the</strong> SM predictionM z =M 2 WM 2 Z1vg 2, (2.35)cos θ W= cos 2 θ W . (2.36)This prediction was tested once <strong>the</strong> W ± and Z vector bosons were discovered <strong>in</strong> 1983 by UA1and UA2 collaborations at <strong>the</strong> CERN SPS [19, 20].The ten <strong>in</strong>dependent fields be<strong>for</strong>e SSB (three massless gauge bosons (W ± , Z), with twopolarization states each, and one SU(2) doublet of complex scalars) are now represented bythree massive bosons, which account <strong>for</strong> n<strong>in</strong>e degrees of freedom, and a new physical scalarparticle called <strong>the</strong> Higgs boson, which accounts <strong>for</strong> <strong>the</strong> last degree of freedom.This new particle, which is <strong>the</strong> miss<strong>in</strong>g piece to confirm <strong>the</strong> Higgs mechanism, has <strong>the</strong>coupl<strong>in</strong>gs completely def<strong>in</strong>ed by <strong>the</strong> o<strong>the</strong>r parameters of <strong>the</strong> model:λ HHH = 3 M2 H(2.37)MZ2λ HV V = 2 √ 2G F MV 2 (2.38)λ Hff = 2 √ 2G F m f (2.39)where V = W, Z and G F is <strong>the</strong> Fermi constant. The vacuum expectation value v is determ<strong>in</strong>edexperimentally from <strong>the</strong> partial width Γ(µ → ν µ¯ν e e) at low energies (q 2
Chapter 2. Theory Introduction 15which sets <strong>the</strong> electroweak symmetry break<strong>in</strong>g scale.This new particle allows Yukawa-like terms <strong>in</strong> <strong>the</strong> Lagrangian:g f [( ¯f L φ)f R + h.c.] , (2.42)which can be written <strong>in</strong> terms of <strong>the</strong> VEV:√12 g fv( ¯f L f R + ¯f R f L ) . (2.43)There<strong>for</strong>e, not only <strong>the</strong> bosons acquire mass through <strong>the</strong> Higgs mechanism but also <strong>the</strong>fermions with m f = g f v/ √ 2. Noticeably, <strong>the</strong> strength of <strong>the</strong> coupl<strong>in</strong>g is proportional to <strong>the</strong>masses. However, <strong>the</strong> masses are not predicted by <strong>the</strong> model, but <strong>the</strong> relation of <strong>the</strong> coupl<strong>in</strong>gs to<strong>the</strong> fermions conta<strong>in</strong> all <strong>the</strong> predictive power of <strong>the</strong> model <strong>for</strong> prov<strong>in</strong>g masses of <strong>the</strong> fermions.2.1.6 Standard Model LimitationsThe SM description of <strong>the</strong> different processes <strong>in</strong>volv<strong>in</strong>g electroweak or strong <strong>in</strong>teractions isextremely accurate. At <strong>the</strong> present time, no experiment has been able to f<strong>in</strong>d any clear deviationfrom <strong>the</strong> SM predictions. Never<strong>the</strong>less, physicists are still push<strong>in</strong>g to f<strong>in</strong>d such deviations.The ma<strong>in</strong> reason is that <strong>the</strong> SM present serious <strong>the</strong>oretically motivated problems, start<strong>in</strong>g from<strong>the</strong> fact that gravity is not accommodated <strong>in</strong> <strong>the</strong> <strong>the</strong>ory, what prevent it from be<strong>in</strong>g <strong>the</strong> ultimate<strong>the</strong>ory, <strong>the</strong> Theory of Everyth<strong>in</strong>g (TOE), that would describe Nature <strong>in</strong> a comprehensive manner.Even accept<strong>in</strong>g <strong>the</strong> peculiar set of group representations and hypercharges required by <strong>the</strong>model, <strong>the</strong> SM conta<strong>in</strong>s at least 19 free parameters, such as coupl<strong>in</strong>gs, masses and mix<strong>in</strong>gs,which are not predicted but must be measured by <strong>the</strong> experiment. In addition, more parameterswould be needed if one wants to accommodate non-accelerator observations such as <strong>the</strong>cosmological baryon asymmetry, neutr<strong>in</strong>o masses and mix<strong>in</strong>gs or <strong>the</strong> problematic cosmologicalconstant.The SM leaves also several questions unanswered such as why are <strong>the</strong>re three generations,spatial dimensions or colors, how do we understand neutr<strong>in</strong>o oscillations and massive neutr<strong>in</strong>os,why are <strong>the</strong> electric charge of <strong>the</strong> proton and <strong>the</strong> electron exactly opposite or whe<strong>the</strong>r <strong>the</strong>Higgs mechanism is really <strong>the</strong> process through which <strong>the</strong> electroweak symmetry break<strong>in</strong>g occursand lay beneath <strong>the</strong> orig<strong>in</strong> of masses. In addition, <strong>the</strong> model cannot expla<strong>in</strong> which are <strong>the</strong>mechanisms to produce <strong>the</strong> matter-antimatter asymmetry observed <strong>in</strong> <strong>the</strong> universe or what is<strong>the</strong> relation between <strong>the</strong> strong and electroweak <strong>for</strong>ces.
16 2.1. Standard ModelPerhaps <strong>the</strong> most surpris<strong>in</strong>g feature of <strong>the</strong> SM is <strong>the</strong> accurate description of <strong>the</strong> <strong>in</strong>teractionsbetween particles with masses 17 orders of magnitude smaller than <strong>the</strong> Planck mass and <strong>the</strong>difficulty to accommodate gravity with<strong>in</strong> this framework [21]. This feature may be an <strong>in</strong>dicationthat <strong>the</strong> SM is an effective <strong>the</strong>ory, that is a “low energy” limit of a more fundamental one. Butthis assumption automatically leads to <strong>the</strong> question of up to which energy scale will <strong>the</strong> SM bevalid.However, sp<strong>in</strong> zero fields are radically different from fermions and gauge bosons. The latterare protected from large radiative corrections to <strong>the</strong>ir masses due to chiral and gauge symmetries,respectively. In <strong>the</strong> SM <strong>the</strong>re is no mechanism to prevent scalar particles from acquir<strong>in</strong>glarge masses through radiative corrections. There<strong>for</strong>e, m 2 H receives enormous quantum correctionsfrom <strong>the</strong> virtual effects of every particle which couples to <strong>the</strong> Higgs field.Due to <strong>the</strong>se corrections, <strong>the</strong> Higgs mass would bem 2 h SM= (m 2 h ) 0 + ∆M 2 H (2.44)where (m 2 h ) 0 is <strong>the</strong> bare Higgs mass and ∆MH 2 is <strong>the</strong> correction given by[ ( ( ))]∆MH 2 = − λ2 fΛ2Λ 2 + O m 216π 2 f ln i (2.45)m fwhere λ f is <strong>the</strong> Yukawa coupl<strong>in</strong>g of <strong>the</strong> fermion f and Λ is an energy cutoff which is <strong>in</strong>terpretedas <strong>the</strong> energy scale at which new physics enters and changes <strong>the</strong> high-energy behavior of <strong>the</strong><strong>the</strong>ory. If <strong>the</strong> SM needs to describe nature until <strong>the</strong> Planck scale, <strong>the</strong>n <strong>the</strong> quantum correction∆M 2 His about 30 orders of magnitude larger than <strong>the</strong> bare Higgs mass square. A cancellationof <strong>the</strong>se corrections at all orders would call <strong>for</strong> an <strong>in</strong>credible “f<strong>in</strong>e tunn<strong>in</strong>g” which seems veryunlikely [22]. This problem is present even if <strong>the</strong>re is no direct coupl<strong>in</strong>g between <strong>the</strong> Standardmodel Higgs boson and <strong>the</strong> unknown heavy particles [23].In a model with spontaneous electroweak symmetry break<strong>in</strong>g, <strong>the</strong> problem affects not only to<strong>the</strong> Higgs mass but also its expectation value and <strong>the</strong> masses of o<strong>the</strong>r particles that get <strong>the</strong>irmasses through this mechanism such as <strong>the</strong> W , Z, quarks and charged leptons. This situationhas also an analogy with <strong>the</strong> self-energy corrections on <strong>the</strong> electron, which is solved by <strong>the</strong>presence of <strong>the</strong> positron [24]. Hence, it is unnatural to have all <strong>the</strong> SM particles masses at <strong>the</strong>electroweak scale unless <strong>the</strong> model is somehow cut off and embedded <strong>in</strong> a richer structure atenergies no bigger than <strong>the</strong> TeV scale.
Chapter 2. Theory Introduction 172.2 M<strong>in</strong>imal Supersymmetric Extension of <strong>the</strong> StandardModelAfter a brief <strong>in</strong>troduction to supersymmetry, this section presents <strong>the</strong> M<strong>in</strong>imal SupersymmetricExtension of <strong>the</strong> SM (MSSM).2.2.1 SupersymmetrySupersymmetry (SUSY) [23] is a symmetry which relates masses and coupl<strong>in</strong>gs of bosons andfermions via sp<strong>in</strong>- 1 operators. In SUSY, particles are comb<strong>in</strong>ed <strong>in</strong>to superfields and an operator2Q generates <strong>the</strong> trans<strong>for</strong>mation of convert<strong>in</strong>g fermions to bosons and vice versa:Q|Boson〉 = |Fermion〉 Q † |Fermion〉 = |Boson〉 (2.46)There<strong>for</strong>e Q is a complex anticommut<strong>in</strong>g sp<strong>in</strong>or and its hermitian conjugate, Q † , is alsoa symmetry generator. Both generators are fermionic <strong>in</strong> nature (S = 1/2) and <strong>for</strong>m a Liealgebra [25], toge<strong>the</strong>r with <strong>the</strong> four-momentum and <strong>the</strong> Lorentz trans<strong>for</strong>mation generators. Infact, SUSY is a generalization of <strong>the</strong> space-time symmetries of quantum field <strong>the</strong>ory and seemsto be <strong>the</strong> last possible extension of <strong>the</strong> Lorentz group [26].In this situation, each chiral fermion f L,R has a scalar partner ˜f L,R and <strong>for</strong> each masslessgauge boson A µ , with <strong>the</strong> helicity states ±1, <strong>the</strong>re is a massless sp<strong>in</strong> 1/2 gaug<strong>in</strong>o partner, withhelicity states ± 1.22.2.2 Supersymmetry and <strong>the</strong> Hierarchy ProblemThe SM hierarchy problem presented <strong>in</strong> section 2.1.6 is very elegantly solved when consider<strong>in</strong>g<strong>the</strong> supersymmetric <strong>the</strong>ory [27]. The reason is that every fermion f has a scalar SUSY partnerS that couples to <strong>the</strong> Higgs as well and contributes with a mass correction term of <strong>the</strong> <strong>for</strong>m:[ ( ( ))]∆MH 2 = λ2 SΛ2Λ 2 + O m 216π 2 S ln(2.47)m SS<strong>in</strong>ce now λ f = λ S and Fermi statistics imply an opposite sign with respect to <strong>the</strong> contributionstated <strong>in</strong> equation 2.47, all <strong>the</strong> terms have a counter-term that naturally cancel all <strong>the</strong> hugecorrections. The terms that do not cancel are of <strong>the</strong> <strong>for</strong>m:∆MH 2 = λ2 ∣ ∣m 216π 2 S − m 2 ∣f(2.48)
18 2.2. M<strong>in</strong>imal Supersymmetric Extension of <strong>the</strong> Standard Modelwhere some smaller contributions have been omitted. This result leads us to <strong>the</strong> follow<strong>in</strong>g“naturalness” argument [28, 29]: s<strong>in</strong>ce <strong>the</strong>se corrections must not be greater than m hSM <strong>in</strong>order to avoid too much f<strong>in</strong>e tun<strong>in</strong>g, <strong>the</strong>n∣ m2S − m 2 ∣f 1TeV 2 . (2.49)Hence, one associates Λ ∼ 1 TeV as <strong>the</strong> scale where <strong>the</strong> SM is no longer valid and must besubstituted by its supersymmetric extension. As a benefit, this new <strong>the</strong>ory would be valid all <strong>the</strong>way up to <strong>the</strong> Planck scale. In any case, this is only a qualitative argument and does not helppredict<strong>in</strong>g exactly whe<strong>the</strong>r new particles should appear at 900 GeV or 2 TeV.2.2.3 O<strong>the</strong>r Benefits from <strong>the</strong> Introduction of SUSYBesides mak<strong>in</strong>g a small Higgs mass natural, SUSY has o<strong>the</strong>r <strong>in</strong>terest<strong>in</strong>g consequences. Oneof <strong>the</strong>m is, when SUSY is locally realized, that it conta<strong>in</strong>s among its gauge fields a possiblecandidate to be <strong>the</strong> graviton. Thus SUSY seems to be a good candidate <strong>for</strong> a <strong>the</strong>ory of all <strong>in</strong>teractions,or at least to play an important rôle <strong>in</strong> any such <strong>the</strong>ory. In addition, Great UnificationsTheories (GUT) also provide good motivation <strong>for</strong> <strong>the</strong> existence of supersymmetry. One can use<strong>the</strong> runn<strong>in</strong>g of <strong>the</strong> three coupl<strong>in</strong>gs of <strong>the</strong> SM, measured at <strong>the</strong> electroweak scale, and f<strong>in</strong>d that, ata certa<strong>in</strong> GUT scale of 10 15 GeV, <strong>the</strong> coupl<strong>in</strong>gs almost become <strong>the</strong> same value [30]. But if oneconsiders SUSY <strong>the</strong>n <strong>the</strong> coupl<strong>in</strong>gs are modified <strong>in</strong> such a way that <strong>the</strong>y become precisely <strong>the</strong>same value at <strong>the</strong> GUT scale. There<strong>for</strong>e, it is a strong <strong>in</strong>dication <strong>for</strong> <strong>the</strong> need of SUSY. However,some people claim that <strong>the</strong>re is noth<strong>in</strong>g special on that [31] provided that o<strong>the</strong>r modelscould do it if <strong>the</strong>y <strong>in</strong>troduce as many parameters as SUSY does.In addition to gauge coupl<strong>in</strong>g unification, SUSY is also a key <strong>in</strong>gredient <strong>for</strong> GUT.These <strong>the</strong>ories have <strong>in</strong>terest<strong>in</strong>g predictions such as a small neutr<strong>in</strong>o mass of <strong>the</strong> order ofm ν ≈ m 2 W /m GUT ≈ 10 −2 eV/c 2 and it can lead to <strong>the</strong> understand<strong>in</strong>g of <strong>the</strong> different quarkand lepton quantum numbers. But without SUSY <strong>the</strong> lifetime of <strong>the</strong> proton would be too smalland <strong>the</strong> prediction <strong>for</strong> s<strong>in</strong> 2 θ W would differ from <strong>the</strong> experiment [32, 31, 33]. In addition, SUSYhas been of greatest <strong>in</strong>terest <strong>in</strong> str<strong>in</strong>g <strong>the</strong>ories s<strong>in</strong>ce it is <strong>the</strong> mechanism which provides a coherentand complete framework which avoids negative square masses <strong>in</strong> some vibrational modes(tachyons) [34].Fur<strong>the</strong>rmore, some SUSY models predict <strong>the</strong> presence of a lightest supersymmetric particle,which is a candidate <strong>for</strong> dark matter <strong>in</strong> <strong>the</strong> universe, provided that it is neutral, weakly<strong>in</strong>teract<strong>in</strong>g and absolutely stable.
Chapter 2. Theory Introduction 19As a f<strong>in</strong>al remark, recent fits on <strong>the</strong> electroweak precision observables, such as <strong>the</strong> effectiveleptonic weak mix<strong>in</strong>g angle, s<strong>in</strong> 2 θ eff , seem to favor supersymmetric models <strong>in</strong> front of<strong>the</strong> SM alone [35]. This can be seen <strong>in</strong> figure 2.5, where <strong>the</strong> SM predictions <strong>for</strong> <strong>the</strong> M W asa function of m t is be<strong>in</strong>g compared with <strong>the</strong> predictions from <strong>the</strong> unconstra<strong>in</strong>ed M<strong>in</strong>imal SupersymmetricStandard Model (MSSM), which will be described <strong>in</strong> <strong>the</strong> next subsection. Thepredictions with<strong>in</strong> <strong>the</strong> two models give rise to two bands with only a relatively small overlapregion. The allowed parameter region <strong>in</strong> <strong>the</strong> SM arises from vary<strong>in</strong>g <strong>the</strong> only free parameterof <strong>the</strong> model, <strong>the</strong> mass of <strong>the</strong> SM Higgs boson from M hSM = GeV/c 2 114 (upper edge of<strong>the</strong> band) to GeV/c 2 400 (lower edge of <strong>the</strong> band). For <strong>the</strong> MSSM area, SUSY masses closeto <strong>the</strong>ir experimental limit are assumed <strong>for</strong> <strong>the</strong> upper edge, while <strong>the</strong> MSSM with large massesyields <strong>the</strong> lower edge of <strong>the</strong> blue area (dark-shaded). The 68% C.L. experimental results slightlyfavours <strong>the</strong> MSSM over <strong>the</strong> SM 2 .80.7080.60experimental errors 68% CL:LEP2/Tevatron (today)Tevatron/LHCILC/GigaZlight SUSYM W[GeV]80.5080.4080.3080.20M H= 114 GeVSMM H= 400 GeVMSSMSMMSSMboth modelsheavy SUSYHe<strong>in</strong>emeyer, Hollik, Stock<strong>in</strong>ger, Weber, Weigle<strong>in</strong> ’07160 165 170 175 180 185m t[GeV]Figure 2.5: M W as a function of m t as predicted by <strong>the</strong> SM <strong>in</strong> red (medium-shaded) and blue (dark-shaded)bands and with <strong>the</strong> MSSM prediction <strong>in</strong> green (light-shaded) and blue (dark-shaded) bands. The perspectives <strong>for</strong><strong>the</strong> present and future generation colliders, are also shown.2 Last top mass measurements from <strong>the</strong> Tevatron [6] <strong>in</strong>dicate even a lower mass <strong>for</strong> <strong>the</strong> top: m t =173.1 ± 0.6(stat) ± 1.1(syst) GeV/c 2 .
20 2.2. M<strong>in</strong>imal Supersymmetric Extension of <strong>the</strong> Standard Model2.2.4 The M<strong>in</strong>imal Supersymmetric Standard ModelSimilarly to <strong>the</strong> SM construction, that was conceived to be <strong>the</strong> m<strong>in</strong>imal group viable to expla<strong>in</strong><strong>the</strong> electroweak sector, <strong>the</strong> MSSM [36] is <strong>the</strong> m<strong>in</strong>imal viable supersymmetric extension of <strong>the</strong>SM. The MSSM obeys <strong>the</strong> same SU(3) C⊗ SU(2) L⊗ U(1) Y gauge symmetries of <strong>the</strong> StandardModel but doubles <strong>the</strong> spectrum of new particles s<strong>in</strong>ce <strong>for</strong> every particle <strong>in</strong> <strong>the</strong> SM, a superpartneris postulated which differs by half a unit of sp<strong>in</strong>. The superpartners are convenientlydescribed by a notation with close correspondence to <strong>the</strong> SM notation <strong>for</strong> bosons and fermions.Hence, <strong>the</strong> superpartners are written with <strong>the</strong> same letter of <strong>the</strong>ir partner but with a tilde overit and <strong>the</strong> superfields are written with a “tilde” superscript. In addition, <strong>the</strong> bosonic partnersof <strong>the</strong> fermions are denoted start<strong>in</strong>g with an extra “s” (e.g. selectron is <strong>the</strong> superpartner of <strong>the</strong>electron) and <strong>the</strong> fermionic partners of <strong>the</strong> bosons f<strong>in</strong>ish with <strong>the</strong> suffix “<strong>in</strong>o” (e.g. glu<strong>in</strong>o is <strong>the</strong>superpartner of <strong>the</strong> gluon).For simplicity and to avoid unnecessary repetitions, consider <strong>the</strong> case of one generationof quarks, leptons and <strong>the</strong>ir superpartners. One can def<strong>in</strong>e ˆQ as <strong>the</strong> superfield conta<strong>in</strong><strong>in</strong>g anSU(2) Ldoublet of quarks:Q =(uLd L)(2.50)and <strong>the</strong>ir scalar partners which are also <strong>in</strong> an SU(2) Ldoublet,˜Q =(ũL˜d L)(2.51)In an analogous <strong>for</strong>m, <strong>the</strong> superfield Ûc ( ˆD c ) conta<strong>in</strong>s <strong>the</strong> right-handed up (down) antiquark,ū R ( ¯d R ), and its scalar partner, ũ ∗ R ( ˜d ∗ R ). Follow<strong>in</strong>g <strong>the</strong> same pattern, leptons are conta<strong>in</strong>ed<strong>in</strong> <strong>the</strong> SU(2) L doublet superfield ˆL which conta<strong>in</strong>s <strong>the</strong> left-handed fermions,( )νLL =(2.52)e Land <strong>the</strong>ir scalar partners,˜L =(˜νLẽ L). (2.53)F<strong>in</strong>ally, <strong>the</strong> superfield Êc conta<strong>in</strong>s <strong>the</strong> right-handed anti-electron, ē R , and its scalar partner,ẽ ∗ R .
Chapter 2. Theory Introduction 21Similarly, <strong>for</strong> every gauge boson it exist a Majorana fermion (gaug<strong>in</strong>o). Ĝ a is def<strong>in</strong>ed as asuperfield that conta<strong>in</strong>s all <strong>the</strong> gluons, g a , and <strong>the</strong>ir fermion partners <strong>the</strong> glu<strong>in</strong>os, ˜g a ; Ŵi conta<strong>in</strong>s<strong>the</strong> SU(2) L gauge bosons, W i , and <strong>the</strong>ir fermion partners, ˜ω i (w<strong>in</strong>os); and ˜B conta<strong>in</strong>s <strong>the</strong> U(1)gauge field, B, and its fermion partner, ˜b (b<strong>in</strong>o).In addition, <strong>in</strong> <strong>the</strong> MSSM <strong>the</strong> Higgs sector is enlarged to avoid triangle gauge anomalies [37,38, 39]. Anomalies are not allowed <strong>in</strong> gauge <strong>the</strong>ories and this is simply achieved by requir<strong>in</strong>gthat <strong>the</strong> sum of all fermion charges vanishes. The Higgs scalar doublet acquires a SUSY partnerwhich is an SU(2) Ldoublet of Majorana fermion fields, ˜h 1 (Higgs<strong>in</strong>os), which will contributeto <strong>the</strong> triangle SU(2) Land U(1) Ygauge anomalies. S<strong>in</strong>ce fermions <strong>in</strong> SM have exactly <strong>the</strong> rightquantum numbers to cancel <strong>the</strong>se anomalies, it follows that <strong>the</strong> contribution from <strong>the</strong> fermionicpartner of <strong>the</strong> Higgs doublet rema<strong>in</strong>s uncanceled. The easiest solution is to require a secondHiggs doublet with precisely <strong>the</strong> opposite U(1) Yquantum number than <strong>the</strong> first Higgs doublet.Fur<strong>the</strong>rmore, <strong>in</strong> <strong>the</strong> SM <strong>the</strong> Higgs doublet (<strong>the</strong> complex conjugate of <strong>the</strong> doublet) can coupleto <strong>the</strong> T 3 = + 1 (T 2 3 = − 1 ) fermions and give mass to all <strong>the</strong> spectrum of fermions. But, <strong>in</strong> a2supersymmetric <strong>the</strong>ory, any doublet can give mass ei<strong>the</strong>r to a T 3 = + 1 or a T 2 3 = − 1 fermion 2but not both. Thus, two Higgs doublets are needed <strong>in</strong> order to generate both up-like and downlikequark masses. As result, one could th<strong>in</strong>k of <strong>the</strong> SM becom<strong>in</strong>g a two Higgs doublet model(2HDM) [40] prior to <strong>in</strong>troduce <strong>the</strong> supersymmetric sector. In Table 2.3 <strong>the</strong> spectrum of <strong>the</strong>MSSM fields is summarized.With two SU(2) doublets, <strong>the</strong> <strong>the</strong>ory has eight real scalar fields and three massless gaugebosons, which accounts <strong>for</strong> fourteen degrees of freedom. After SUSY break<strong>in</strong>g, <strong>the</strong> three gaugebosons acquire masses (n<strong>in</strong>e degrees of freedom), which means that <strong>the</strong>re should exist five sp<strong>in</strong>zeroHiggs fields <strong>in</strong> <strong>the</strong> spectrum: three neutral scalars (h, H, A) and two charged pairs (H + ,H − ).The parameters of <strong>the</strong> supersymmetry-conserv<strong>in</strong>g sector consist of:• Gauge coupl<strong>in</strong>gs: g s , g and g ′ , correspond<strong>in</strong>g to <strong>the</strong> Standard Model gauge groupSU(3) C⊗ SU(2) L⊗ U(1) Y , respectively.• Higgs mass parameter, µ.• Higgs-fermion Yukawa coupl<strong>in</strong>g constants: λ u , λ d , and λ e , correspond<strong>in</strong>g to <strong>the</strong> coupl<strong>in</strong>gof quarks or leptons and <strong>the</strong>ir superpartners to <strong>the</strong> Higgs bosons and higgs<strong>in</strong>os.The supersymmetry-break<strong>in</strong>g sector conta<strong>in</strong>s <strong>the</strong> follow<strong>in</strong>g set of parameters:
22 2.2. M<strong>in</strong>imal Supersymmetric Extension of <strong>the</strong> Standard ModelNames 2HDM particle SUSY partner⎛⎜⎝SU(3) CSU(2) L⎞⎟⎠squarks, quarks(× 3 families)sleptons, leptons(× 3 families)EWK bosonsStrong bosonsHiggs, higgs<strong>in</strong>osU(1) Y1ˆQ (u L d L ) (ũ2 L ˜dL ) 0 (3, 2, 1)3Û u † 1Rũ ∗ 2 R 0 (¯3, 1, − 4)3ˆD˜d ∗ R 0 (¯3, 1, 2)3d † R121ˆL (ν e L ) (˜ν ẽ2 L ) 0 (1, 2, −1)Ê e † 1Rẽ ∗ 2 R 0 (1, 1, 2)Ŵ W 1 W 2 W 3 1 2 3 11 ˜W ˜W ˜W (1, 3, 0)21ˆB B 1 ˜B (1, 1, 0)21Ĝ a g a 1 ˜g a (8, 1, 0)2Ĥ u (H u + H0 u ) 0 ( ˜H u + ˜H u 0) 1(1, 2, 1)2Ĥ d (Hd 0 H− d ) 0 ( ˜H d 0 ˜H − d ) 1(1, 2, −1)2Table 2.3: Superfields and particle content of <strong>the</strong> MSSM. Symbols <strong>for</strong> each of <strong>the</strong> chiral supermultiplets as awhole are <strong>in</strong>dicated <strong>in</strong> <strong>the</strong> second column.• Gaug<strong>in</strong>o Majorana masses M 3 , M 2 and M 1 , associated with <strong>the</strong> SU(3) C, SU(2) LandU(1) Y subgroups, respectively. These masses may be connected <strong>in</strong> some cases as will beseen later.• Five scalar squared-mass parameters <strong>for</strong> <strong>the</strong> squarks and sleptons: M 2˜Q , M2 , , ŨM2˜DM2˜Land M 2 , correspond<strong>in</strong>g to <strong>the</strong> five electroweak gauge multiplets.Ẽ• Three scalar Higgs squared-mass parameters, two of which (m 2 1 and m2 2 ) contribute to <strong>the</strong>diagonal Higgs squared-masses and a third which corresponds to <strong>the</strong> off-diagonal termsm 2 12≡ µB. These three parameters can be re-expressed <strong>in</strong> terms of <strong>the</strong> two Higgs vacuumexpectation values (v d = 〈H 0 d 〉 and v u = 〈H 0 u〉) 3 , usually taken through <strong>the</strong> ratioand one physical Higgs mass 4 .tanβ ≡ v uv d, (2.54)3 Notation v u (v d ) is used to dist<strong>in</strong>guish vacuum expectation values of <strong>the</strong> Higgs field which couples exclusivelyto up-type (down-type) quarks.4 Note that v 2 d + v2 u = 4M 2 W /g2 = (246 GeV/c 2 ) 2 is fixed by <strong>the</strong> W mass and <strong>the</strong> gauge coupl<strong>in</strong>g, but tan βis a free parameter of <strong>the</strong> model.
Chapter 2. Theory Introduction 23• Tril<strong>in</strong>ear <strong>in</strong>teraction terms of <strong>the</strong> <strong>for</strong>m Higgs-squark-squark and Higgs-slepton-slepton,with coefficients A u , A d and A e .The glu<strong>in</strong>o is <strong>the</strong> color octet Majorana (<strong>the</strong>re is no dist<strong>in</strong>ct antigluon) fermion partner of <strong>the</strong>gluon. It has 16 degrees of freedom s<strong>in</strong>ce <strong>the</strong>re are 8 massless gluons (2 sp<strong>in</strong> degrees of freedom,each). The supersymmetric partners of <strong>the</strong> electroweak gauge and Higgs bosons (gaug<strong>in</strong>osand higgs<strong>in</strong>os) can mix. As a result, <strong>the</strong> physical mass eigenstates are model-dependent l<strong>in</strong>earcomb<strong>in</strong>ations of <strong>the</strong>se states, called charg<strong>in</strong>os and neutral<strong>in</strong>os, which are obta<strong>in</strong>ed by diagonaliz<strong>in</strong>g<strong>the</strong> correspond<strong>in</strong>g mass matrices. There are two charg<strong>in</strong>os (˜χ ± i ) and four neutral<strong>in</strong>os(˜χ 0 i ), which are by convention ordered <strong>in</strong> masses (˜χ± 1 is <strong>the</strong> lowest charg<strong>in</strong>o and ˜χ0 1 is <strong>the</strong> lowestneutral<strong>in</strong>o). Depend<strong>in</strong>g whe<strong>the</strong>r <strong>the</strong> charg<strong>in</strong>o or neutral<strong>in</strong>o eigenstate approximates a particulargaug<strong>in</strong>o or higgs<strong>in</strong>o state, <strong>the</strong>y can become more phot<strong>in</strong>o-like, b<strong>in</strong>o-like... and result <strong>in</strong>strik<strong>in</strong>gly different phenomenology.The supersymmetric partners of <strong>the</strong> quarks and leptons are sp<strong>in</strong>-zero bosons and <strong>the</strong> result<strong>in</strong>gsquarks and sleptons can also mix <strong>the</strong>ir left- and right-handed components yield<strong>in</strong>g <strong>the</strong> masseigenstates (denoted by <strong>the</strong> <strong>in</strong>dices 1,2 <strong>in</strong>stead of L, R). This mix<strong>in</strong>g is proportional to <strong>the</strong> massof <strong>the</strong> SM partner quark or lepton and to tanβ. Thus, <strong>the</strong> mix<strong>in</strong>g can lead to an important splitt<strong>in</strong>g<strong>in</strong> <strong>the</strong> mass spectrum of heavy squarks, specially at large tanβ. In contrast, <strong>the</strong> first twofamilies can be considered degenerate <strong>in</strong> mass. All physical particles of <strong>the</strong> MSSM are given <strong>in</strong>Table 2.4.2HDM particle sp<strong>in</strong> SUSY particle sp<strong>in</strong>1quarks: q2squarks: ˜q 1 , ˜q 2 01leptons: l2sleptons: ˜l1 , ˜l 2 01gluons: g a 1 glu<strong>in</strong>os: ˜g a 2gauge bosons: W ± , Z 0 1, γ 1 neutral<strong>in</strong>os: ˜χ0 1 , ˜χ0 2 , ˜χ0 3 , ˜χ0 4 2Higgs bosons: h 0 , H 0 , A 0 , H ± 0 charg<strong>in</strong>os: χ±˜1 , χ±˜12 2Table 2.4: The particle content of <strong>the</strong> MSSM.2.2.5 MSSM Lagrangian and R-parityThe MSSM Lagrangian is constructed us<strong>in</strong>g <strong>the</strong> already def<strong>in</strong>ed particle content and follow<strong>in</strong>gan analogy with <strong>the</strong> L SM . Follow<strong>in</strong>g a similar notation as <strong>in</strong> <strong>the</strong> SM, <strong>the</strong> k<strong>in</strong>etic term of <strong>the</strong>
24 2.2. M<strong>in</strong>imal Supersymmetric Extension of <strong>the</strong> Standard ModelLagrangian can be written as:{(D µ S i ) † (D µ S i ) + i 2 ¯ψ i γ µ D µ ψ i}L KE = ∑ i+∑{− 1 4 F µν A F µνA +2¯λ i }A Dλ A.(2.55)AHere, S i (ψ i ) is <strong>the</strong> scalar (fermion) component of <strong>the</strong> i th chiral superfield, D is <strong>the</strong> SU(3)⊗SU(2) L ⊗ U(1) gauge <strong>in</strong>variant derivative, Fµν A is <strong>the</strong> Yang-Mills gauge field and λ A is <strong>the</strong>gaug<strong>in</strong>o superpartner of <strong>the</strong> correspond<strong>in</strong>g gauge boson. It is worth notic<strong>in</strong>g that <strong>the</strong> ∑ i is asum over all fermion fields of <strong>the</strong> SM, <strong>the</strong> scalar partners and <strong>the</strong> 2 Higgs doublets with <strong>the</strong>irfermion partners. On <strong>the</strong> o<strong>the</strong>r hand, ∑ A is over <strong>the</strong> SU(3) c, SU(2) L and U(1) Y gauge fieldswith <strong>the</strong>ir fermion partners, <strong>the</strong> gaug<strong>in</strong>os.The <strong>in</strong>teractions between bosons and fermions are completely determ<strong>in</strong>ed by <strong>the</strong> gaugesymmetries and by <strong>the</strong> supersymmetry:L <strong>in</strong>t = − √ 2 ∑ [g A S∗i T A ¯ψiL λ A + h.c. ]i,A− 1 2(∑ ∑iAg A S ∗ i T A S i) 2,(2.56)where ψ L ≡ 1 2 (1 − γ 5)ψ, T A is <strong>the</strong> matrix of <strong>the</strong> group generators and g A <strong>the</strong> gauge coupl<strong>in</strong>gconstants. It can be seen that <strong>the</strong>re are no adjustable parameter, hence, all <strong>in</strong>teraction strengthsare completely fixed <strong>in</strong> terms of SM coupl<strong>in</strong>g constants.Once <strong>the</strong> superfields and <strong>the</strong> gauge symmetries are chosen, <strong>the</strong> only freedom <strong>in</strong> construct<strong>in</strong>gL MSSM is conta<strong>in</strong>ed <strong>in</strong> a function called superpotential, W. This is an analytic <strong>for</strong>m of <strong>the</strong>chiral superfields, Ŝ, that has <strong>the</strong> <strong>for</strong>m:W = ǫ ij µĤi uĤj d + ǫ ij[λ L Ĥd¯ˆL i j ¯Ê + λD Ĥd i ˆQ ¯ˆD + λU Ĥu j ˆQ]i ¯Û + W RP (2.57)where i and j are SU(2) L doublet <strong>in</strong>dices and ǫ ij = −ǫji (with ǫ 12 = 1) contracts <strong>the</strong> SU(2) Ldoublet fields. No derivative <strong>in</strong>teractions are allowed <strong>in</strong> order that W be an analytical function.The term µĤi uĤj dgives mass terms <strong>for</strong> <strong>the</strong> Higgs bosons and so µ is often called <strong>the</strong> Higgsmass parameter. The terms <strong>in</strong> <strong>the</strong> square brackets proportional to λ L , λ D and λ U give <strong>the</strong> usualYukawa <strong>in</strong>teractions of <strong>the</strong> fermions with <strong>the</strong> Higgs bosons. Hence, unlike <strong>the</strong> SM case, <strong>the</strong>secoefficients are determ<strong>in</strong>ed <strong>in</strong> terms of <strong>the</strong> fermion masses and <strong>the</strong> vacuum expectation valuesof <strong>the</strong> neutral members of <strong>the</strong> scalar components, and are not arbitrary coupl<strong>in</strong>gs.
Chapter 2. Theory Introduction 25In <strong>the</strong> most general superpotential one can add more terms which are grouped under W RP<strong>in</strong> equation 2.57. These terms are of <strong>the</strong> <strong>for</strong>m:W RP = λ αβγ ˆLαˆLβ ¯Êγ + λ ′ ˆL αβγ α ˆQβ ¯ˆDγ + λ ′′ αβγ¯Û α ¯ˆDβ ¯ˆDγ + µ ′ˆLĤ (2.58)where <strong>the</strong> <strong>in</strong>dices α, β and γ label <strong>the</strong> 3 generations of quarks and leptons. These terms constitutea problem <strong>in</strong> <strong>the</strong> sense that <strong>the</strong> first two contribute to lepton number violation <strong>in</strong>teractionsand <strong>the</strong> third one to baryon number violation <strong>in</strong>teractions 5 . The comb<strong>in</strong>ation of leptonand baryon violation terms can contribute to <strong>the</strong> proton decay at tree level through <strong>the</strong>exchange of <strong>the</strong> scalar partner of <strong>the</strong> down quark. S<strong>in</strong>ce this process is experimentally restricted[42, 43, 44, 45, 46, 47, 48, 49] it put <strong>in</strong>to question <strong>the</strong> validity of <strong>the</strong> model. Onesolution is to assume that <strong>the</strong> parameters are small enough to avoid experimental limits. Eventhis is certa<strong>in</strong>ly allowed experimentally, this would imply <strong>the</strong> <strong>in</strong>troduction of an artificial tun<strong>in</strong>g.The o<strong>the</strong>r solution is to <strong>in</strong>troduce a new symmetry called R-parity [50, 51, 52, 53, 54, 55, 56].R-parity (R p ) is a multiplicative quantum number def<strong>in</strong>ed as:R = (−1) 3(B−L)+2s , (2.59)where B and L are <strong>the</strong> baryon and lepton quantum numbers and s is <strong>the</strong> sp<strong>in</strong> of <strong>the</strong> particle.Thus, all SM particles have R p = +1 while <strong>the</strong>ir SUSY partners have R p = −1.The assumption of such a symmetry prevents lepton and baryon number violat<strong>in</strong>g terms buthas also dramatic phenomenological consequences: exists no mix<strong>in</strong>g between <strong>the</strong> sparticles and<strong>the</strong> R P = 1 particles, SUSY particles can only be pair-produced <strong>in</strong> <strong>the</strong> collisions of SM particlesand a SUSY particle would undergo a cha<strong>in</strong> of decays until <strong>the</strong> lightest SUSY particle (LSP) isproduced. Then, this LSP cannot decay fur<strong>the</strong>r and constitutes a cold dark matter candidate 6 .2.2.6 SUSY Break<strong>in</strong>gAt this po<strong>in</strong>t, <strong>the</strong> MSSM Lagrangian does not provide mass terms <strong>for</strong> all <strong>the</strong> particles (fermions,scalars, gauge fields). If supersymmetry was an exact symmetry, squarks and quarks wouldhave equal masses and glu<strong>in</strong>os would be massless. S<strong>in</strong>ce this is not <strong>the</strong> case <strong>in</strong> nature, at lowenergies supersymmetry must be a broken symmetry and new SUSY-break<strong>in</strong>g terms need to be<strong>in</strong>troduced <strong>in</strong> <strong>the</strong> Lagrangian. To prevent dangerous quadratic divergences, only a certa<strong>in</strong> subset5 The fourth term can be ignored s<strong>in</strong>ce one can implement a rotation <strong>in</strong> <strong>the</strong> lepton field ˆL such that this termvanishes [41].6 Due to cosmological constra<strong>in</strong>ts, a cold dark matter candidate need to be stable and neutral [57, 58].
26 2.2. M<strong>in</strong>imal Supersymmetric Extension of <strong>the</strong> Standard Modelof supersymmetry-break<strong>in</strong>g terms are allowed to be present <strong>in</strong> <strong>the</strong> <strong>the</strong>ory and <strong>the</strong>ir coupl<strong>in</strong>gsare denoted as soft parameters. Then, <strong>the</strong> so-called soft Lagrangian which break SUSY is (firstgeneration only):−L soft = 1 []M 3 ĝĝ + M 2 ŴŴ 2+ M 1 ˆB ˆB+ ǫ αβ[−bHd α Hβ u − Hα ˆQ β u i  uij¯Ûj + Hd α ˆQ β i  dij¯ˆDj + Hd αˆL ]βi  eij¯Êj + h.c.+ m 2 H d|H d | 2 + m 2 H u|H u | 2 + ˆQ α i m2 Q ij ˆQα∗ j+ ˆL α i m2 L ij ˆLα∗ j + ¯Û ∗ i m2 U ij¯Ûj + ¯ˆD∗ i m 2 D ij¯ˆDj + ¯Ê ∗ i m2 E ij¯Êj ,(2.60)where i and j are <strong>the</strong> SU(2) L doublet <strong>in</strong>dices. This Lagrangian has arbitrary masses <strong>for</strong> <strong>the</strong>scalars and gaug<strong>in</strong>os and also arbitrary bi-l<strong>in</strong>ear and tri-l<strong>in</strong>ear mix<strong>in</strong>g terms. The scalar andgaug<strong>in</strong>o mass terms have <strong>the</strong> desired effect of break<strong>in</strong>g <strong>the</strong> mass degeneracy between <strong>the</strong> particlesand <strong>the</strong>ir SUSY partners. The tri-l<strong>in</strong>ear A terms affect primarily <strong>the</strong> particles of <strong>the</strong> thirdgeneration. The µB term mixes <strong>the</strong> scalar components of <strong>the</strong> two Higgs doublets. In <strong>the</strong> mostgeneral case, all of <strong>the</strong> mass and <strong>in</strong>teraction terms of equation 2.60 are matrices <strong>in</strong>volv<strong>in</strong>g allthree generators. However, <strong>the</strong> orig<strong>in</strong> of all <strong>the</strong>se terms is left unspecified. How supersymmetrybreak<strong>in</strong>g is transmitted to <strong>the</strong> superpartners is encoded <strong>in</strong> <strong>the</strong> parameters of L soft . All of <strong>the</strong>quantities <strong>in</strong> L soft receive radiative corrections and thus are scale-dependent, satisfy<strong>in</strong>g knownRenormalisation Group Equations (RGEs).For phenomenological purposes, <strong>the</strong> described Lagrangian is simply a low energy effectiveLagrangian with a number of <strong>in</strong>put parameters. The fact that except <strong>for</strong> <strong>the</strong> assumption of <strong>the</strong>presence of supersymmetric particles, R p , and gauge and Po<strong>in</strong>caré <strong>in</strong>variance, noth<strong>in</strong>g else hasbeen assumed, makes <strong>the</strong> MSSM a very simple framework but one needs to <strong>in</strong>troduce plentyof free <strong>in</strong>put parameters. MSSM <strong>in</strong>cludes at least 105 new parameters that added to <strong>the</strong> 19parameters of <strong>the</strong> SM, <strong>the</strong> model has 124 parameters to be determ<strong>in</strong>ed 7 . While often onlysubsets of <strong>the</strong>se parameters are relevant <strong>for</strong> particular experimental processes and <strong>the</strong>re existsome phenomenological constra<strong>in</strong>ts <strong>in</strong> <strong>the</strong>se parameters, <strong>the</strong> number is too large <strong>for</strong> practicalpurposes to carry out phenomenological analyses <strong>in</strong> full generality.However, unlike <strong>in</strong> <strong>the</strong> SM case, now <strong>the</strong>re is <strong>the</strong> possibility to stablish a top-down approachby which <strong>the</strong> MSSM parameters are predicted with<strong>in</strong> <strong>the</strong> context of an underly<strong>in</strong>g <strong>the</strong>ory, oftenas functions of fewer basic parameters. The basic question to be addressed is how to understand<strong>the</strong> explicit soft supersymmetry break<strong>in</strong>g encoded <strong>in</strong> <strong>the</strong> L soft parameters as <strong>the</strong> result ofspontaneous supersymmetry break<strong>in</strong>g <strong>in</strong> a more fundamental <strong>the</strong>ory. S<strong>in</strong>ce this is not known,7 For this particular reason, sometimes it is referred to as MSSM-124.
Chapter 2. Theory Introduction 27different models have been constructed as an attempt to f<strong>in</strong>d an answer <strong>for</strong> this question. S<strong>in</strong>ceTeV-scale supersymmetry-break<strong>in</strong>g models have reported negative results [59], o<strong>the</strong>r modelswhich assume that <strong>the</strong> <strong>the</strong>ory can be splitted <strong>in</strong>to at least two sectors have been considered.These two sectors have no direct renormalizable coupl<strong>in</strong>gs between <strong>the</strong>m and <strong>the</strong>y are divided<strong>in</strong>to observable or visible sector, which conta<strong>in</strong>s <strong>the</strong> SM fields and <strong>the</strong>ir superpartners, and <strong>the</strong>hidden sector, <strong>in</strong> which supersymmetry is spontaneously broken by a dynamical mechanism.With<strong>in</strong> this framework, SUSY break<strong>in</strong>g is communicated from <strong>the</strong> hidden sector where itorig<strong>in</strong>ates to <strong>the</strong> observable sector via suppressed <strong>in</strong>teractions <strong>in</strong>volv<strong>in</strong>g a third set of fields,<strong>the</strong> mediator or messenger fields. This hidden sector implies that <strong>the</strong> fundamental scale ofsupersymmetry break<strong>in</strong>g µ s is hierarchically larger than <strong>the</strong> TeV scale. Depend<strong>in</strong>g on <strong>the</strong> modelthis µ s can be postulated to be at <strong>the</strong> GUT scale, Majorana neutr<strong>in</strong>o mass scale or <strong>in</strong> extradimensionalbraneworlds. There<strong>for</strong>e, different models account <strong>for</strong> specific mechanisms <strong>for</strong> howsupersymmetry break<strong>in</strong>g is mediated between <strong>the</strong> hidden and observable sectors and <strong>in</strong>volvespecific energy scales at which <strong>the</strong> soft terms are generated. These values are <strong>the</strong>n used tocompute <strong>the</strong> correspond<strong>in</strong>g values at observable energy scales, all predicted at <strong>the</strong> TeV scale by<strong>the</strong> models, us<strong>in</strong>g <strong>the</strong> scale dependence of <strong>the</strong> L soft parameters as dictated by <strong>the</strong>ir RGEs.2.3 <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong>In <strong>the</strong> MSSM, <strong>the</strong> SM quark helicity states q L and q R have scalar MSSM super-partners, whichare also <strong>the</strong> mass eigenstates (<strong>in</strong> good approximation) <strong>for</strong> <strong>the</strong> first two generations. However,<strong>for</strong> <strong>the</strong> third generation, strong mix<strong>in</strong>g of <strong>the</strong>se states may appear depend<strong>in</strong>g on <strong>the</strong> <strong>the</strong>oreticalparameters: tan β and A t,b (<strong>the</strong> Higgs-sbottom tril<strong>in</strong>ear coupl<strong>in</strong>g).This <strong>the</strong>sis presents two searches <strong>for</strong> third generation squarks at CDF Run II. The follow<strong>in</strong>gsections discuss <strong>the</strong> motivation <strong>for</strong> <strong>the</strong> particular f<strong>in</strong>al states selected <strong>in</strong> <strong>the</strong>se analyses.2.3.1 Scalar Bottom from Glu<strong>in</strong>o DecaySeveral models [60], assum<strong>in</strong>g large tanβ, predict that <strong>the</strong> mix<strong>in</strong>g <strong>in</strong> <strong>the</strong> mass eigenstates mightbe substantial <strong>for</strong> <strong>the</strong> scalar bottom, yield<strong>in</strong>g a ˜b mass eigenstate significantly lighter than o<strong>the</strong>rsquarks:m 2˜b1,2 = 1 2 [m2˜bL + m 2˜bR ±√(m 2˜bL − m 2˜bR ) 2 + 4m 2 b (A b − µtanβ) 2 ] (2.61)
28 2.3. <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong>Moreover, <strong>the</strong> glu<strong>in</strong>o pair production cross section is almost an order of magnitude largerthan a sbottom of similar mass [61]. At <strong>the</strong> Tevatron energies, glu<strong>in</strong>os are produced ma<strong>in</strong>lythrough quark-antiquark annihilation and gluon fusion, figure 2.6, with <strong>the</strong> <strong>for</strong>mer dom<strong>in</strong>at<strong>in</strong>g<strong>for</strong> high x. If <strong>the</strong> sbottom is light enough, <strong>the</strong>n <strong>the</strong> two body decay ˜g → b˜b would be k<strong>in</strong>ematicallyallowed.qg~gg~q~q g ~ g ~_q_qg~gg~Figure 2.6: Lead<strong>in</strong>g order glu<strong>in</strong>o pair production mechanisms at <strong>the</strong> Tevatron center of mass energies.In <strong>the</strong> region of <strong>in</strong>terest <strong>for</strong> this analysis (m t , m˜χ + > m˜b> m˜χ 0), <strong>the</strong> dom<strong>in</strong>ant decaychannel is sbottom <strong>in</strong>to bottom quark and neutral<strong>in</strong>o ˜b → b˜χ 0 , with no o<strong>the</strong>r available decayschannels, s<strong>in</strong>ce we require m˜b< m t , m˜χ +. Hence, we assume a Branch<strong>in</strong>g Ratio of 100% <strong>for</strong><strong>the</strong> ˜b → b˜χ 0 decay, and <strong>the</strong> fully glu<strong>in</strong>o decay cha<strong>in</strong> will be as shown <strong>in</strong> figure 2.7.~g~bbb~χ 0Figure 2.7: Glu<strong>in</strong>o decay <strong>in</strong>to bottom quark and sbottom.One could also th<strong>in</strong>k a scenario where <strong>the</strong> second neutral<strong>in</strong>o ˜χ 0 2 is lighter than <strong>the</strong> sbottomquark. In this case ˜b → b˜χ 0 2, with <strong>the</strong> second lightest neutral<strong>in</strong>o decay<strong>in</strong>g <strong>in</strong>to leptons and LSP(˜χ 0 2 → ll˜χ0 1 ). Such a signature could be observed by multileptons search and is not consideredhere.In order to get <strong>the</strong> predictions <strong>for</strong> our signal, we use <strong>the</strong> program PROSPINO [61] to compute<strong>the</strong> total production cross section and PYTHIA [62] to estimate <strong>the</strong> event acceptance <strong>in</strong> <strong>the</strong>
Chapter 2. Theory Introduction 29detector and <strong>in</strong> <strong>the</strong> application of our selection cuts.For <strong>the</strong> NLO cross sections of glu<strong>in</strong>o pairs, <strong>the</strong> calculation does not depend on <strong>the</strong> sbottommass or <strong>the</strong> neutral<strong>in</strong>o mass. However, <strong>the</strong>re is a dependence on <strong>the</strong> mass of <strong>the</strong> first squarks dueto <strong>the</strong>ir presence <strong>in</strong> <strong>the</strong> diagrams. The ma<strong>in</strong> dom<strong>in</strong>ant contribution is com<strong>in</strong>g from those squarksassociated to <strong>the</strong> lightest quarks, specifically ũ and ˜d due to <strong>the</strong>ir presence as valence quarks<strong>in</strong> <strong>the</strong> proton and antiproton. Figure 2.8 shows <strong>the</strong> cross section of glu<strong>in</strong>o-pair production <strong>for</strong>m(˜g) = 250 GeV/c 2 and m(˜g) = 350 GeV/c 2 as a function of <strong>the</strong> squark masses 8 . Weobserve a strong dependence <strong>for</strong> <strong>the</strong> Lead<strong>in</strong>g-order and Next-to-lead<strong>in</strong>g cross sections on <strong>the</strong>mass of <strong>the</strong> squarks.Cross Section [pb]43.532.52M(~q)-dependence <strong>for</strong> M(~g)=250.0 GeV/cPROSPINO LO (CTEQ6L1)PROSPINO NLO (CTEQ6M)2Cross Section [pb]0.30.250.20.15M(~q)-dependence <strong>for</strong> M(~g)=350.0 GeV/cPROSPINO LO (CTEQ6L1)PROSPINO NLO (CTEQ6M)21.510.10.5pp→~g~g ats=1.96 GeV0.05pp→~g~g ats=1.96 GeV2.5 LO-to-NLO K-factor21.51 ~102M( q) [TeV/c ]2.5 LO-to-NLO K-factor21.51 ~102M( q) [TeV/c ]Figure 2.8: LO and NLO cross section of glu<strong>in</strong>o-pair production at <strong>the</strong> Tevatron Run II as predicted byPROSPINO as a function of <strong>the</strong> mass of <strong>the</strong> squarks of <strong>the</strong> first two families. The predictions are shown <strong>for</strong>values of <strong>the</strong> glu<strong>in</strong>o mass of 250 GeV/c 2 (left) and 350 GeV/c 2 (right).Due to this dependence, <strong>the</strong> analysis needs to be per<strong>for</strong>med with a clear assumption on <strong>the</strong>mass of <strong>the</strong> squarks. We decided to use <strong>the</strong> value of 500 GeV/c 2 as it was done <strong>in</strong> previousanalyses [63]. This value leads to a reasonably conservative estimate of <strong>the</strong> cross section s<strong>in</strong>ce<strong>the</strong> larger <strong>the</strong> mass of <strong>the</strong> squark, <strong>the</strong> larger <strong>the</strong> cross section. Us<strong>in</strong>g a value much smaller than500 GeV/c 2 may break <strong>the</strong> assumption that <strong>the</strong> decay of <strong>the</strong> glu<strong>in</strong>o is dom<strong>in</strong>ated by ˜g → b˜b 1 .Under this assumption, we compute <strong>the</strong> cross section of <strong>the</strong> glu<strong>in</strong>o-pair production process8 As this is done <strong>in</strong> PROSPINO, <strong>the</strong> masses of <strong>the</strong> squarks associated to <strong>the</strong> light quarks are degenerated, andwe always assume that.
30 2.3. <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong><strong>for</strong> <strong>the</strong> range of masses we are <strong>in</strong>terested <strong>in</strong>. This is shown <strong>in</strong> figure 2.9 us<strong>in</strong>g <strong>the</strong> CTEQ6Mset of Parton Distribution Functions [64, 65]. The cross section falls very rapidly when <strong>in</strong>creas<strong>in</strong>g<strong>the</strong> mass of <strong>the</strong> glu<strong>in</strong>o, but <strong>the</strong> absolute values are reasonable <strong>for</strong> <strong>the</strong> analysis to reachunexcluded regions of <strong>the</strong> parameter space.As a comparison, figure 2.9 also shows <strong>the</strong> equivalent cross section <strong>for</strong> sbottom-pair production.It should be noticed that <strong>for</strong> similar masses of <strong>the</strong> glu<strong>in</strong>o and sbottom, <strong>the</strong> productionof glu<strong>in</strong>o has a much larger cross section, lead<strong>in</strong>g to <strong>the</strong> fact that even <strong>for</strong> smaller mass of <strong>the</strong>sbottom, <strong>the</strong> channel we are consider<strong>in</strong>g here provides larger sensitivity than <strong>the</strong> direct search ofsbottom-pair production due to a larger cross section and a signature that is much cleaner thanthat of <strong>the</strong> sbottom-pair production. This makes specially <strong>in</strong>terest<strong>in</strong>g <strong>the</strong> degeneration massregion <strong>for</strong> which, we per<strong>for</strong>m an specific optimization <strong>in</strong> <strong>the</strong> analysis.Cross Section [pb]101pp→~g~g ats=1.96 GeVµ = µ = M(~g)R FM(~q)=500 GeV/c2Cross Section [pb]210101pp→ b ~ 1 b~ 1 ats=1.96 GeVµ = µ = M(b ~ )R F 11010-1-2PROSPINO NLO (CTEQ6M)PROSPINO LO (CTEQ6L1)1010-1-2PROSPINO NLO (CTEQ6M)PROSPINO LO (CTEQ6L1)200 250 300 350 4002M(~g) [GeV/c]100 150 200 250 3002M(b ~ ) [GeV/c]1Figure 2.9: LO and NLO cross sections of glu<strong>in</strong>o-pair production (left), and sbottom-pair production (right) at<strong>the</strong> Tevatron Run II as predicted by PROSPINO as a function of <strong>the</strong>ir masses. A mass of 500 GeV/c 2 has beenassumed, <strong>for</strong> <strong>the</strong> squarks of <strong>the</strong> first two families, <strong>in</strong> <strong>the</strong> glu<strong>in</strong>o-pair production calculation.We also have studied <strong>the</strong> dependence of <strong>the</strong> acceptance with <strong>the</strong> mass of <strong>the</strong> squarks, us<strong>in</strong>gsamples generated with different values of that parameter. It should be remarked that <strong>the</strong> assumedmasses <strong>for</strong> <strong>the</strong> squarks of <strong>the</strong> first two families are degenerated. The result of this studyis shown <strong>in</strong> figure 2.10 where we observe that such a dependence is really marg<strong>in</strong>al. This implythat <strong>the</strong> analysis may be per<strong>for</strong>med <strong>in</strong>dependently of <strong>the</strong> assumed mass of <strong>the</strong> squarks. However,due to <strong>the</strong> large dependence of <strong>the</strong> glu<strong>in</strong>o-pair production cross section on this parameter,
Chapter 2. Theory Introduction 31<strong>the</strong> <strong>in</strong>terpretation of <strong>the</strong> f<strong>in</strong>al result can only be done with <strong>the</strong> assumption of a specific value ofthat mass, be<strong>in</strong>g that 500 GeV/c 2 , as motivated above.Acceptance0.70.60.5Acceptance~M( b) = 250 GeV/c2M(χ ∼ ) = 60 GeV/c20.40.3~M( q) = 1000 GeV/c~2M( q) = 500 GeV/c20.20.10260 280 300 320 340 360 380 4002Glu<strong>in</strong>o Mass (GeV/c )Figure 2.10: Acceptance efficiency as a function of <strong>the</strong> glu<strong>in</strong>o mass <strong>for</strong> two different assumptions of <strong>the</strong> squarkmass <strong>for</strong> fixed values of <strong>the</strong> o<strong>the</strong>r parameters.2.3.2 Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>oDue to <strong>the</strong> large mass of <strong>the</strong> top quark, <strong>the</strong> mass splitt<strong>in</strong>g between <strong>the</strong> two stop quarks states(˜t 1 , ˜t 2 ) may be large, allow<strong>in</strong>g ˜t 1 to likely be <strong>the</strong> lightest squark, and possibly even lighter than<strong>the</strong> top quark:m 2˜t 1,2= 1 2 [m2˜t L+ m 2˜t R±√(m 2˜t L− m 2˜t R) 2 + 4m 2 t(A t − µcotβ) 2 ] (2.62)Assum<strong>in</strong>g R-parity conservation, scalar top quarks are pair produced, as is shown <strong>in</strong> figure2.11, and <strong>the</strong> Lightest Supersymetric Particle (LSP) must be stable. If it is colorless andneutral, <strong>the</strong>n it will escape from <strong>the</strong> detector undetected yield<strong>in</strong>g large miss<strong>in</strong>g transverse energy( / E T ).This scenario is accessible <strong>in</strong> <strong>the</strong> range m˜t 1< m b + m˜χ + and m˜t 1< m W + m b + m˜χ 0 <strong>in</strong>which <strong>the</strong> dom<strong>in</strong>ant ˜t 1 decay mode is <strong>the</strong> flavor chang<strong>in</strong>g process ˜t 1 → c˜χ 0 which is typicallyassumed to occur with 100% branch<strong>in</strong>g fraction, as shown <strong>in</strong> figure 2.12. The ˜t 1 → t˜χ 0 decay
32 2.3. <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong>g~tq~tg~- tg~- tq-~- tg~tFigure 2.11: Lead<strong>in</strong>g order stop pair production diagrams at <strong>the</strong> Tevatron center of mass energies.is k<strong>in</strong>ematically <strong>for</strong>bidden over <strong>the</strong> ˜t 1 mass range currently accessible at Tevatron, and <strong>the</strong> treelevel four-body decays ˜t 1 → bff ′˜χ 0 is negligible. In this particular case <strong>the</strong> experimentalsignature consists of two c jets and / E T from <strong>the</strong> undetected ˜χ 0 .~tb~χ +Wc~χ 0Figure 2.12: Stop decay <strong>in</strong>to charm and neutral<strong>in</strong>o.In order to get <strong>the</strong> predictions <strong>for</strong> our signal, similarly to <strong>the</strong> glu<strong>in</strong>o-sbottom analysis, we use<strong>the</strong> program PROSPINO to compute <strong>the</strong> total production cross section and PYTHIA to estimate<strong>the</strong> event acceptance <strong>in</strong> <strong>the</strong> detector and <strong>in</strong> <strong>the</strong> application of our selection cuts.We compute <strong>the</strong> cross section of <strong>the</strong> stop-pair production process <strong>for</strong> <strong>the</strong> range of masses weare <strong>in</strong>terested <strong>in</strong>. This is shown <strong>in</strong> figure 2.13 us<strong>in</strong>g <strong>the</strong> CTEQ6M set of PDFs. The cross sectionfalls very rapidly when <strong>in</strong>creas<strong>in</strong>g <strong>the</strong> mass of <strong>the</strong> stop, but <strong>the</strong> absolute values are reasonable<strong>for</strong> <strong>the</strong> analysis to reach unexcluded regions of <strong>the</strong> parameter space.For <strong>the</strong> NLO cross sections of stop pairs, <strong>the</strong> calculation does not depend on <strong>the</strong> neutral<strong>in</strong>omass, and <strong>the</strong> dependence on masses of o<strong>the</strong>r sparticles is very small, s<strong>in</strong>ce it appears as part of<strong>the</strong> NLO corrections.
Chapter 2. Theory Introduction 33Cross Section [pb]210101~ ~pp→ t 1t 1ats=1.96 GeV~µ = µ = M( t 1)R F1010-1-2PROSPINO NLO (CTEQ6M)PROSPINO LO (CTEQ6L1)100 150 200 250 300~2M(t 1 ) [GeV/c]Figure 2.13: LO and NLO cross sections of stop-pair production at <strong>the</strong> Tevatron Run II as computed us<strong>in</strong>gPROSPINO as a function of <strong>the</strong> stop mass.
34 2.3. <strong>Third</strong> <strong>Generation</strong> <strong>Squarks</strong>
Chapter 3Experimental SetupThe Fermilab Tevatron is <strong>the</strong> highest energy hadron collider <strong>in</strong> operation, until <strong>the</strong> completion of<strong>the</strong> Large Hadron Collider (LHC) at CERN. After a major upgrade, <strong>the</strong> Tevatron Run II providesproton-antiproton (p¯p) collisions with a center of mass energy of 1.96 TeV and a bunch cross<strong>in</strong>gperiod of 396 ns. Two detectors were designed to extract <strong>the</strong> full scientific potential of <strong>the</strong>secollisions: CDF, <strong>the</strong> Collider Detector at Fermilab and DØ . Both of <strong>the</strong>m follow <strong>the</strong> usualstructure of high energy physics experiments with a tracker, <strong>in</strong>side a solenoidal magnetic field,a calorimeter and a muon spectrometer, arranged <strong>in</strong> concentrical layers and two plugs.The results presented <strong>in</strong> <strong>the</strong> <strong>the</strong>sis make use of approximately 2.6 fb −1 amount good-qualityof data collected by CDF. A brief description of <strong>the</strong> accelerator cha<strong>in</strong> and <strong>the</strong> detector is presented<strong>in</strong> <strong>the</strong> follow<strong>in</strong>g sections.3.1 The Tevatron ColliderThe Tevatron Collider [66] located at <strong>the</strong> Fermi National Accelerator Laboratory (Fermilab)<strong>in</strong> Batavia (Ill<strong>in</strong>ois, USA) is a proton-antiproton (p¯p) collider with a center-of-mass energy of1.96 TeV. As shown <strong>in</strong> figure 3.1, this complex has five major accelerators and storage r<strong>in</strong>gsused <strong>in</strong> successive steps, as is expla<strong>in</strong>ed <strong>in</strong> detail below, to produce, store, and accelerate <strong>the</strong>particles up to 980 GeV.The acceleration cycle starts with <strong>the</strong> production of protons from ionized hydrogen atomsH − , which are accelerated to 750 KeV by a Cockroft-Walton electrostatic accelerator. Preacceleratedhydrogen ions are <strong>the</strong>n <strong>in</strong>jected <strong>in</strong>to <strong>the</strong> L<strong>in</strong>ac where <strong>the</strong>y are accelerated up to 400MeV by pass<strong>in</strong>g through a 150 m long cha<strong>in</strong> of radio-frequency (RF) accelerator cavities. A35
36 3.1. The Tevatron Collidercarbon foil strips off <strong>the</strong> electrons of <strong>the</strong> H − ions, thus produc<strong>in</strong>g protons. Inside <strong>the</strong> Booster<strong>the</strong> protons are merged <strong>in</strong>to bunches and accelerated up to an energy of 8 GeV prior to enter<strong>in</strong>g<strong>the</strong> Ma<strong>in</strong> Injector. In <strong>the</strong> Ma<strong>in</strong> Injector, a synchrotron with a circumference of 3 km, <strong>the</strong>proton bunches are accelerated fur<strong>the</strong>r to an energy of 150 GeV and coalesced 1 toge<strong>the</strong>r be<strong>for</strong>e<strong>in</strong>jection <strong>in</strong>to <strong>the</strong> Tevatron.Figure 3.1: The Tevatron Collider Cha<strong>in</strong> at Fermilab.The production of <strong>the</strong> antiproton beam is significantly more complicated. The cycle startswith extract<strong>in</strong>g a 120 GeV proton beam from <strong>the</strong> Ma<strong>in</strong> Injector onto a sta<strong>in</strong>less steel target.This process produces a variety of different particles, among which antiprotons appear 2 . Theparticles come off <strong>the</strong> target at many different angles and <strong>the</strong>y are focused <strong>in</strong>to a beam l<strong>in</strong>e witha Lithium lens. In order to select only <strong>the</strong> antiprotons, <strong>the</strong> beam is sent through a pulsed magnetwhich acts as a charge-mass spectrometer. The produced antiprotons are <strong>the</strong>n <strong>in</strong>jected <strong>in</strong>to <strong>the</strong>Debuncher, an 8 GeV synchrotron, which reduces <strong>the</strong> spread <strong>in</strong> <strong>the</strong> energy distribution of <strong>the</strong>antiprotons. After that, <strong>the</strong> antiproton beam is directed <strong>in</strong>to <strong>the</strong> Accumulator, a storage r<strong>in</strong>g <strong>in</strong><strong>the</strong> Antiproton Source, where <strong>the</strong> antiprotons are stored at an energy of 8 GeV and stacked to10 12 particles per bunch. The antiproton bunches are <strong>the</strong>n <strong>in</strong>jected <strong>in</strong>to <strong>the</strong> Ma<strong>in</strong> Injector andaccelerated to 150 GeV.1 Coalesc<strong>in</strong>g is <strong>the</strong> process of merg<strong>in</strong>g proton bunches <strong>in</strong>to one dense, high density beam2 The production rate, <strong>for</strong> 8 GeV antiprotons, is about 18 ¯p per 10 6 p
Chapter 3. Experimental Setup 37F<strong>in</strong>ally, 36 proton and antiproton bunches are <strong>in</strong>serted <strong>in</strong>to <strong>the</strong> Tevatron, a double accelerationr<strong>in</strong>g of 1 km of radius, where <strong>the</strong>ir energy is <strong>in</strong>creased up to 980 GeV. Proton and antiprotonbunches circulate around <strong>the</strong> Tevatron <strong>in</strong> opposite directions guided by superconduct<strong>in</strong>g magnetsand where <strong>the</strong>ir orbits cross at <strong>the</strong> two collision po<strong>in</strong>ts to produce <strong>the</strong> p¯p <strong>in</strong>teraction thatare observed. These <strong>in</strong>teractions are observed by <strong>the</strong> CDF and DØ detectors.In <strong>the</strong> absence of a cross<strong>in</strong>g angle or position offset, <strong>the</strong> lum<strong>in</strong>osity at <strong>the</strong> <strong>in</strong>teraction po<strong>in</strong>tsis given by <strong>the</strong> expression:L = f bcN b N p N¯p2π(σ 2 p + σ2¯p) F (σlβ ∗ ), (3.1)where f bc is <strong>the</strong> revolution frequency, N b is <strong>the</strong> number of bunches, N p(¯p) is <strong>the</strong> number of protons(antiprotons) per bunch, and σ p(¯p) is <strong>the</strong> transverse and longitud<strong>in</strong>al rms proton (antiproton)beam size at <strong>the</strong> <strong>in</strong>teraction po<strong>in</strong>t. F is a <strong>for</strong>m factor with a complicated dependence on <strong>the</strong> socalledbeta function, β ∗ , and <strong>the</strong> bunch length, σ l . The beta function is a measure of <strong>the</strong> beamwidth, and it is proportional to <strong>the</strong> beam’s x and y extent <strong>in</strong> phase space. Table 3.1 shows <strong>the</strong>design Run II accelerator parameters [67].ParameterRun IInumber of bunches (N b ) 36revolution frequency [MHz] (f bc ) 1.7bunch rms [m] σ l 0.37bunch spac<strong>in</strong>g [ns] 396protons/bunch (N p ) 2.7 × 10 11antiprotons/bunch (N¯p ) 3.0 × 10 10total antiprotons 1.1 × 10 12β ∗ [cm] 35Table 3.1: Accelerator parameters <strong>for</strong> Run II configuration.Figure 3.2 and figure 3.3 show, respectively, <strong>the</strong> evolution <strong>in</strong> <strong>the</strong> <strong>in</strong>tegrated lum<strong>in</strong>osity, def<strong>in</strong>edas L = ∫ L dt, and <strong>the</strong> <strong>in</strong>stantaneous lum<strong>in</strong>osity delivered by Tevatron s<strong>in</strong>ce <strong>the</strong>mach<strong>in</strong>e was turned on up to July 2009. The progressive <strong>in</strong>crease <strong>in</strong> <strong>the</strong> <strong>in</strong>tegrated lum<strong>in</strong>osityand <strong>the</strong> cont<strong>in</strong>uous records <strong>in</strong> <strong>the</strong> <strong>in</strong>stantaneous lum<strong>in</strong>osity 3 prove <strong>the</strong> good per<strong>for</strong>mance of <strong>the</strong>accelerator.3 As of July 2009, <strong>the</strong> record <strong>in</strong> <strong>the</strong> <strong>in</strong>stantaneous lum<strong>in</strong>osity was close to 3.5 × 10 32 cm −2 s −1 .
38 3.1. The Tevatron ColliderFigure 3.2: Tevatron Collider Run II Integrated Lum<strong>in</strong>osity. The vertical green bar shows each week’s totallum<strong>in</strong>osity as measured <strong>in</strong> pb −1 . The diamond connected l<strong>in</strong>e displays <strong>the</strong> <strong>in</strong>tegrated lum<strong>in</strong>osity.Figure 3.3: Tevatron Collider Run II Peak Lum<strong>in</strong>osity. The blue squares show <strong>the</strong> peak lum<strong>in</strong>osity at <strong>the</strong>beg<strong>in</strong>n<strong>in</strong>g of each store and <strong>the</strong> red triangle displays a po<strong>in</strong>t represent<strong>in</strong>g <strong>the</strong> last 20 peak values averaged toge<strong>the</strong>r.
Chapter 3. Experimental Setup 393.2 CDF Run II DetectorThe CDF Run II detector [68], <strong>in</strong> operation s<strong>in</strong>ce 2001, is an azimuthally and <strong>for</strong>ward-backwardsymmetric apparatus designed to study p¯p collisions at <strong>the</strong> Tevatron. It is a general purpose,cyl<strong>in</strong>drical-shaped detector which comb<strong>in</strong>es:• A track<strong>in</strong>g system, that provides a measurement of <strong>the</strong> charged particle momenta, eventz vertex position and allows <strong>the</strong> reconstruction of secondary vertices.• A non-compensated calorimeter system, with <strong>the</strong> purpose of measur<strong>in</strong>g <strong>the</strong> energy ofcharged and neutral particles produced <strong>in</strong> <strong>the</strong> <strong>in</strong>teraction.• Drift chambers and sc<strong>in</strong>tillators <strong>for</strong> muon detection.Figure 3.4: Isometric view of <strong>the</strong> CDF Run II detector with human-size references. Only half of <strong>the</strong> detector isshown.The detector is shown <strong>in</strong> figure 3.4 and figure 3.5. CDF uses a cyl<strong>in</strong>drical coord<strong>in</strong>ate systemwhere <strong>the</strong> positive z-axis lies along <strong>the</strong> direction of <strong>the</strong> <strong>in</strong>cident proton beam, θ and φ are <strong>the</strong>polar and azimuthal angles, respectively, and pseudorapidity is η = − ln(tan( θ)). The p 2 T andE T are <strong>the</strong> components of momentum and energy, <strong>in</strong> <strong>the</strong> transverse plane. The miss<strong>in</strong>g E T( ⃗ / ET ) is def<strong>in</strong>ed by ⃗ / ET = − ∑ i Ei Tˆn i, i = calorimeter tower number, where ˆn i is a unit vector/perpendicular to <strong>the</strong> beam axis and po<strong>in</strong>t<strong>in</strong>g at <strong>the</strong> i th calorimeter tower. ⃗E T is corrected <strong>for</strong>high-energy muons and jet energy. A description of all <strong>the</strong> systems start<strong>in</strong>g from <strong>the</strong> devicesclosest to <strong>the</strong> beam and mov<strong>in</strong>g outward is presented <strong>in</strong> <strong>the</strong> next sections, where <strong>the</strong> detectorsmost relevant <strong>in</strong> <strong>the</strong> analysis are expla<strong>in</strong>ed <strong>in</strong> more detail.
40 3.2. CDF Run II DetectorFigure 3.5: r × η side view of <strong>the</strong> CDF Run II detector.3.2.1 Track<strong>in</strong>g and Time of Flight SystemsThe track<strong>in</strong>g and time of flight systems are conta<strong>in</strong>ed <strong>in</strong> a superconduct<strong>in</strong>g solenoid, 1.5 m <strong>in</strong>radius and 4.8 m <strong>in</strong> length, which generates a 1.4 T magnetic field parallel to <strong>the</strong> beam axis.The part of <strong>the</strong> track<strong>in</strong>g system closest to <strong>the</strong> beam pipe is a silicon microstrip detector [69],which is radiation-hard due its proximity to <strong>the</strong> beam. It extends from a radius of 1.2 cm, <strong>the</strong>beam pipe, to 28 cm, cover<strong>in</strong>g |η| < 2 and has eight layers <strong>in</strong> a barrel geometry. The <strong>in</strong>nermostlayer is a s<strong>in</strong>gle-sided silicon microstrip detector called Layer 00 (L00) which provides a r × φposition measurement. The first five layers after <strong>the</strong> L00 constitute <strong>the</strong> Silicon Vertex Detector(SVXII) and <strong>the</strong> two outer layers comprise <strong>the</strong> Intermediate Silicon Layers system (ISL).These seven layers are made of double-sided silicon sensors, giv<strong>in</strong>g r × φ and z position <strong>in</strong><strong>for</strong>mation.The best position resolution achieved is 9 µm <strong>in</strong> SVXII and <strong>the</strong> impact parameterresolution, <strong>in</strong>clud<strong>in</strong>g L00, reaches 40 µm <strong>for</strong> tracks with p T > 3 GeV/c.Surround<strong>in</strong>g <strong>the</strong> silicon detector is <strong>the</strong> Central Outer Tracker (COT) [70], <strong>the</strong> anchor of<strong>the</strong> CDF Run II track<strong>in</strong>g system. It is a 3.1 m long cyl<strong>in</strong>drical drift chamber that covers <strong>the</strong>radial range from 40 to 137 cm and full coverage up to |η| ∼ 1. The COT conta<strong>in</strong>s 96 sensewire layers, which are radially grouped <strong>in</strong>to eight “superlayers”, as <strong>in</strong>ferred from <strong>the</strong> end plate
Chapter 3. Experimental Setup 41section shown <strong>in</strong> figure 3.6.Figure 3.6: Layout of wire planes on a COT endplate.Each superlayer is divided <strong>in</strong> φ <strong>in</strong>to “supercells”, and each supercell has 12 sense wiresand a maximum drift distance that is approximately <strong>the</strong> same <strong>for</strong> all superlayers. There<strong>for</strong>e,<strong>the</strong> number of supercells <strong>in</strong> a given superlayer scales approximately with <strong>the</strong> radius of <strong>the</strong>superlayer. The entire COT conta<strong>in</strong>s 30,240 sense wires. Approximately half <strong>the</strong> wires runalong <strong>the</strong> z direction (“axial”). The o<strong>the</strong>r half are strung at a small angle (±2 ◦ ) with respectto <strong>the</strong> z direction (“stereo”). The comb<strong>in</strong>ation of <strong>the</strong> axial and stereo <strong>in</strong><strong>for</strong>mation allows <strong>the</strong>measurement <strong>the</strong> z positions. Particles orig<strong>in</strong>ated from <strong>the</strong> <strong>in</strong>teraction po<strong>in</strong>t, hav<strong>in</strong>g |η| < 1,pass through all 8 superlayers of <strong>the</strong> COT.The supercell layout, shown <strong>in</strong> figure 3.7 <strong>for</strong> superlayer 2, consists of a wire plane conta<strong>in</strong><strong>in</strong>gsense and potential wires, <strong>for</strong> field shap<strong>in</strong>g and a field (or cathode) sheet on ei<strong>the</strong>r side.Both <strong>the</strong> sense and potential wires are 40 µm diameter gold plated tungsten. The field sheet is6.35 µm thick Mylar with vapor-deposited gold on both sides. Each field sheet is shared with<strong>the</strong> neighbor<strong>in</strong>g supercell.
42 3.2. CDF Run II DetectorPotential wiresSense wiresShaper wiresGold on Mylar (Field Panel)R52 54 56 58 60 62 64 R (cm)66SL2Figure 3.7: Layout of wires <strong>in</strong> a COT supercell.The COT is filled with an Argon-Ethane gas mixture and Isopropyl alcohol (49.5 : 49.5 : 1).The mixture is chosen to have a constant drift velocity, approximately 50 µm/ns across <strong>the</strong> cellwidth and <strong>the</strong> small content of isopropyl alcohol is <strong>in</strong>tended to reduce <strong>the</strong> ag<strong>in</strong>g and build up ofdebris on <strong>the</strong> wires. When a charged particle passes through, <strong>the</strong> gas is ionized. Electrons drifttoward <strong>the</strong> sense wires. Due to <strong>the</strong> magnetic field that <strong>the</strong> COT is immersed <strong>in</strong>, electrons driftat a Lorentz angle of 35 ◦ . The supercell is tilted by 35 ◦ with respect to <strong>the</strong> radial direction tocompensate <strong>for</strong> this effect. The momentum resolution of <strong>the</strong> tracks <strong>in</strong> <strong>the</strong> COT chamber dependson <strong>the</strong> p T and is measured to be approximately 0.15%, with correspond<strong>in</strong>g hit resolution ofabout 140 µm [71]. In addition to <strong>the</strong> measurement of <strong>the</strong> charged particle momenta, <strong>the</strong> COTis used to identify particles, with p T > 2 GeV, based on dE/dx measurements.Just outside <strong>the</strong> track<strong>in</strong>g system, CDF II has a Time of Flight (TOF) detector [72, 73, 74].It consist on a barrel of sc<strong>in</strong>tillator, almost 3 m long, located at 140 cm from <strong>the</strong> beam l<strong>in</strong>ewith a total of 216 bars, each cover<strong>in</strong>g 1.7 o <strong>in</strong> φ and pseudorapidity range |η| < 1. Particleidentification is achieved by measur<strong>in</strong>g <strong>the</strong> time of arrival of a particle at <strong>the</strong> sc<strong>in</strong>tillators withrespect to <strong>the</strong> collision time. Thus, comb<strong>in</strong><strong>in</strong>g <strong>the</strong> measured time-of-flight and <strong>the</strong> momentumand path length, measured by <strong>the</strong> track<strong>in</strong>g system, <strong>the</strong> mass of <strong>the</strong> particle can <strong>the</strong>n determ<strong>in</strong>ed.The resolution <strong>in</strong> <strong>the</strong> time-of-flight measurement has achieved ≈ 100 ps and it provides at leasttwo standard deviation separation between K ± and π ± <strong>for</strong> momenta p < 1.6 GeV/c .As a summary, figure 3.8 illustrates <strong>the</strong> Track<strong>in</strong>g and Time of Flight systems.
Chapter 3. Experimental Setup 43Figure 3.8: The CDF II tracker layout show<strong>in</strong>g <strong>the</strong> different subdetector systems.3.2.2 Calorimeter SystemThe calorimeter system is located surround<strong>in</strong>g <strong>the</strong> CDF track<strong>in</strong>g volume, outside of <strong>the</strong> solenoidcoil. The different calorimeters that compose <strong>the</strong> system are sc<strong>in</strong>tillator-based detectors, segmented<strong>in</strong> projective towers (or wedges), <strong>in</strong> η × φ space, that po<strong>in</strong>t to <strong>the</strong> <strong>in</strong>teraction region.The total coverage of <strong>the</strong> system is 2π <strong>in</strong> φ and about |η| < 3.64 units <strong>in</strong> pseudorapidity.The calorimeter system is divided <strong>in</strong> two regions: central and plug. The central calorimetercovers <strong>the</strong> region |η| < 1.1 and is split <strong>in</strong>to two halves at |η| = 0. It conceived as a hybrid systemof sampl<strong>in</strong>g scitilators and strip wire proportional chambers. The <strong>for</strong>ward plug calorimeterscover <strong>the</strong> angular range correspond<strong>in</strong>g to 1.1 < |η| < 3.64, as it is shown <strong>in</strong> figure 3.9. Due tothis structure, two “gap” regions are found at |η| = 0 and |η| ∼ 1.1.3.2.3 Central CalorimetersThe central calorimeters consist of 478 towers, each one is 15 o <strong>in</strong> azimuth times approximately0.11 <strong>in</strong> pseudorapidity. Each wedge consists of an electromagnetic component backed by ahadronic section. In <strong>the</strong> central electromagnetic calorimeter (CEM) [75], <strong>the</strong> sc<strong>in</strong>tillators are
44 3.2. CDF Run II DetectorFigure 3.9: Elevation view of 1/4 of <strong>the</strong> CDF detector shower<strong>in</strong>g <strong>the</strong> components of <strong>the</strong> CDF calorimeter: CEM,CHA, WHA, PEM and PHA.<strong>in</strong>terleaved with lead layers. The total material has a depth of 18 radiation lengths 4 (X 0 ). Thecentral hadronic section (CHA) [76] has alternative layers of steel and sc<strong>in</strong>tillator and is 4.7 <strong>in</strong>teractionlength deep 5 (λ 0 ). The endwall hadron calorimeter (WHA), with similar constructionto CHA, is located with half of <strong>the</strong> detector beh<strong>in</strong>d <strong>the</strong> CEM/CHA and <strong>the</strong> o<strong>the</strong>r half beh<strong>in</strong>d <strong>the</strong>plug calorimeter. The function of <strong>the</strong> WHA detector is to provide a hadronic coverage <strong>in</strong> <strong>the</strong>region 0.9 < |η| < 1.3. In <strong>the</strong> central calorimeter <strong>the</strong> light from <strong>the</strong> sc<strong>in</strong>tillator is redirected bytwo wavelength shift<strong>in</strong>g (WLS) fibers, which are located on <strong>the</strong> φ surface between wedges cover<strong>in</strong>g<strong>the</strong> same pseudorapidity region, up through <strong>the</strong> light-guides <strong>in</strong>to two photo-tubes (PMTs)per tower.The energy resolution <strong>for</strong> each section was measured <strong>in</strong> <strong>the</strong> testbeam and, <strong>for</strong> a perpendicular<strong>in</strong>cident beam, and it is parameterized as:(σ/E) 2 = (σ 1 / √ E) 2 + (σ 2 ) 2 , (3.2)4 The radiation length X 0 describes <strong>the</strong> characteristic amount of matter transversed, <strong>for</strong> high-energy electronsto lose all but 1/e of its energy by bremsstrahlung, which is equivalent to 7 9of <strong>the</strong> length of <strong>the</strong> mean free path<strong>for</strong> pair e + e − production of high-energy photons. The average energy loss due to bremsstrahlung <strong>for</strong> an electronof energy E is related to <strong>the</strong> radiation length by ( )dEdx= − E brems X 0and <strong>the</strong> probability <strong>for</strong> an electron pair to becreated by a high-energy photon is 7 9 X 0.5 An <strong>in</strong>teraction length is <strong>the</strong> average distance a particle will travel be<strong>for</strong>e <strong>in</strong>teract<strong>in</strong>g with a nucleus: λ = AρσN A,where A is <strong>the</strong> atomic weight, ρ is <strong>the</strong> material density, σ is <strong>the</strong> cross section and N A is <strong>the</strong> Avogadro’s number.
Chapter 3. Experimental Setup 45where <strong>the</strong> first term comes from sampl<strong>in</strong>g fluctuations and <strong>the</strong> photostatistics of PMTs, and <strong>the</strong>second term comes from <strong>the</strong> non-uni<strong>for</strong>m response of <strong>the</strong> calorimeter. In <strong>the</strong> CEM, <strong>the</strong> energyresolution <strong>for</strong> high energy electrons and photons is σ(E T )E T= 13.5% √ ET⊕ 1.5%, where E T =Es<strong>in</strong>θ,be<strong>in</strong>g θ <strong>the</strong> beam <strong>in</strong>cident angle. Charge pions were used to obta<strong>in</strong> <strong>the</strong> energy resolution <strong>in</strong> <strong>the</strong>CHA and WHA detectors that are σ(E T )E T= 50% √ ET⊕ 3% and σ(E T )E T= 75% √ ET⊕ 4%, respectively.3.2.4 Plug CalorimetersOne of <strong>the</strong> major upgrades <strong>for</strong> <strong>the</strong> Run II was <strong>the</strong> plug calorimeter [77]. The new plug calorimetersare built with <strong>the</strong> same technology as <strong>the</strong> central components and replace <strong>the</strong> previous Run Igas calorimeters <strong>in</strong> <strong>the</strong> <strong>for</strong>ward region. The η ×φ segmentation depends on <strong>the</strong> tower pseudorapiditycoverage. For towers <strong>in</strong> <strong>the</strong> region |η| < 2.1, <strong>the</strong> segmentation is 7.5 o <strong>in</strong> φ and from 0.1to 0.16 <strong>in</strong> <strong>the</strong> pseudorapidity direction. For more <strong>for</strong>ward wedges, <strong>the</strong> segmentation changes to15 o <strong>in</strong> φ and about 0.2 to 0.6 <strong>in</strong> η.As <strong>in</strong> <strong>the</strong> central calorimeters, each wedge consists of an electromagnetic (PEM) and ahadronic section (PHA). The PEM, with 23 layers composed of lead and sc<strong>in</strong>tillator, has a totalthickness of about 21 X 0 . The PHA is a steel/sc<strong>in</strong>tillator device with a depth of about 7 λ 0 . Inboth sections <strong>the</strong> sc<strong>in</strong>tillator tiles are read out by WLS fibers embedded <strong>in</strong> <strong>the</strong> sc<strong>in</strong>tillator. TheWLS fibers carry <strong>the</strong> light out to PMTs tubes located on <strong>the</strong> back plane of each endplug. Unlike<strong>the</strong> central calorimeters, each tower is only read out by one PMT.Testbeam measurements determ<strong>in</strong>ed that <strong>the</strong> energy resolution of <strong>the</strong> PEM <strong>for</strong> electrons andphotons is σ E = 16% √E⊕ 1%. The PHA energy resolution is σ E = 80% √E⊕ 5% <strong>for</strong> charged pionsthat do not <strong>in</strong>teract <strong>in</strong> <strong>the</strong> electromagnetic component. Table 3.2 summarizes <strong>the</strong> calorimetersubsystems and <strong>the</strong>ir characteristics.Calorimeter Coverage Thickness Energy resolution (E <strong>in</strong> GeV)CEM |η| < 1.1 18 X 013.5%√ ET⊕ 2%CHA |η| < 0.9 4.7 λ 050%√ ET⊕ 3%WHA 0.9 < |η| < 1.3 4.7 λ 075%√ ET⊕ 4%PEM 1.1 < |η| < 3.6 21 X 0 , 1 λ 016% √E⊕ 1%PHA 1.2 < |η| < 3.6 7 λ 080% √E⊕ 5%Table 3.2: CDF II Calorimeter subsystems and characteristics. The energy resolution <strong>for</strong> <strong>the</strong> EM calorimeter isgiven <strong>for</strong> a s<strong>in</strong>gle <strong>in</strong>cident electron and that <strong>for</strong> <strong>the</strong> hadronic calorimeter <strong>for</strong> a s<strong>in</strong>gle <strong>in</strong>cident pion.
46 3.2. CDF Run II DetectorThe central and <strong>for</strong>ward parts of <strong>the</strong> calorimeter have <strong>the</strong>ir own shower profile detectors:shower maximum and preshower detectors. The Central Shower Maximum (CES) and <strong>the</strong> PlugShower Maximum (PES) are positioned at about 6 X 0 , while <strong>the</strong> Central Preradiator (CPR) and<strong>the</strong> Plug Preradiator (PPR) are located at <strong>the</strong> <strong>in</strong>ner face of <strong>the</strong> calorimeters. These detectorshelp on particle identification, separat<strong>in</strong>g e ± , γs and π 0 s.3.2.5 Muons SystemThe muon system, which consists of sets of drift chambers and sc<strong>in</strong>tillators, is <strong>in</strong>stalled beyond<strong>the</strong> calorimetry system as <strong>the</strong> radially outermost component of CDF Run II detector (r∼3.5 m).The muon system [78] is divided <strong>in</strong>to different subsystems: <strong>the</strong> Central Muon Detector, CMU,<strong>the</strong> Central Muon Upgrade Detector, CMP, <strong>the</strong> Central Muon Extension Detector, CMX, and<strong>the</strong> Intermediate Muon Detector, IMU.The coverage of <strong>the</strong> muon systems is almost complete <strong>in</strong> phi, except some gaps, and spans<strong>in</strong> polar angle up to |η| ≈ 1.5, figure 3.10. Attached to <strong>the</strong> calorimeter modules, <strong>the</strong> CMUconsists of a stack of 4 layers of drift chambers. The different layers are slightly shifted <strong>in</strong> phi<strong>for</strong> better per<strong>for</strong>mance. These chambers are s<strong>in</strong>gle-wired and <strong>the</strong> read-out is equipped with aTDC and an ADC at each end of <strong>the</strong> wire. The φ-position is <strong>the</strong>n calculated from <strong>the</strong> drift time,measured with <strong>the</strong> TDC, while <strong>the</strong> hit z-position is found through harge division with <strong>the</strong> ADC.The CMP <strong>for</strong>ms a box around <strong>the</strong> detector of stacked drift chambers. A layer of 60 cmof steel, partially used <strong>for</strong> <strong>the</strong> magnetic field return, provides <strong>the</strong> needed shield<strong>in</strong>g to absorbparticles, o<strong>the</strong>r than muons, leak<strong>in</strong>g <strong>the</strong> calorimeter. This system overlaps with <strong>the</strong> CMU, andcovers <strong>the</strong> central part.The CMX detector, located <strong>for</strong>ward than CMU and CMP, consists of stacked cells of drifttubes con<strong>for</strong>m<strong>in</strong>g a conical section. The chambers are stacked at a small angle, allow<strong>in</strong>g <strong>for</strong>polar angle measurement. Given <strong>the</strong> space constra<strong>in</strong>ts <strong>in</strong> <strong>the</strong> collision hall, <strong>the</strong> coverage is notcomplete <strong>in</strong> φ.The ma<strong>in</strong> component of <strong>the</strong> IMU are <strong>the</strong> Barrel Chambers (BMU). This detector is shapedas two contiguous barrels of drift chambers located on <strong>the</strong> outer radius of <strong>the</strong> toroids. Thesechambers expand <strong>the</strong> muon coverage of CDF up to |η| ≈ 1.5, but only cover <strong>the</strong> upper 270 ◦ <strong>in</strong>azimuth.Sets of sc<strong>in</strong>tillators were also <strong>in</strong>stalled <strong>for</strong> trigger confirmation and spurious signal rejection.The central muon sc<strong>in</strong>tillator upgrade, CSP, are counters <strong>in</strong>stalled on <strong>the</strong> outer surface of <strong>the</strong>
00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000Chapter 3. Experimental Setup 47CMP chambers. Two layers of sc<strong>in</strong>tillators are mounted on <strong>the</strong> <strong>in</strong>ternal and external sides of <strong>the</strong>CMX, <strong>the</strong> so-called central muon extension sc<strong>in</strong>tillator, CSX. F<strong>in</strong>ally, <strong>the</strong> IMU <strong>in</strong>corporates twosc<strong>in</strong>tillator systems: <strong>the</strong> barrel sc<strong>in</strong>tillator upgrade, BSU, and <strong>the</strong> Toroid Sc<strong>in</strong>tillator Upgrade,TSU. The BSU detector is made of rectangular sc<strong>in</strong>tillators mounted on <strong>the</strong> outside of <strong>the</strong> BMUchambers and with <strong>the</strong> same azimuthal coverage. The TSU detector is made of trapezoidalsc<strong>in</strong>tillators mounted on <strong>the</strong> <strong>in</strong>ner face of <strong>the</strong> toroid and cover<strong>in</strong>g 2π <strong>in</strong> azimuth.- CMX - CMP - CMU000000000000000000000000000000- IMU0000000000000000000000000000000000000-10 10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000φηFigure 3.10: η-φ coverage of <strong>the</strong> different muon subsystems: central muon detector (CMU), central muonupgrade detector (CMP), central muon extension (CMX), and <strong>the</strong> <strong>in</strong>termediate muon detector (IMU). The IMU<strong>in</strong>cludes <strong>the</strong> barrel chambers (BMU) and some sc<strong>in</strong>tillator detectors.3.3 Lum<strong>in</strong>osity MeasurementThe Cherenkov Lum<strong>in</strong>osity Counter (CLC) [79] was designed <strong>for</strong> <strong>the</strong> Tevatron Run II <strong>in</strong> orderto achieve a precision measurement of <strong>the</strong> <strong>in</strong>stantaneous lum<strong>in</strong>osity up to ≈ 4·10 32 cm −2 s −1and to cope with <strong>the</strong> 132 ns bunch-spac<strong>in</strong>g that was orig<strong>in</strong>ally envisioned.3.3.1 CLC detectorIn CDF, <strong>the</strong> beam lum<strong>in</strong>osity is determ<strong>in</strong>ed us<strong>in</strong>g gas Čerenkov counters located <strong>in</strong> <strong>the</strong> pseudorapidityregion 3.7 < |η| < 4.7, which measure <strong>the</strong> average number of <strong>in</strong>elastic <strong>in</strong>teraction
48 3.3. Lum<strong>in</strong>osity Measurementper bunch cross<strong>in</strong>g. Each module consists of 48 th<strong>in</strong>, gas-filled, Čerenkov counters. The countersare arranged around <strong>the</strong> beam pipe <strong>in</strong> three concentric layers, with 16 counters each, andpo<strong>in</strong>t<strong>in</strong>g to <strong>the</strong> center of <strong>the</strong> <strong>in</strong>teraction region. The cones <strong>in</strong> <strong>the</strong> two outer layers are about 180cm long and <strong>the</strong> <strong>in</strong>ner layer counters, closer to <strong>the</strong> beam pipe, have a length of 110 cm. TheČerenkov light is detected with photomultiplier tubes located at <strong>the</strong> end of <strong>the</strong> tubes, figure 3.11.Figure 3.11: Schematic draw<strong>in</strong>g of a cone of <strong>the</strong> Čerenkov lum<strong>in</strong>osity counters, CLC. An alum<strong>in</strong>um lightcollector directs <strong>the</strong> light reflected <strong>in</strong> <strong>the</strong> mylar cone to <strong>the</strong> photomultiplier, PMT, attached at <strong>the</strong> end of <strong>the</strong> tube.3.3.2 Measurement of <strong>the</strong> Lum<strong>in</strong>osityThe average number of primary <strong>in</strong>teractions, µ, is related to <strong>the</strong> <strong>in</strong>stantaneous lum<strong>in</strong>osity, L, by<strong>the</strong> expression:µ · f bc = σ tot · L , (3.3)where f bc is <strong>the</strong> bunch cross<strong>in</strong>gs frequency at Tevatron, on average 1.7 MHz <strong>for</strong> 36 × 36 bunchoperations, and σ tot is <strong>the</strong> total p¯p cross section.S<strong>in</strong>ce <strong>the</strong> CLC is not sensitive at all to <strong>the</strong> elastic component of <strong>the</strong> p¯p scatter<strong>in</strong>g, <strong>the</strong> equation3.3 can be rewritten us<strong>in</strong>g <strong>the</strong> <strong>in</strong>elastic cross section, σ <strong>in</strong> , asL = µ · f bcσ <strong>in</strong>, (3.4)where now µ is <strong>the</strong> average number of <strong>in</strong>elastic p¯p <strong>in</strong>teractions. The method used <strong>in</strong> CDF <strong>for</strong><strong>the</strong> lum<strong>in</strong>osity measurement is based on <strong>the</strong> count<strong>in</strong>g of empty cross<strong>in</strong>gs [80]. This methoddeterm<strong>in</strong>es µ by measur<strong>in</strong>g <strong>the</strong> first b<strong>in</strong> of <strong>the</strong> distribution which corresponds to <strong>the</strong> probabilityof hav<strong>in</strong>g zero <strong>in</strong>elastic <strong>in</strong>teractions, P 0 , through <strong>the</strong> relation:P 0 (µ) = e −µ , (3.5)
Chapter 3. Experimental Setup 49which is correct if <strong>the</strong> acceptance of <strong>the</strong> detector and its efficiency were 100%. Given <strong>the</strong>limited extent of this statement, <strong>the</strong>re are some selection criteria, α, to def<strong>in</strong>e an “<strong>in</strong>teraction”.An “<strong>in</strong>teraction” is def<strong>in</strong>ed as a p¯p cross<strong>in</strong>g with hits above a fixed threshold on both sides of <strong>the</strong>CLC detector. Follow<strong>in</strong>g this, an empty cross<strong>in</strong>g is def<strong>in</strong>ed as a p¯p cross<strong>in</strong>g with no <strong>in</strong>teractions.Given <strong>the</strong>se selection criteria, <strong>the</strong> experimental quantity P 0 , called P exp0 {α}, is related to µ as:P exp0 {µ; α} = (e ǫω·µ + e −ǫe·µ − 1) · e −(1−ǫ 0)·µ , (3.6)where <strong>the</strong> acceptances ǫ 0 and ǫ ω/e are, respectively, <strong>the</strong> probability to have no hits <strong>in</strong> <strong>the</strong> comb<strong>in</strong>edeast and west CLC modules and <strong>the</strong> probability to have at least one hit exclusively <strong>in</strong>west/east CLC module. The evaluation of <strong>the</strong>se parameters is based on Monte Carlo simulations,and typical values are ǫ 0 = 0.07 and ǫ ω/e = 0.12.To obta<strong>in</strong> <strong>the</strong> lum<strong>in</strong>osity measurement us<strong>in</strong>g <strong>the</strong> equation 3.4, <strong>the</strong> value of σ <strong>in</strong> is still needed.At <strong>the</strong> beg<strong>in</strong>n<strong>in</strong>g of Run II, an extrapolation to 2 TeV of <strong>the</strong> value measured at √ s = 1.8 TeV byCDF [81] was used. The cross section would be σ <strong>in</strong> = 60.4 mb. To facilitate <strong>the</strong> comparison ofCDF and DØ cross section measurements <strong>in</strong> Run II, <strong>the</strong> collaborations agreed to use a common<strong>in</strong>elastic cross section [82], σ <strong>in</strong> = 59.3 mb that is about 1.9% smaller than previous value.S<strong>in</strong>ce CDF never modified <strong>the</strong> actual lum<strong>in</strong>osity value used <strong>in</strong>ternally with<strong>in</strong> <strong>the</strong> collaboration,<strong>the</strong> CDF quoted lum<strong>in</strong>osity is multiplied offl<strong>in</strong>e by a factor of 1.019.Different sources of uncerta<strong>in</strong>ties have been taken <strong>in</strong>to account to evaluate <strong>the</strong> systematicuncerta<strong>in</strong>ties on <strong>the</strong> lum<strong>in</strong>osity measurement [83]. The dom<strong>in</strong>ated contributions are related to<strong>the</strong> detector simulation and <strong>the</strong> event generator used, and have been evaluated to be about 3%.The total systematic uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> CLC lum<strong>in</strong>osity measurements is 5.8%, which <strong>in</strong>cludesuncerta<strong>in</strong>ties on <strong>the</strong> measurement, 4.2%, and on <strong>the</strong> <strong>in</strong>elastic cross section value, 4%.3.4 Trigger and Data AcquisitionThe average <strong>in</strong>teraction rate at <strong>the</strong> Tevatron is 1.7 MHz <strong>for</strong> 36 × 36 bunches. In fact, <strong>the</strong>actual <strong>in</strong>teraction rate is higher because <strong>the</strong> bunches circulate <strong>in</strong> three tra<strong>in</strong>s of 12 bunches <strong>in</strong>each group spaced 396 ns which leads to a cross<strong>in</strong>g rate of 2.53 MHz. The <strong>in</strong>teraction rate isorders of magnitude higher than <strong>the</strong> maximum rate that <strong>the</strong> data acquisition system can handle.Fur<strong>the</strong>rmore, <strong>the</strong> majority of collisions are not of <strong>in</strong>terest. This leads to implementation of atrigger system that preselects events onl<strong>in</strong>e and decides if <strong>the</strong> correspond<strong>in</strong>g event <strong>in</strong><strong>for</strong>mationis written to tape or discarded.
50 3.4. Trigger and Data AcquisitionThe CDF trigger system consists of three trigger levels, see figure 3.12 and figure 3.13.The first two levels are hardware based, while <strong>the</strong> third one consists on a processor farm. Thedecisions taken by <strong>the</strong> system are based on <strong>in</strong>creas<strong>in</strong>gly more complex event <strong>in</strong><strong>for</strong>mation. Thetwo hardware levels are monitored and controlled by <strong>the</strong> Trigger Supervisor Interface, TSI,which distributes signals from <strong>the</strong> different sections of <strong>the</strong> trigger and DAQ system, a globalclock and bunch cross<strong>in</strong>g signal.Figure 3.12: Block diagram show<strong>in</strong>g <strong>the</strong> global trigger and DAQ systems at CDF II.
Chapter 3. Experimental Setup 513.4.1 Level 1 TriggerThe Level 1 trigger is a synchronous system that reads events and takes a decision every beamcross<strong>in</strong>g. The depth of <strong>the</strong> Level 1 decision pipel<strong>in</strong>e is approximately 4 µs, L1 latency. The L1buffer must be at least as deep as this process<strong>in</strong>g pipel<strong>in</strong>e or <strong>the</strong> data associated with a particularLevel 1 decision would be lost be<strong>for</strong>e <strong>the</strong> decision is made. The L1 buffer is 14 cross<strong>in</strong>gs deep(5544 ns at 396 ns bunch spac<strong>in</strong>g) to provide a marg<strong>in</strong> <strong>for</strong> unanticipated <strong>in</strong>creases <strong>in</strong> L1 latency.The Level 1 reduces <strong>the</strong> event rates from 2.53 MHz to less than 50 kHz.The Level 1 hardware consists of three parallel process<strong>in</strong>g streams which feed <strong>in</strong>puts of <strong>the</strong>Global Level 1 decision unit. One stream f<strong>in</strong>ds calorimeter based objects, L1 CAL, ano<strong>the</strong>rf<strong>in</strong>ds muons, L1 MUON, while <strong>the</strong> third one f<strong>in</strong>ds tracks <strong>in</strong> <strong>the</strong> COT, L1 TRACK. S<strong>in</strong>ce <strong>the</strong>muons and <strong>the</strong> electrons (calorimeter-based) require <strong>the</strong> presence of a track po<strong>in</strong>t<strong>in</strong>g at <strong>the</strong>correspond<strong>in</strong>g outer detector element, <strong>the</strong> tracks must be sent to <strong>the</strong> calorimeter and muonstreams as well as <strong>the</strong> track only stream.• The L1 CAL calorimeter trigger is employed to detect electrons, photons, jets, total transverseenergy and miss<strong>in</strong>g transverse energy, E / T . The calorimeter triggers are divided <strong>in</strong>totwo types: object triggers (electron, photons and jets) and global triggers ( ∑ E T and E / T ).The calorimeter towers are summed <strong>in</strong>to trigger towers of 15 o <strong>in</strong> φ and by approximately0.2 <strong>in</strong> η. There<strong>for</strong>e, <strong>the</strong> calorimeter is divided <strong>in</strong> 24 x 24 towers <strong>in</strong> η × φ space [84].The object triggers are <strong>for</strong>med by apply<strong>in</strong>g thresholds to <strong>in</strong>dividual calorimeter triggertowers, while thresholds <strong>for</strong> <strong>the</strong> global triggers are applied after summ<strong>in</strong>g energies fromall towers.• The L1 TRACK trigger is designed to reconstruct tracks on <strong>the</strong> COT. An eXtremely FastTracker, XFT, [85] uses hits from 4 axial layers of <strong>the</strong> COT to f<strong>in</strong>d tracks with a p T greaterthan some threshold, ∼ 2 GeV/c. The result<strong>in</strong>g track list is sent to <strong>the</strong> extrapolation box,XTRP,[86] that distributes <strong>the</strong> tracks to <strong>the</strong> Level 1 and Level 2 trigger subsystems.• L1 MUON system uses muon primitives, generated from various muon detector elements,and XFT tracks extrapolated to <strong>the</strong> muon chambers by <strong>the</strong> XTRP to <strong>for</strong>m muon triggerobjects. For <strong>the</strong> sc<strong>in</strong>tillators of <strong>the</strong> muon system, <strong>the</strong> primitives are derived from s<strong>in</strong>glehits or co<strong>in</strong>cidences of hits. In <strong>the</strong> case of <strong>the</strong> wire chambers, <strong>the</strong> primitives are obta<strong>in</strong>edfrom patterns of hits on projective wire with <strong>the</strong> requirement that <strong>the</strong> difference <strong>in</strong><strong>the</strong> arrival times of signals be less than a given threshold. This maximum allowed timedifference imposes a m<strong>in</strong>imum p T requirement <strong>for</strong> hits from s<strong>in</strong>gle tracks.
52 3.4. Trigger and Data AcquisitionF<strong>in</strong>ally, <strong>the</strong> Global Level 1 makes <strong>the</strong> L1 trigger decision based on <strong>the</strong> objects of <strong>in</strong>terestfound by <strong>the</strong> different Level 1 processes. Different sets of Level 1 conditions are assigned to<strong>the</strong> L1 trigger bits. If <strong>the</strong>se conditions are met, <strong>the</strong> bit is set to true. All this <strong>in</strong><strong>for</strong>mation is laterhandled by <strong>the</strong> TSI and transfered to <strong>the</strong> o<strong>the</strong>r trigger levels, and eventually, to tape.3.4.2 Level 2 TriggerThe Level 2 trigger is an asynchronous system which processes events that have received a L1accept <strong>in</strong> FIFO (First In - First Out) manner. It is structured as a two-stage pipel<strong>in</strong>e with databuffer<strong>in</strong>g at <strong>the</strong> <strong>in</strong>put of each stage. The first stage is based on a dedicated hardware processorwhich assembles <strong>in</strong><strong>for</strong>mation from a particular section of <strong>the</strong> detector. The second stage consistsof a programmable processors operat<strong>in</strong>g on lists of objects generated by <strong>the</strong> first stage. Each of<strong>the</strong> L2 stages is expected to take approximately 10 µs giv<strong>in</strong>g a latency of approximately 20 µs.The L2 buffers provide a storage of four events. After <strong>the</strong> Level 2, <strong>the</strong> event rate is reduced toabout 400-1000 Hz.In addition of <strong>the</strong> trigger primitives generated <strong>for</strong> Level 1, data <strong>for</strong> <strong>the</strong> Level 2 come from<strong>the</strong> shower maximum strip chambers <strong>in</strong> <strong>the</strong> central calorimeter and <strong>the</strong> r × φ strips of <strong>the</strong>SVX II. There are three hardware systems generat<strong>in</strong>g primitives at Level 2: Level 2 clusterf<strong>in</strong>der, L2CAL, shower maximum strip chambers <strong>in</strong> <strong>the</strong> central calorimeter, XCES, and <strong>the</strong>Silicon Vertex Tracker (SVT).• The L2CAL hardware carries out <strong>the</strong> hardware cluster f<strong>in</strong>der functions. It receives triggertower energies from <strong>the</strong> L1 CAL and applies seed and “shoulder” thresholds <strong>for</strong> clusterf<strong>in</strong>d<strong>in</strong>g. It is basically designed <strong>for</strong> trigger<strong>in</strong>g on jets, but specific reconstruction ofclusters <strong>for</strong> trigger<strong>in</strong>g on electrons, taus, and photons is also per<strong>for</strong>med.• The shower maximum detector provides a much better spacial resolution than a calorimetertower. The XCES boards per<strong>for</strong>m sum of <strong>the</strong> energy on groups of four adjacent CESwires and compare <strong>the</strong>m to a threshold (around 4 GeV). This <strong>in</strong><strong>for</strong>mation is matched toXFT tracks to generate a Level 2 trigger. This trigger hardware provides a significantreduction <strong>in</strong> comb<strong>in</strong>atorial background <strong>for</strong> electrons and photons.• Silicon Vertex Tracker, SVT, [87] uses hits from <strong>the</strong> r ×φ strips of <strong>the</strong> SVX II and tracksfrom <strong>the</strong> XFT to f<strong>in</strong>d tracks <strong>in</strong> SVX II. SVT improves on <strong>the</strong> XFT resolution <strong>for</strong> φ andp T and adds a measurement of <strong>the</strong> track impact parameter, d 0 . Hereby <strong>the</strong> efficiency and
Chapter 3. Experimental Setup 53resolution are comparable to those of <strong>the</strong> offl<strong>in</strong>e track reconstruction. The SVT enablestrigger<strong>in</strong>g on displaced tracks, that have a large d 0 .When <strong>the</strong> objects reconstructed by <strong>the</strong> Level 2 processors meet <strong>the</strong> conditions stated <strong>in</strong> <strong>the</strong>trigger table <strong>for</strong> <strong>the</strong> Level 2, <strong>the</strong> event is assigned <strong>the</strong> correspond<strong>in</strong>g Level 2 trigger bit, providedthat <strong>the</strong> correspond<strong>in</strong>g Level 1 bit is already set. At that moment, <strong>the</strong> TSI sends <strong>the</strong> event to <strong>the</strong>Level 3 farm.Detector ElementsRUN II TRIGGER SYSTEMCALCOTMUONSVXCESXFTMUONPRIM.XCESXTRPL1CALL1TRACKL1MUONGLOBALLEVEL 1L2CALSVTGLOBALLEVEL 2TSI/CLKPJW 9/23/96Figure 3.13: Block diagram show<strong>in</strong>g <strong>the</strong> Level 1 and Level 2 trigger systems.
54 3.5. Level 2 Trigger Upgrade <strong>for</strong> High Lum<strong>in</strong>osity3.4.3 Level 3 TriggerAfter an event is accepted at Level 2, it has to be read out completely. This operation <strong>in</strong>volvescollect<strong>in</strong>g data from over a couple of hundreds of VME Readout Buffers (VRBs). The EventBuilder assembles <strong>the</strong> event from pieces of data from <strong>the</strong> L2 system <strong>in</strong>to complete events. Itis divided <strong>in</strong>to 16 sub-farms, each consist<strong>in</strong>g of 12 to 16 processor nodes. Once <strong>the</strong> event isbuilt, it is sent to one node <strong>in</strong> <strong>the</strong> Level 3 farm. The Level 3 trigger reconstructs <strong>the</strong> event follow<strong>in</strong>ggiven algorithms. These algorithms take advantage of <strong>the</strong> full detector <strong>in</strong><strong>for</strong>mation andimproved resolution not available to <strong>the</strong> lower trigger levels. This <strong>in</strong>cludes a full 3-dimensionaltrack reconstruction and tight match<strong>in</strong>g of tracks to calorimeter and muon-system <strong>in</strong><strong>for</strong>mation.Events that satisfy <strong>the</strong> Level 3 trigger requirements are <strong>the</strong>n transfered onward to <strong>the</strong> ConsumerServer/Data Logger (CSL) system <strong>for</strong> storage first on disk and later on tape. The average process<strong>in</strong>gtime per event <strong>in</strong> Level 3 is on <strong>the</strong> order of a few seconds. The Level 3 leads to a fur<strong>the</strong>rreduction <strong>in</strong> <strong>the</strong> output rate, roughly 50 Hz.A set of requirements that an event has to fulfill at Level 1, Level 2 and Level 3 constitutesa trigger path. The CDF II trigger system implements about 200 trigger paths. An event willbe accepted if it passes <strong>the</strong> requirements of any one of <strong>the</strong>se paths and, depend<strong>in</strong>g of <strong>the</strong> triggerpath, it will be stored <strong>in</strong> a trigger dataset. A complete description of <strong>the</strong> different datasets atCDF Run II can be found <strong>in</strong> [88].Ano<strong>the</strong>r important feature of <strong>the</strong> trigger system of CDF is that Level 1 and Level 2 acceptscan be pre-scaled. This means that only a fraction of <strong>the</strong> events that fulfill <strong>the</strong> trigger requirementsare actually accepted. Even if this implies loos<strong>in</strong>g potentially useful events, it becomesnecessary at high lum<strong>in</strong>osity. Given <strong>the</strong> cont<strong>in</strong>uous improv<strong>in</strong>g per<strong>for</strong>mance of <strong>the</strong> Tevatron,pre-scal<strong>in</strong>g trigger has become common practice <strong>in</strong> <strong>the</strong> last years. Moreover, <strong>the</strong> trigger systemallows <strong>for</strong> dynamic pre-scal<strong>in</strong>g of trigger accepts, mean<strong>in</strong>g that <strong>the</strong> scal<strong>in</strong>g factor varies with<strong>the</strong> <strong>in</strong>stantaneous lum<strong>in</strong>osity, so <strong>the</strong> output bandwidth is maximally utilized.3.5 Level 2 Trigger Upgrade <strong>for</strong> High Lum<strong>in</strong>osityThe Level 2 trigger has worked well <strong>for</strong> Run II at low lum<strong>in</strong>osity. However, as <strong>the</strong> Tevatron<strong>in</strong>stantaneous lum<strong>in</strong>osity <strong>in</strong>creases, <strong>the</strong> limitation due to <strong>the</strong> simple algorithms used, starts tobecome clear. As a result, some of <strong>the</strong> most important jet and E / T related triggers have largegrowth terms <strong>in</strong> cross section and completely dom<strong>in</strong>ate <strong>the</strong> Level 2 accept bandwidth at <strong>the</strong>high lum<strong>in</strong>osity regimes (∼ 300 · 10 30 cm −2 s −1 ).
Chapter 3. Experimental Setup 55For this reason, two major trigger upgrades were implemented dur<strong>in</strong>g 2007, <strong>the</strong> Level 2XFT stereo upgrade and <strong>the</strong> Level 2 calorimer upgrade.3.5.1 Level 2 XFT Stereo UpgradeThe XFT Stereo upgrade provides many benefits over <strong>the</strong> purely axial trigger<strong>in</strong>g system usedpreviously. One of <strong>the</strong> achievements of this project is to reduce <strong>the</strong> rate of fake tracks <strong>in</strong> manytriggers. Fake rates <strong>in</strong>crease very rapidly with lum<strong>in</strong>osity, much faster than <strong>the</strong> real track rates.By remov<strong>in</strong>g as many of <strong>the</strong> fake tracks as possible at trigger level, it is possible to keep <strong>the</strong>setriggers, without a pre-scale, up to much higher <strong>in</strong>stantaneous lum<strong>in</strong>osities. The Level 1 pathis used to confirm <strong>the</strong> exist<strong>in</strong>g XFT track, reconstructed with <strong>the</strong> axial COT layers only, goesthrough <strong>the</strong> stereo layers at <strong>the</strong> expected locations. At Level 2 <strong>the</strong> segmentation is much f<strong>in</strong>erthan at Level 1 allow<strong>in</strong>g a better fake rejection rate and also provid<strong>in</strong>g <strong>in</strong><strong>for</strong>mation about <strong>the</strong>position of <strong>the</strong> track. In particular it is possible to measure <strong>the</strong> angle of <strong>the</strong> track with respect to<strong>the</strong> beam axis as well as <strong>the</strong> distance z from <strong>the</strong> center of <strong>the</strong> detector along <strong>the</strong> beam axis anduse this <strong>in</strong><strong>for</strong>mation to po<strong>in</strong>t <strong>the</strong> track to o<strong>the</strong>r detectors. This 3D track<strong>in</strong>g opens up several additionalcapabilities such as trigger level multi-track mass calculations or isolation requirementsand z-vertex reconstruction at Level 2.3.5.2 Level 2 Calorimeter UpgradeThe new Level 2 calorimeter system makes <strong>the</strong> full calorimeter trigger tower <strong>in</strong><strong>for</strong>mation directlyavailable to <strong>the</strong> Level 2 decision CPU. The upgraded system allows more sophisticatedalgorithms to be implemented <strong>in</strong> software; both Level 2 jets and E / T can be made nearly equivalentto offl<strong>in</strong>e quality, thus significantly improv<strong>in</strong>g <strong>the</strong> purity as well as <strong>the</strong> efficiency of <strong>the</strong> jetand E / T related triggers. The jet triggers are improved by us<strong>in</strong>g a cone algorithm <strong>in</strong> <strong>the</strong> Level 2CPU <strong>for</strong> jet cluster f<strong>in</strong>d<strong>in</strong>g. The jet algorithm is similar to JetClu (which is used to reconstructLevel 3 and offl<strong>in</strong>e jets) except that <strong>the</strong> cluster<strong>in</strong>g is done <strong>in</strong> a s<strong>in</strong>gle iteration, <strong>in</strong> order to saveprocess<strong>in</strong>g time.
56 3.5. Level 2 Trigger Upgrade <strong>for</strong> High Lum<strong>in</strong>osity
Chapter 4Event ReconstructionTo per<strong>for</strong>m a data analysis, <strong>the</strong> <strong>in</strong><strong>for</strong>mation obta<strong>in</strong>ed from <strong>the</strong> detector have to be process <strong>in</strong>order to reconstruct observables. This reconstruction implies ma<strong>the</strong>matical algorithms and def<strong>in</strong>itionshardly related with <strong>the</strong> detector itself.The analyses described <strong>in</strong> this <strong>the</strong>sis are based on jets, E / T , and <strong>in</strong> an <strong>in</strong>direct way, electronsand muons. All <strong>the</strong>se objects are briefly expla<strong>in</strong>ed <strong>in</strong> this Chapter.4.1 Track and Primary Vertex ReconstructionThe trajectories of charged particles are found (<strong>in</strong> a first approximation) as a series of segments<strong>in</strong> <strong>the</strong> axial superlayers of <strong>the</strong> COT. Two complementary algorithms associate <strong>the</strong> segmentsly<strong>in</strong>g on a common circle to def<strong>in</strong>e an axial track. Segments <strong>in</strong> <strong>the</strong> stereo layers are associatedwith <strong>the</strong> axial tracks to reconstruct 3D tracks. For muons and electrons used <strong>in</strong> this analysis,COT tracks are required to have at least 3 axial and 2 stereo segments with at least 5 hits persuperlayer. The efficiency <strong>for</strong> f<strong>in</strong>d<strong>in</strong>g isolated high momentum COT tracks <strong>in</strong> <strong>the</strong> COT fiducialvolume with p T > 10 GeV/c is measured us<strong>in</strong>g electrons from W ± → e ± ν events and isfound to be (98.3 ± 0.1)%. Silicon hit <strong>in</strong><strong>for</strong>mation is added to reconstructed COT tracks us<strong>in</strong>gan “outside-<strong>in</strong>” track<strong>in</strong>g algorithm. The COT tracks are extrapolated to <strong>the</strong> silicon detectorand <strong>the</strong> track is refit us<strong>in</strong>g <strong>the</strong> <strong>in</strong><strong>for</strong>mation from <strong>the</strong> silicon measurements. The <strong>in</strong>itial trackparameters provide a width <strong>for</strong> a search region <strong>in</strong> a given layer. For each candidate hit <strong>in</strong> thatlayer, <strong>the</strong> track is refit and used to def<strong>in</strong>e <strong>the</strong> search region <strong>in</strong>to <strong>the</strong> next layer. The search uses<strong>the</strong> two best candidate hits <strong>in</strong> each layer to generate a small tree of f<strong>in</strong>al track candidates, and<strong>the</strong> one with <strong>the</strong> best fit χ 2 is selected. The efficiency to associate at least three silicon hits with57
58 4.2. Lepton Identificationan isolated COT track is found to be (91 ± 1)%.The primary vertex location <strong>for</strong> a given event is found by fitt<strong>in</strong>g well-measured tracks to acommon po<strong>in</strong>t of orig<strong>in</strong>. At high lum<strong>in</strong>osities, more than one collision can occur on a givenbunch cross<strong>in</strong>g. For a lum<strong>in</strong>osity of ∼10 32 cm −2 s −1 , <strong>the</strong>re are ∼2.3 <strong>in</strong>teractions per bunchcross<strong>in</strong>g. The lum<strong>in</strong>ous region is long, with σ z = 29 cm; <strong>the</strong>re<strong>for</strong>e <strong>the</strong> primary vertices of eachcollision are typically separate <strong>in</strong> z. The first estimate of <strong>the</strong> primary vertices (x V , y V , z V ) isb<strong>in</strong>ned <strong>in</strong> <strong>the</strong> z coord<strong>in</strong>ate, and <strong>the</strong> z position of each vertex is <strong>the</strong>n calculated from <strong>the</strong> weightedaverage of <strong>the</strong> z coord<strong>in</strong>ate of all tracks with<strong>in</strong> 1 cm of <strong>the</strong> first iteration vertex, with a typicalresolution of 100 µm. The primary vertex is determ<strong>in</strong>ed event by event by an iterative algorithmwhich uses tracks around a seed vertex, def<strong>in</strong>ed as above, to <strong>for</strong>m a new vertex. The χ 2 <strong>for</strong> alltracks relative to <strong>the</strong> new vertex is calculated, tracks with bad χ 2 are removed, and <strong>the</strong> cycle isrepeated until all tracks have a good χ 2 . The locus of all primary vertices def<strong>in</strong>es <strong>the</strong> beaml<strong>in</strong>e,<strong>the</strong> position of <strong>the</strong> lum<strong>in</strong>ous region of <strong>the</strong> beam-beam collisions through <strong>the</strong> detector. A l<strong>in</strong>earfit to (x V , y V ) vs. z V yields <strong>the</strong> beaml<strong>in</strong>e <strong>for</strong> each stable runn<strong>in</strong>g period. The beaml<strong>in</strong>e is usedas a constra<strong>in</strong>t to ref<strong>in</strong>e <strong>the</strong> knowledge of <strong>the</strong> primary vertex <strong>in</strong> a given event. The transversebeam cross section is circular, with a rms width of ≈ 30 µm at z = 0, ris<strong>in</strong>g to ≈ 50 - 60 µm at|z| = 40 cm. The beam is not necessarily parallel nor centered <strong>in</strong> <strong>the</strong> detector.4.2 Lepton IdentificationNo leptons are expected <strong>in</strong> none of <strong>the</strong> signals under study <strong>in</strong> this <strong>the</strong>sis. There<strong>for</strong>e, we rejectleptons dur<strong>in</strong>g <strong>the</strong> optimization process. We however require leptons <strong>in</strong> one control region todef<strong>in</strong>e orthogonal conditions to <strong>the</strong> signal region.The leptons required <strong>in</strong> <strong>the</strong> analyses are electrons reconstructed <strong>in</strong> <strong>the</strong> central calorimeterand muons identified as isolated high-p T tracks.4.2.1 Electron ReconstructionElectrons are measured <strong>in</strong> <strong>the</strong> Electromagnetic Calorimeters. Incident electrons <strong>in</strong>duce showersacross multiple calorimeter towers. The energy of <strong>the</strong> showers appears <strong>in</strong> clusters <strong>in</strong> <strong>the</strong> η − φcoord<strong>in</strong>ate system. The cluster<strong>in</strong>g algorithm looks <strong>for</strong> EM-objects <strong>in</strong> <strong>the</strong> CEM. It starts bycreat<strong>in</strong>g an E T -ordered list of possible seed towers that are <strong>in</strong> <strong>the</strong> fiducial region and haveE emT> 2 GeV. Then towers with<strong>in</strong> <strong>the</strong> fiducial regions (<strong>in</strong>clud<strong>in</strong>g seeds) adjacent to <strong>the</strong> available
Chapter 4. Event Reconstruction 59highest E T seed are checked. They may belong to <strong>the</strong> cluster if <strong>the</strong>y are <strong>in</strong> <strong>the</strong> same detector as<strong>the</strong> seed, and have not been already used. Clusters <strong>in</strong> CEM can grow only away by 1 physicaltower from <strong>the</strong> seed. A cluster is found if <strong>the</strong> total EM-energy passes ETem > 2 GeV (default),and EThad /ETem < 0.125, where EThad is <strong>the</strong> hadronic energy with<strong>in</strong> <strong>the</strong> seed tower <strong>in</strong> CEM. Afterall clusters are found, tracks from <strong>the</strong> default collection are matched with <strong>the</strong>m comput<strong>in</strong>g <strong>the</strong>cluster center with <strong>the</strong> energy weighted average of <strong>the</strong> CES coord<strong>in</strong>ates of <strong>the</strong> cluster towers.The central electron candidates must have a match<strong>in</strong>g COT track.In our selection, we apply additional cuts listed <strong>in</strong> Table 4.1 <strong>for</strong> discrim<strong>in</strong>at<strong>in</strong>g electronswith at least 10 GeV transverse energy from electron fak<strong>in</strong>g objects such as photons, isolatedcharged hadrons, and jets.CEM Electron selectionTransverse energyCOT axial segmentsCOT stereo segmentsCorrected d 0Corrected z 0CutE T 10 GeV/cThree or more (with 5 hits each)Two or more (with 5 hits each)|d 0,corr | 0.02 cm (with Si hits)|d 0,corr | 0.2 cm (without Si hits)< 3 cmE over P E/p 2 (or track p T 50 GeV/c )CES fiducialYesHAD over EM energy ratio E HAD /E EM 0.055 + 0.00045 ∗ E TOTTrack L shrL shr 0.2 (if valid value)CES Dz|Dz| 3 cmCES Dx−3 Q × Dx 1.5 (cm)CES χ 2 (strip) χ 2 10Isolation Iso(0.4) 0.1 × p T (<strong>for</strong> p T 20 GeV/c )Iso(0.4) 2 GeV/c (<strong>for</strong> p T < 20 GeV/c )Table 4.1: Central electrons identification cuts.The ratios between <strong>the</strong> hadronic and <strong>the</strong> electromagnetic cluster energies E HAD /E EM andbetween <strong>the</strong> cluster energy and <strong>the</strong> track momentum E/p are required to be consistent with anelectron’s energy deposition <strong>in</strong> <strong>the</strong> calorimeters. The cluster is fur<strong>the</strong>r required to be isolated,
60 4.2. Lepton Identification<strong>the</strong> isolation be<strong>in</strong>g def<strong>in</strong>ed as <strong>the</strong> ratio of <strong>the</strong> additional transverse energy <strong>in</strong> a cone of radiusR = √ (∆φ) 2 + (∆η) 2 = 0.4 around <strong>the</strong> cluster to <strong>the</strong> transverse energy of <strong>the</strong> cluster itself.The position of <strong>the</strong> electromagnetic shower measured by <strong>the</strong> CES detector is used to def<strong>in</strong>ematch<strong>in</strong>g requirements between <strong>the</strong> extrapolated track and <strong>the</strong> cluster <strong>in</strong> <strong>the</strong> CES x and z localcoord<strong>in</strong>ates. In particular, a charge dependent cut <strong>in</strong> <strong>the</strong> x position is applied to take <strong>in</strong>to account<strong>the</strong> different flow of energy deposited by bremsstrahlung photons emitted by an electron or apositron. In addition, <strong>the</strong> CES provides electron identification through <strong>the</strong> observed showershape. The CES shower shape is fitted <strong>in</strong> <strong>the</strong> z view to <strong>the</strong> distribution expected <strong>for</strong> an electron,and <strong>the</strong> chisquare probability <strong>for</strong> <strong>the</strong> fit, χ 2 strip , is used as a cut on <strong>the</strong> shower profile. F<strong>in</strong>ally,<strong>the</strong> shar<strong>in</strong>g of energy between adjacent calorimeter towers is quantified by <strong>the</strong> lateral showerprofile L shr , which measures how close <strong>the</strong> energy distribution <strong>in</strong> <strong>the</strong> CEM towers adjacent to<strong>the</strong> cluster seed is to <strong>the</strong> electron hypo<strong>the</strong>sis.4.2.2 Isolated TracksMuons are detected by <strong>the</strong> muon-system placed <strong>in</strong> <strong>the</strong> outermost layer of <strong>the</strong> CDF detector becauseof <strong>the</strong> highly penetrat<strong>in</strong>g nature of muons. Hits <strong>in</strong> <strong>the</strong> muon detectors are l<strong>in</strong>ked toge<strong>the</strong>rto <strong>for</strong>m track segments called stubs. These track segments are matched to extrapolated COTtracks with at least p T > 15 GeV and energy deposition <strong>in</strong> <strong>the</strong> calorimeter that is consistentwith m<strong>in</strong>imum ioniz<strong>in</strong>g particles. Isolated tracks with p T > 15 GeV that do not have associatedstubs are also considered muon candidates (called stubless muons).S<strong>in</strong>ce all muons reconstructed at CDF have associated isolated tracks, it makes sense toloosen up <strong>the</strong> muon selection to <strong>the</strong> level of stubless muons <strong>for</strong> <strong>the</strong> analyses purposes. Anisolated track veto will also reject events with hadronically decay<strong>in</strong>g high-p T tau leptons. Theisolated track identification cuts are listed <strong>in</strong> Table 4.2.The COT track must have p T ≥ 10 GeV/c , and at least 3 axial and 2 stereo segments witha m<strong>in</strong>imum of 5 hits per segment. The distance of closest approach of <strong>the</strong> track to <strong>the</strong> beaml<strong>in</strong>e<strong>in</strong> <strong>the</strong> transverse plane, d 0 , must be small <strong>in</strong> order to select prompt muons (com<strong>in</strong>g from <strong>the</strong><strong>in</strong>teraction primary vertex) and reject cosmics and <strong>in</strong>-flight decays. The energy deposition <strong>in</strong><strong>the</strong> EM and HAD calorimeters, E EM and E HAD , must be small as expected <strong>for</strong> <strong>the</strong> passage ofa m<strong>in</strong>imum ioniz<strong>in</strong>g particle. Isolation is def<strong>in</strong>ed as <strong>the</strong> ratio between any additional transverseenergy <strong>in</strong> a cone of radius R = 0.4 around <strong>the</strong> track direction and <strong>the</strong> muon p T , and it is requiredto be smaller than 0.1.
Chapter 4. Event Reconstruction 61Loose Muon selectionTransverse momentumCutp T 10 GeV/cCOT axial segments Two or more (with 5 hits each)COT stereo segments One or more (with 5 hits each)COT χ 2 χ 2 /ndof 3Corrected d 0|d 0,corr | 0.02 cm (with Si hits)|d 0,corr | 0.2 cm (without Si hits)Corrected z 0< 3 cmEM energyHAD energyTotal CAL EnergyE EM 2 GeV/cE HAD 6 GeV/cE EM + E HAD 0.1 GeV/cIsolation Iso(0.4) 0.1 × p T (<strong>for</strong> p T 20 GeV/c )Iso(0.4) 2 GeV/c (<strong>for</strong> p T < 20 GeV/c )Table 4.2: Stubless muons identification cuts.4.3 Jet ReconstructionCollision events that trigger <strong>the</strong> detector conta<strong>in</strong> one or more hard scatter<strong>in</strong>g processes fromparton <strong>in</strong>teractions. We are <strong>in</strong>terested <strong>in</strong> detect<strong>in</strong>g <strong>the</strong> products of <strong>the</strong>se hard <strong>in</strong>teractions. Lightparticles such as electrons and muons are stable or have long lifetime and reach <strong>the</strong> subdetectorsdesigned <strong>for</strong> <strong>the</strong>ir identification. Quarks and gluons, however, participate <strong>in</strong> more complexprocesses. First, <strong>the</strong>y undergo a process called fragmentation where <strong>the</strong>y create partons viaa cascade of gluon emissions and decays. The fragmentation cont<strong>in</strong>ues until <strong>the</strong> momentumsquare of <strong>the</strong> partons is at <strong>the</strong> order of <strong>the</strong> <strong>in</strong>frared cut-off scale. Partons <strong>the</strong>n <strong>for</strong>m colorlesshadrons <strong>in</strong> a process called hadronization. The non-stable hadrons decay to stable particleswhich reach <strong>the</strong> detector material. The showers of particles appear as clusters of energy deposited<strong>in</strong> localized areas of <strong>the</strong> calorimeter, called jets.There are several algorithms developed <strong>for</strong> calorimeter jets. Some algorithms may also<strong>in</strong>corporate track<strong>in</strong>g <strong>in</strong><strong>for</strong>mation <strong>in</strong> search<strong>in</strong>g <strong>for</strong> charged jets or <strong>in</strong> measur<strong>in</strong>g <strong>the</strong>ir transversemomenta. The jet identification algorithm used <strong>in</strong> <strong>the</strong>se searches is called JETCLU [89] whichrelies only on calorimetry. The jets are def<strong>in</strong>ed as towers <strong>in</strong> circular regions of <strong>the</strong> η − φ plane,
62 4.4. Miss<strong>in</strong>g Transverse Energy Reconstructioncalled cones, with radius:R = √ (∆η i ) 2 − (∆φ i ) 2 (4.1)where ∆η i = η cent −η i and ∆φ i = φ cent −φ i are differences between <strong>the</strong> E T -weighted averageof <strong>the</strong> tower locations (centroid) and <strong>the</strong> i th tower location <strong>in</strong> pseudo-rapidity and azimuthalangle. The algorithm starts search<strong>in</strong>g <strong>for</strong> towers with E T > 1 GeV, whereE T = E em s<strong>in</strong> θ em + E had s<strong>in</strong> θ had (4.2)θ em (θ had ) is <strong>the</strong> polar angle of <strong>the</strong> EM(HAD) cell of <strong>the</strong> tower <strong>in</strong> <strong>the</strong> detector coord<strong>in</strong>ate systemwith orig<strong>in</strong> placed at <strong>the</strong> highest p T vertex <strong>in</strong> <strong>the</strong> event. Then preclusters are created bygroup<strong>in</strong>g adjacent towers with<strong>in</strong> <strong>the</strong> cone radius proceed<strong>in</strong>g from <strong>the</strong> highest energy tower to<strong>the</strong> lowest one. One tower is assigned to only one precluster. In <strong>the</strong> next step, <strong>the</strong> centroidsof <strong>the</strong> preclusters are calculated, and new cones are def<strong>in</strong>ed <strong>in</strong>clud<strong>in</strong>g towers with at least 100MeV. If <strong>the</strong> centroid of a new cluster changes, <strong>the</strong> cone is redef<strong>in</strong>ed and new towers are addediteratively (but not taken away). When a stable solution is found, overlaps between clusters areremoved by ei<strong>the</strong>r comb<strong>in</strong><strong>in</strong>g or separat<strong>in</strong>g contiguous clusters, and jets are def<strong>in</strong>ed.The energy of <strong>the</strong> jets is corrected [90] <strong>for</strong> <strong>the</strong> pseudo-rapidity dependence of <strong>the</strong> calorimeterresponse, <strong>the</strong> calorimeter time dependence, and extra E T from any multiple <strong>in</strong>teractions.4.4 Miss<strong>in</strong>g Transverse Energy ReconstructionThe presence of undetectable particles <strong>in</strong> an event is <strong>in</strong>ferred by an imbalance of transverseenergy <strong>in</strong> <strong>the</strong> detector. The miss<strong>in</strong>g transverse energy, / E T , is reconstructed entirely based oncalorimeter <strong>in</strong><strong>for</strong>mation and def<strong>in</strong>ed as <strong>the</strong> magnitude:N/ ∑ towersE T x = −i=0E T,i cos(φ i ) (4.3)andN/ ∑ towersE T y = −i=0E T,i s<strong>in</strong>(φ i ) (4.4)
Chapter 4. Event Reconstruction 63/E T =√ /ET2x + / E T2y (4.5)where E T,i is <strong>the</strong> transverse energy of <strong>the</strong> calorimeter tower i calculated with respect to <strong>the</strong> zcoord<strong>in</strong>ate of <strong>the</strong> event, φ i is its azimuthal angle, and <strong>the</strong> sum is over all calorimeter towers.The / E T is corrected by objet participat<strong>in</strong>g <strong>in</strong> <strong>the</strong> event, <strong>in</strong> our case jets, <strong>in</strong> follow<strong>in</strong>g way:/corrE T x = E / N∑ jetsrawT x −i=1/corrE T y = E / N∑ jetsrawT y −i=1(E corr,ix(E corr,iy− E raw,ix ) (4.6)− E raw,iy ) (4.7)s<strong>in</strong>ce leptons are not expected <strong>in</strong> <strong>the</strong> f<strong>in</strong>al state, corrections are not applied <strong>for</strong> electrons ormuons.4.5 Quality Selection Cuts <strong>in</strong> / E T AnalysisAll <strong>the</strong> CDF II analyses based on <strong>the</strong> / E T data sample apply a set of quality cuts on <strong>the</strong> data(“clean-up cuts”). Here is a summary of <strong>the</strong>se cuts organized <strong>in</strong> three passes:• Pass 1 requirements– At least one central jet (|η| < 0.9) with E T > 10 GeV ,– Event Electromagnetic Fraction (EEMF):EEMF =∑ Njetsj=1 Ej T · EMF j∑ Njetsj=1 Ej T> 0.1where EMF j is <strong>the</strong> fraction of <strong>the</strong> jet energy deposited <strong>in</strong> <strong>the</strong> electromagneticcalorimeter. Only jets with E rawT> 10 GeV are considered,– At least one COT track with p T > 0.5 GeV/c and an axial super layer with six ormore hits.
64 4.5. Quality Selection Cuts <strong>in</strong> / E T Analysis• Pass 2 requirements– Event Charge Fraction (ECHF):ECHF =∑ Njetsj=1 CHF jN jets> 0.1where CHF j is <strong>the</strong> jet charge fraction def<strong>in</strong>ed as <strong>the</strong> sum of <strong>the</strong> p T of <strong>the</strong> tracksmatched to <strong>the</strong> jet over <strong>the</strong> jet ET :CHF j =∑ Ntracksj=1p jiTE j T– At least one good primary vertex <strong>in</strong> <strong>the</strong> event• Pass 3 requirements> 0.1– The chimney is a hole <strong>in</strong> <strong>the</strong> calorimeter at φ = (60 ◦ ; 100 ◦ ) and η = (0.5; 1.0) thathosts cryogenic and <strong>in</strong>strumental connections to <strong>the</strong> <strong>in</strong>ner detector. Jets that fall<strong>in</strong>to <strong>the</strong> chimney region are almost certa<strong>in</strong>ly mismeasured, <strong>the</strong>re<strong>for</strong>e we discard anyevent that has such a jet with E T > 10 GeV .– Event primary vertex falls with<strong>in</strong> z < 60 cm of <strong>the</strong> nom<strong>in</strong>al <strong>in</strong>teraction po<strong>in</strong>t at <strong>the</strong>detector center.– The beam halo energy usually appears <strong>in</strong> a row of towers at φ = 0. It was foundthat <strong>the</strong> previous selection criteria are suficient to elim<strong>in</strong>ate events with beam halomuons, <strong>the</strong>re<strong>for</strong>e no fur<strong>the</strong>r treatment is required.– Total calorimeter energy less than 2 TeV.
Chapter 5Heavy Flavor Tagg<strong>in</strong>gThe fact that <strong>the</strong> majority of background events conta<strong>in</strong> only light quarks <strong>in</strong> <strong>the</strong>ir f<strong>in</strong>al states,makes <strong>the</strong> heavy flavor tagg<strong>in</strong>g one of <strong>the</strong> most powerful tools remov<strong>in</strong>g backgrounds. Differentalgorithms and flavor separators are extensively used <strong>in</strong> high energy physics analysis.The specific tagg<strong>in</strong>g tools used dur<strong>in</strong>g <strong>the</strong> analyses signal optimization processes are expla<strong>in</strong>ed<strong>in</strong> this Chapter.5.1 Secondary Vertex algorithmThe B hadrons <strong>in</strong> jets com<strong>in</strong>g from b quark fragmentation have an average flight path of about500 microns, yield<strong>in</strong>g secondary vertices relative to <strong>the</strong> <strong>in</strong>teraction po<strong>in</strong>t. These hadrons travelaway from <strong>the</strong> primary vertex and subsequently decay to hadrons through a cascade of particles.The charged decay products are often reconstructed as displaced tracks. The <strong>in</strong>tersections of<strong>the</strong>se tracks <strong>for</strong>m secondary vertices at <strong>the</strong> po<strong>in</strong>ts where <strong>the</strong> hadrons decay.The SecVtx algorithm [91] searches <strong>for</strong> displaced secondary vertices by comb<strong>in</strong><strong>in</strong>g trackswith<strong>in</strong> “taggable” jets (figure 5.1). Jets are taggable if ETraw >10 GeV, η
66 5.2. Mistag Estimationmentum. Thus L xy is positive if <strong>the</strong> displacement po<strong>in</strong>ts along <strong>the</strong> jet momentum, and negativeif it po<strong>in</strong>ts to <strong>the</strong> opposite direction. Jets are tagged positively if L xy /σ Lxy > 3 and negativelyif L xy /σ Lxy < −3. Negative tags are due to resolution effects <strong>in</strong> <strong>the</strong> tagg<strong>in</strong>g, and are usuallyhigh-p T light flavor (uds) jets. Similar phenomena are observed <strong>in</strong> <strong>the</strong> simulation of positivetags. The positively tagged light flavor jets are called mistags (section 5.2).Figure 5.1: Schematic diagram of <strong>the</strong> secondary vertex heavy flavor tagg<strong>in</strong>g.There are two sett<strong>in</strong>gs <strong>for</strong> SecVtx, one with looser and one with tighter track requirements.The loose tagger has higher efficiency <strong>for</strong> b-jets than <strong>the</strong> tight, but it also suffers a higher mistagrate. The efficiency <strong>for</strong> <strong>the</strong> two sett<strong>in</strong>gs are shown <strong>in</strong> figure 5.2 and figure 5.3 as functions of <strong>the</strong>jet E T and η. A degradation of track reconstruction efficiency is observed at |η| > 1.1 outside<strong>the</strong> COT coverage. The efficiency is def<strong>in</strong>ed with respect to taggable jets.The detector simulation is reported to overestimate <strong>the</strong> track<strong>in</strong>g resolution. As a consequence,<strong>the</strong> tagg<strong>in</strong>g efficiency is higher <strong>in</strong> Monte Carlo than <strong>in</strong> data. We apply a weight<strong>in</strong>gfactor to Monte Carlo events to compensate <strong>for</strong> this effect.5.2 Mistag EstimationThe mistags, light-flavor jets falsely tagged as heavy flavor jets, are <strong>in</strong>separable companions ofany tagg<strong>in</strong>g algorithms. The mistag rate is only few per cent depend<strong>in</strong>g on <strong>the</strong> SecVtx’s sett<strong>in</strong>gs
Chapter 5. Heavy Flavor Tagg<strong>in</strong>g 67SecVtx Tag Efficiency <strong>for</strong> Top b-Jets0.70.60.50.40.30.20.10Loose SecVtxTight SecVtx20 40 60 80 100 120 140 160 180 200Jet Et (GeV)Figure 5.2: Tagg<strong>in</strong>g efficiency of <strong>the</strong> tight and loose SecVtx algorithm as function of <strong>the</strong> tagged jet E T <strong>in</strong> topquark Monte Carlo samples.(figures 5.4 and 5.5). Although <strong>the</strong> mistag efficiency is more than an order of magnitude smallerthan <strong>the</strong> heavy flavor tagg<strong>in</strong>g efficiency, <strong>the</strong> large cross section of processes that produce lightflavor jets make <strong>the</strong> mistag background one of <strong>the</strong> largest <strong>in</strong> <strong>the</strong> s<strong>in</strong>gle-tag data sample.Mistags are estimated from <strong>in</strong>clusive jet-sample data by comput<strong>in</strong>g a mistag rate [91](R + mistags ). This R+ mistags is a six-dimensional matrix which is parametrized by <strong>the</strong> jet E T ,|η|, secondary-vertex track-multiplicity, <strong>the</strong> number of primary vertices <strong>in</strong> <strong>the</strong> event, primaryvertex z-position, and <strong>the</strong> scalar sum of E T of all jets <strong>in</strong> <strong>the</strong> event.The s<strong>in</strong>gle mistag is estimated by runn<strong>in</strong>g on a pre-tag sample with total light and heavyflavor events N prelight + Npre heavy. The pre-tag data consists of events that pass all relevant selectioncuts without any tag requirements. Double mistags are estimated from <strong>the</strong> same data afterrequir<strong>in</strong>g one observed positive tag. This predicts <strong>the</strong> rate at which <strong>the</strong> non-tagged jet producesa second tag that is a mistag.It is generally not known if a positive tag is real or a mistag; <strong>the</strong>re<strong>for</strong>e, it is not possible toconstruct a mistag matrix directly from data. S<strong>in</strong>ce negative tags are mostly fakes, <strong>the</strong> constructionof <strong>the</strong> mistag matrix starts by creat<strong>in</strong>g a negative tag matrix R − def<strong>in</strong>ed as <strong>in</strong> equation 5.2where N − light + N − heavyis <strong>the</strong> number of negative tags <strong>in</strong> <strong>the</strong> data.
68 5.2. Mistag EstimationSecVtx Tag Efficiency <strong>for</strong> Top b-Jets0.70.60.5Loose SecVtxTight SecVtx0.40.30.20.100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2Jet EtaFigure 5.3: Tagg<strong>in</strong>g efficiency of <strong>the</strong> tight and loose SecVtx algorithm as function of <strong>the</strong> tagged jet η <strong>in</strong> topquark Monte Carlo samples.R − = N − light + N − heavyN prelight + Npre heavyNegative tags are ma<strong>in</strong>ly due to resolution effects <strong>in</strong> <strong>the</strong> track<strong>in</strong>g. The majority of <strong>the</strong>mistags (light flavor positive tags) are produced similarly. The rest comes from physical sources,<strong>for</strong> example long-lived particle decays (K s or Λ) and <strong>in</strong>teractions <strong>in</strong> <strong>the</strong> beam-pipe or with <strong>the</strong>detector material. These processes enhance <strong>the</strong> mistag rate with respect to <strong>the</strong> <strong>the</strong> negative tagrate. We correct <strong>for</strong> <strong>the</strong>se effects by multiply<strong>in</strong>g <strong>the</strong> negative tags with an asymmetry factor.Templates of signed tag mass distributions obta<strong>in</strong>ed from Monte Carlo simulations of light andheavy flavor jets are fitted to <strong>the</strong> tag mass observed <strong>in</strong> <strong>the</strong> data. The fit provides normalization<strong>for</strong> <strong>the</strong> various light and heavy flavor jet productions and fixes <strong>the</strong> heavy flavor fraction <strong>in</strong> <strong>the</strong>simulation. It is not possible to fit both, <strong>the</strong> negative and <strong>the</strong> positive tag mass distributionssimultaneously, because <strong>the</strong> Monte Carlo underestimates <strong>the</strong> fraction of negative tags with respectto <strong>the</strong> positive ones. In o<strong>the</strong>r words, it provides a too optimistic description of <strong>the</strong> detectorresolution. The positive tag excess over <strong>the</strong> negative tags, however, is physically motivated andexpected to be better reproduced by <strong>the</strong> simulation. It is reasonable to assume that <strong>the</strong> simulationunderestimates <strong>the</strong> part of <strong>the</strong> mistag rate which is due to resolution effects as much as <strong>the</strong>negative tag rate; <strong>the</strong>re<strong>for</strong>e, <strong>the</strong> fit is done <strong>in</strong> two steps. In <strong>the</strong> first step, <strong>the</strong> negative templates(5.2)
Chapter 5. Heavy Flavor Tagg<strong>in</strong>g 69SecVtx Mistag Rate0.060.050.040.030.020.010Loose SecVtxTight SecVtx20 40 60 80 100 120 140 160 180 200Jet Et (GeV)Figure 5.4: Mistag rate of <strong>the</strong> tight and loose SecVtx algorithm as function of <strong>the</strong> tagged jet E T <strong>in</strong> top quarkMonte Carlo samples.are subtracted from <strong>the</strong> positive ones <strong>in</strong> order to get templates <strong>for</strong> <strong>the</strong> positive tag excess. Thesum of <strong>the</strong>se Monte Carlo templates is fitted to <strong>the</strong> data, and <strong>the</strong> correct normalization <strong>for</strong> <strong>the</strong>simulations is computed. In <strong>the</strong> second step, <strong>the</strong> negative templates are fitted to <strong>the</strong> data suchthat <strong>the</strong> relative fractions of <strong>the</strong> various flavors are kept <strong>the</strong> same as measured <strong>in</strong> <strong>the</strong> first step.The result<strong>in</strong>g overall scale factor is called <strong>the</strong> Negative Scale Factor, and it is assumed to be <strong>the</strong>same <strong>in</strong> all Monte Carlo processes regardless of <strong>the</strong> flavor. The second fit is required to obta<strong>in</strong><strong>the</strong> number of mistags that were subtracted <strong>in</strong> <strong>the</strong> first step. The mistag asymmetry is def<strong>in</strong>edas <strong>the</strong> ratio between <strong>the</strong> number of positively tagged light flavor jets <strong>in</strong> <strong>the</strong> simulation and <strong>the</strong>sum of all <strong>the</strong> negative tags:α =N + lightN − light + N − heavy(5.3)where N + lightis <strong>the</strong> number of mistag jets. This def<strong>in</strong>ition still conta<strong>in</strong>s <strong>the</strong> heavy flavor contributionto <strong>the</strong> negative tags. By scal<strong>in</strong>g <strong>the</strong> negative tags only with this asymmetry factor <strong>in</strong>order to estimate <strong>the</strong> actual mistag contribution, one <strong>in</strong>troduces an uncerta<strong>in</strong>ty due to possibledifferences <strong>in</strong> <strong>the</strong> flavor compositions between <strong>the</strong> generic jet sample from which <strong>the</strong> matrixwas produced and <strong>the</strong> analysis sample <strong>in</strong> which <strong>the</strong> matrix is applied. This uncerta<strong>in</strong>ty is small<strong>for</strong> s<strong>in</strong>gle mistags. However, <strong>the</strong> first real tag requirement <strong>in</strong> <strong>the</strong> double mistag estimation en-
70 5.2. Mistag EstimationSecVtx Mistag Rate0.060.050.04Loose SecVtxTight SecVtx0.030.020.0100 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 2.2Jet EtaFigure 5.5: Mistag rate of <strong>the</strong> tight and loose SecVtx algorithm as function of <strong>the</strong> tagged jet η <strong>in</strong> top quark MonteCarlo samples.hances <strong>the</strong> heavy flavor fraction. In order to get <strong>the</strong> right prediction <strong>in</strong> both s<strong>in</strong>gle and doubletags, ano<strong>the</strong>r scale factor is applied on <strong>the</strong> top of <strong>the</strong> asymmetry factor that cancels <strong>the</strong> heavyflavor contribution <strong>in</strong> <strong>the</strong> sample where <strong>the</strong> mistag matrix was produced:β = Npre light + Npre heavyN prelight(5.4)Thus <strong>the</strong> elements of <strong>the</strong> mistag matrix product αβR −R + = α × β × R − = N+ lightN prelight(5.5)Consequently, this operator is no longer applicable on <strong>the</strong> entire pre-tag sample. The heavyflavor contribution should be removed from <strong>the</strong> pre-tag data be<strong>for</strong>e apply<strong>in</strong>g <strong>the</strong> matrix. Thisis done <strong>in</strong>directly by apply<strong>in</strong>g <strong>the</strong> matrix on <strong>the</strong> heavy flavor simulation and subtract<strong>in</strong>g <strong>the</strong>result from <strong>the</strong> total prediction obta<strong>in</strong>ed <strong>in</strong> <strong>the</strong> data. This correction is often not significantwith respect to <strong>the</strong> systematic uncerta<strong>in</strong>ties that are generally considered <strong>in</strong> this analysis. Thet¯t process, <strong>for</strong> example, is corrected by 5% <strong>in</strong> <strong>the</strong> s<strong>in</strong>gle tagged and 8% <strong>in</strong> <strong>the</strong> double taggedevents.
Chapter 5. Heavy Flavor Tagg<strong>in</strong>g 715.3 Charm Hadron Analysis Oriented SeparatorThe Charm Hadron Analysis Oriented Separator (CHAOS) is used to determ<strong>in</strong>e whe<strong>the</strong>r atagged jet has been produced from <strong>the</strong> hadronization process of a light quark, falsely tagged asa heavy flavor jet, a b quark, or a c quark. Depend<strong>in</strong>g on <strong>the</strong> flavor of <strong>the</strong> orig<strong>in</strong>al parton, <strong>the</strong>tagged jet and its secondary vertex have different characteristics, ma<strong>in</strong>ly related to <strong>the</strong> track<strong>in</strong>g.Us<strong>in</strong>g properties of <strong>the</strong> tracks <strong>for</strong>m<strong>in</strong>g <strong>the</strong> secondary vertex and <strong>the</strong> tracks of <strong>the</strong> jets with<strong>in</strong> aneural network, CHAOS allows to enhance <strong>the</strong> jet selection with a desired flavor, <strong>in</strong> particularc jets.CHAOS is a neural network based on SNNS v4.3 [92]. The structure <strong>in</strong>cludes three layers.One <strong>in</strong>put layer with 22 nodes plus one bias node, one hidden layer with 22 nodes, and oneoutput layer with two nodes produc<strong>in</strong>g a two-dimensional output. The neural network makesuse of 22 variables, ma<strong>in</strong>ly related to tagg<strong>in</strong>g properties of <strong>the</strong> jets. These variables, listed <strong>in</strong>Table 5.1, were carefully chosen to be well reproduced by <strong>the</strong> simulation, and to have a stablebehavior <strong>in</strong> different samples avoid<strong>in</strong>g dependences with <strong>the</strong> jet k<strong>in</strong>ematics. All of <strong>the</strong>m are<strong>in</strong>tr<strong>in</strong>sically related to <strong>the</strong> applied tagg<strong>in</strong>g algorithm, <strong>in</strong> this case <strong>the</strong> SecVtx algorithm.Mass of <strong>the</strong> vertexCharge of <strong>the</strong> vertexCHAOS <strong>in</strong>put variablesAverage |d 0 | of good tracksAverage |d 0 significance| of good tracksL xy significance Fraction of good tracks with |d 0 significance| >1Number of pass−1 tracksFraction of good tracks with |dNumber of good tracks0 significance| >3Number of vertex ′ s tracksFraction of good tracks with |dNumber of good tracks0 significance| >5∑pT (good tracks)PE, where E T is <strong>the</strong> jet E TT T E T, where P T is <strong>the</strong> P T of <strong>the</strong> secondary vertex∑z t = ∑ pT (pass−1 tracks)pT (good tracks)Fraction of vertex p T <strong>in</strong> <strong>the</strong> lead<strong>in</strong>g trackFraction of vertex p T <strong>in</strong> <strong>the</strong> second lead<strong>in</strong>g trackr vtx = p T of <strong>the</strong> vertex∑pT (good tracks)Signed d 0 of <strong>the</strong> lead<strong>in</strong>g vertex trackSigned d 0 of <strong>the</strong> second lead<strong>in</strong>g vertex trackSigned d 0 significance of <strong>the</strong> lead<strong>in</strong>g vertex trackSigned d 0 significance of <strong>the</strong> second lead<strong>in</strong>g vertex trackφ jetη jetTable 5.1: List of <strong>in</strong>put variables used <strong>in</strong> CHAOS.The neural network is tra<strong>in</strong>ed with three pure flavor samples extracted from a W+ jet <strong>in</strong>clusivesample generated with PYTHIA [62] event generator. The samples are extracted byselect<strong>in</strong>g events with at least one tagged jet, requir<strong>in</strong>g loose SecVtx, where <strong>the</strong> tagged jet comesfrom a b quark, c quark, light quark, or a τ lepton falsely tagged as heavy flavor jet.
72 5.3. Charm Hadron Analysis Oriented SeparatorThe two-dimensional output structure permits to separate tree different targets dur<strong>in</strong>g <strong>the</strong>same tra<strong>in</strong><strong>in</strong>g process. The output is distributed <strong>in</strong> a plane with<strong>in</strong> <strong>in</strong>tervals between 0 and 1.Events with tagged jets from b quarks are targeted to (1,0), jets from c quarks to (1,1), and jetsfrom light quarks or τ leptons to (0,1). The two-dimensional output is shown <strong>in</strong> figure 5.6 whenCHAOS is applied to <strong>the</strong> three flavor samples used <strong>for</strong> <strong>the</strong> tra<strong>in</strong><strong>in</strong>g. In an analysis context, <strong>the</strong>CHAOS application has as purpose <strong>the</strong> event selection, enhanc<strong>in</strong>g <strong>the</strong> sample with a def<strong>in</strong>edjet flavor, <strong>in</strong> particular c jets. An easy way to select c jets is to apply a cut on <strong>the</strong> sum of <strong>the</strong>one-dimensional outputs. The sum of outputs is a discrim<strong>in</strong>ant that separates c jets from <strong>the</strong> restof <strong>the</strong> tagged jets. Figure 5.7 shows <strong>the</strong> two CHAOS outputs and <strong>the</strong>ir sum.The cut applied <strong>in</strong> <strong>the</strong> search <strong>for</strong> scalar top (Chapter 7) to select c jets, cutt<strong>in</strong>g on 1.65 <strong>in</strong>sum of <strong>the</strong> CHAOS outputs, is shown as an arrow <strong>in</strong> figure 5.8. This cut is used to compute <strong>the</strong>flavor efficiency and <strong>the</strong> scale factor discussed <strong>in</strong> <strong>the</strong> next section 5.4.SNNS Output 1 (anti-bottom)10.90.80.70.60.50.40.30.22-D Network Output <strong>for</strong> test Light+TausSNNS Output 1 (anti-bottom)2-D Network Output <strong>for</strong> test Bottom10.90.80.70.60.50.40.30.20.10.10.100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1SNNS Output 0 (anti-light)SNNS Output 0 (anti-light)SNNS Output 0 (anti-light)SNNS Output 1 (anti-bottom)2-D Network Output <strong>for</strong> test Charm10.90.80.70.60.50.40.30.2Figure 5.6: Chaos output <strong>in</strong> 2-D <strong>for</strong> light + τ jets (left), b jets (center), and c jets (right) apply<strong>in</strong>g <strong>the</strong> NN to <strong>the</strong>samples used <strong>for</strong> tra<strong>in</strong><strong>in</strong>g.
Chapter 5. Heavy Flavor Tagg<strong>in</strong>g 73Fraction of objects [%]6050403020Network Output <strong>for</strong> Node 0CharmBottomLight+TausFraction of objects [%]6050403020Network Output <strong>for</strong> Node 1CharmBottomLight+TausFraction of objects [%]16141210864Sum of network outputsCharmBottomLight+Taus1010200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1SNNS Output 0 (anti-light)00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1SNNS Output 1 (anti-bottom)00.8 1 1.2 1.4 1.6 1.8 2Sum of outputsFigure 5.7: Chaos outputs <strong>in</strong> 1-D. Output-0 dist<strong>in</strong>guish<strong>in</strong>g light + τ from b and c jets (left), output-1 dist<strong>in</strong>guish<strong>in</strong>gb from light + τ and c jets (center), and <strong>the</strong> sum of both (right) apply<strong>in</strong>g <strong>the</strong> NN to <strong>the</strong> samples used <strong>for</strong>tra<strong>in</strong><strong>in</strong>g <strong>in</strong>clud<strong>in</strong>g test events (dots).Fraction of objects [%]1614121086Sum of network outputsCharmBottomLight+Taus4200.8 1 1.2 1.4 1.6 1.8 2Sum of outputsFigure 5.8: Sum of <strong>the</strong> CHAOS outputs <strong>in</strong> 1D apply<strong>in</strong>g <strong>the</strong> neural network to <strong>the</strong> samples used <strong>for</strong> tra<strong>in</strong><strong>in</strong>g. Thearrow <strong>in</strong>dicates <strong>the</strong> cut on 1.65, used <strong>in</strong> <strong>the</strong> analysis described <strong>in</strong> Chapter 7.
74 5.4. CHAOS Efficiency and Scale Factors5.4 CHAOS Efficiency and Scale FactorsThe method used to measure <strong>the</strong> CHAOS flavor selection efficiency <strong>for</strong> heavy flavor jets is described<strong>in</strong> this section. The events used to study this efficiency are dijet events enriched <strong>in</strong> heavyflavor. A sample triggered on medium p T <strong>in</strong>clusive muons which is enriched <strong>in</strong> semileptonicdecays of bottom and charm hadrons is used. The efficiency is also measured <strong>for</strong> simulated jetsby us<strong>in</strong>g a Monte Carlo sample. Muons are identified us<strong>in</strong>g a selection similar to that described<strong>in</strong> section 4.2.2, except that <strong>the</strong>y are not required to be isolated and have a lower energy threshold(track p T > 8 GeV/c ). The heavy flavor content of <strong>the</strong> sample is fur<strong>the</strong>r enhanced byrequir<strong>in</strong>g two jets <strong>in</strong> <strong>the</strong> event, a “muon jet”, presumed to conta<strong>in</strong> <strong>the</strong> decay products of a heavyflavor hadron, and an “away jet”. The muon requirements are summarized <strong>in</strong> Table 5.2. Themuon jet must have E T > 25 GeV and be with<strong>in</strong> 0.4 of <strong>the</strong> muon direction <strong>in</strong> η-φ space. Theaway jet is required to have E T > 25 GeV, and it must be approximately back-to-back with <strong>the</strong>muon jet (∆φ µ−j > 2 rad).Muon selectionCutCMU stub |dx| 7cm or (p T < 20 GeV/c and χ 2 9)CMP stub |dx| 5cm or (p T < 20 GeV/c and χ 2 9)Transverse momentump T 8 GeV/cCorrected z 0 3cmCOT axial segmentsTwo or more (with 5 hits each)COT stereo segments One or more (with 5 hits each)COT χ 2 χ 2 /ndof 3Table 5.2: Required muon cuts to def<strong>in</strong>e a “muon jet”.The fraction of b and c away jets is obta<strong>in</strong>ed fitt<strong>in</strong>g flavor templates, extracted from a HFmultijet MC sample, to <strong>the</strong> mass of <strong>the</strong> vertex distribution. The efficiency of <strong>the</strong> CHAOS cuton 1.65 (as shows figure 5.8) is computed fitt<strong>in</strong>g <strong>the</strong> flavor templates to <strong>the</strong> data distribution,be<strong>for</strong>e and after <strong>the</strong> cut, as shown <strong>in</strong> figure 5.9. The efficiency obta<strong>in</strong>ed <strong>in</strong> this way is def<strong>in</strong>ed as<strong>the</strong> central value. The error on this estimation is computed repeat<strong>in</strong>g <strong>the</strong> procedure us<strong>in</strong>g flavortemplates extracted from a W+jet MC sample.The efficiencies to select a c or b tagged jet <strong>in</strong> data are summarized <strong>in</strong> Table 5.3 <strong>for</strong> a CHAOScut on 1.65. The ratio of data efficiency to Monte Carlo simulation efficiency provides <strong>the</strong> scale
Chapter 5. Heavy Flavor Tagg<strong>in</strong>g 751000]Jets [×30 Muon-jet+Tag-jetData25Light20Charm1000]Jets [×43.532.5Muon-jet+Tag-jetDataLightCharm15Bottom2Bottom1051.510.500 1 2 3 4 5 62Vertex mass [GeV/c]00 1 2 3 4 5 62Vertex mass [GeV/c]Figure 5.9: Vertex mass distributions <strong>in</strong> <strong>the</strong> medium-P T muon sample with fitted flavour templates from a HFmultijet sample, be<strong>for</strong>e (left) and after (right) <strong>the</strong> cut on CHAOS output at 1.65.factor (SF CHAOS ), that is used to correct <strong>the</strong> MC-based predictions to match <strong>the</strong> efficiency asmeasured <strong>in</strong> data.c jets b jetsEff. (Data) 0.346 ± 0.052 0.073 ± 0.014SF CHAOS 1.01 ± 0.15 1.14 ± 0.22Table 5.3: Efficiency select<strong>in</strong>g c and b tagged jets and scale factor (SF CHAOS ) <strong>for</strong> sum of <strong>the</strong> outputs CHAOScut of 1.65.In <strong>the</strong> particular case of light jets falsely tagged as heavy flavor, <strong>the</strong> scale factor is notneeded, s<strong>in</strong>ce <strong>the</strong>ir contribution is estimated directly from data. However, <strong>the</strong> efficiency <strong>for</strong> <strong>the</strong>CHAOS cut is computed from MC, be<strong>in</strong>g 4.9%.
76 5.4. CHAOS Efficiency and Scale Factors
Chapter 6<strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated BottomSquarkThis chapter describes <strong>the</strong> search <strong>for</strong> bottom squarks (˜b) produced though glu<strong>in</strong>o (˜g) decay [93].We look <strong>for</strong> glu<strong>in</strong>o pair production p¯p → ˜g˜g, where <strong>the</strong> glu<strong>in</strong>o decays to ˜g → b˜b, with <strong>the</strong>subsequent sbottom decay to a b quark and <strong>the</strong> lightest neutral<strong>in</strong>o ( ˜χ 0 ), ˜b → b ˜χ 0 . The neutral<strong>in</strong>ois taken to be <strong>the</strong> Lightest Supersymetric particle and R-parity conservation is assumed.There<strong>for</strong>e, <strong>the</strong> glu<strong>in</strong>o signature is 4 b-jets and large miss<strong>in</strong>g transverse energy.The <strong>the</strong>oretical motivation is described <strong>in</strong> chapter 2, section 2.3.1. In <strong>the</strong> follow<strong>in</strong>g sections,<strong>the</strong> analysis procedure, techniques, and result are discussed.6.1 Dataset and Basic SelectionThe described analysis is based on 2.5 fb −1 of CDF Run II data collected between March 2003and April 2008.The data were collected with <strong>the</strong> three-level logic trigger MET45. A sequence of cuts on<strong>the</strong> / E T is required at each level. At Level 1 it requires / E T above 25 GeV, at Level 2 it requires/E T above 35 GeV and at Level 3 it requires / E T above 45 GeV.Events computed <strong>in</strong> <strong>the</strong> present analysis are required to have a reconstructed vertex withz-position with<strong>in</strong> 60 cm of <strong>the</strong> nom<strong>in</strong>al <strong>in</strong>teraction po<strong>in</strong>t, / E T ≥ 70 GeV and track<strong>in</strong>g activityconsistent with <strong>the</strong> energy measured <strong>in</strong> <strong>the</strong> calorimeter to reject cosmics and beam-halo background.Two or more jets are required to accept <strong>the</strong> event. Jets are def<strong>in</strong>ed us<strong>in</strong>g a cone-based77
78 6.2. Trigger Efficiencyalgorithm [89] with radius 0.4 and required to have a transverse energy above 25 GeV and apseudorapidity |η| ≤ 2.4. At least one of <strong>the</strong> jets is required to be central (|η| ≤ 0.9) and <strong>the</strong> jetwith <strong>the</strong> highest transverse energy must satisfy E T ≥ 35 GeV. Table 6.1 shows <strong>the</strong> list of basiccuts applied <strong>in</strong> <strong>the</strong> analysis.Basic cuts/E T quality cuts (section 4.5)At least 2 jetsE T,jets > 25 GeV|η jets | ≤ 2.4E T,j1 ≥ 35 GeV/E T > 70 GeVTable 6.1: Basic selection applied <strong>in</strong> <strong>the</strong> analysis.S<strong>in</strong>ce it is expected a 4 b-jets f<strong>in</strong>al state, two categories are made by requir<strong>in</strong>g only one of<strong>the</strong> jets or at least two jets to be tagged as orig<strong>in</strong>at<strong>in</strong>g from a heavy-flavour quark. In order toidentify jets orig<strong>in</strong>at<strong>in</strong>g from a b-quark, <strong>the</strong> SecVtx tagg<strong>in</strong>g algorithm (section 5.1) is used. Thedouble tag category provides much more sensitivity than <strong>the</strong> s<strong>in</strong>gle tag, <strong>the</strong>re<strong>for</strong>e <strong>the</strong> <strong>for</strong>mer isused to extract <strong>the</strong> limits and <strong>the</strong> latter is used to provide an additional control sample.6.2 Trigger EfficiencyThis section describes <strong>the</strong> trigger efficiency of <strong>the</strong> MET45 path computed <strong>for</strong> <strong>the</strong> analysis. Theefficiency is obta<strong>in</strong>ed us<strong>in</strong>g data and applied to <strong>the</strong> Monte Carlo predictions <strong>for</strong> signal andbackgrounds.A sequence of cuts on E / T are required at each trigger level <strong>in</strong> <strong>the</strong> path under study. Theresolution of <strong>the</strong> computed E / T <strong>in</strong>creases with <strong>the</strong> trigger decision level:• Level 1: / E T > 25 GeV• Level 2: / E T > 35 GeV• Level 3: / E T > 45 GeV
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 79To compute <strong>the</strong> f<strong>in</strong>al trigger efficiency we parametrize <strong>the</strong> trigger turn-on at each level us<strong>in</strong>gfour different samples, shown <strong>in</strong> Table 6.2.Sample descriptionMuon sample with p T > 18 GeV requirementJet sample requir<strong>in</strong>g at least one jet with E T > 50 GeVJet sample requir<strong>in</strong>g at least one jet with E T > 20 GeV/E T requir<strong>in</strong>g 25 GeV and prescaledCDF nameHIGH PT MUONJET50JET20MET Back-upTable 6.2: Samples used <strong>for</strong> trigger studies.Us<strong>in</strong>g <strong>the</strong> parameterization of all <strong>the</strong> considered levels and samples, we compute <strong>the</strong> totalefficiency of <strong>the</strong> path by multiply<strong>in</strong>g <strong>the</strong> fitted functions, at <strong>the</strong> different levels, <strong>for</strong> each sample.We consider that <strong>the</strong> muon sample is <strong>the</strong> one closest to <strong>the</strong> selection of signal events conta<strong>in</strong><strong>in</strong>greal E / T . There<strong>for</strong>e, it is taken as <strong>the</strong> central prediction <strong>for</strong> <strong>the</strong> efficiency.The o<strong>the</strong>r predictions are used to estimate <strong>the</strong> uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> turn-on parameterization. Itshould be noted that <strong>the</strong> precision <strong>in</strong> <strong>the</strong> fit is larger than <strong>the</strong> differences among <strong>the</strong> results obta<strong>in</strong>edby us<strong>in</strong>g <strong>the</strong> different samples. We quote <strong>the</strong> follow<strong>in</strong>g uncerta<strong>in</strong>ty as a parameterizationof <strong>the</strong> relative uncerta<strong>in</strong>ty.⎧ [ ] 3∆ǫ/ǫ( E / ⎨0.07 · 90− /ETif E / 30 T < 90 GeV,T ) =⎩0.00 if E / T 90 GeV.Due to <strong>the</strong> large grow<strong>in</strong>g term, motivated by <strong>the</strong> differences with <strong>the</strong> jet samples, <strong>the</strong> useof <strong>the</strong> sample <strong>for</strong> E / T < 50 − 60 GeV is clearly discouraged. In that region a more sophisticatedmulti-variable parameterization is needed to reduce <strong>the</strong> systematic uncerta<strong>in</strong>ty due to <strong>the</strong>possible <strong>in</strong>fluence of <strong>the</strong> topology <strong>in</strong> <strong>the</strong> selection. For this purpose, more suitable triggers areavailable.Figure. 6.1 shows <strong>the</strong> trigger turn-on efficiency as a function of E / T . The turn-on efficiencyis obta<strong>in</strong>ed multiply<strong>in</strong>g <strong>the</strong> fitted functions computed at each trigger level. Four different triggerturn-on functions are shown and <strong>the</strong> ratio of this functions to <strong>the</strong> central one (extracted from <strong>the</strong>muon sample). In <strong>the</strong> ratio, we compare <strong>the</strong> measured differences with <strong>the</strong> estimated uncerta<strong>in</strong>tyand confirm that <strong>the</strong> uncerta<strong>in</strong>ty covers <strong>the</strong> difference among <strong>the</strong> samples.It should be noted that <strong>the</strong> parameterization from <strong>the</strong> MET Back-up sample has a small biasdue to <strong>the</strong> fact that no function at Level 1 was fitted. However, s<strong>in</strong>ce <strong>the</strong> ma<strong>in</strong> effect <strong>in</strong> <strong>the</strong> region
80 6.3. Monte Carlo Signal SamplesEfficiency10.8MET-45 Trigger PathMuon sample0.6MET-BACKUP sampleJET-50 sample0.4JET-20 sample0.2Ratio1.21.110.90.81.2Ratio to reference and uncerta<strong>in</strong>ty20 40 60 80 100 120 140E T[GeV]Figure 6.1: Total efficiency <strong>for</strong> <strong>the</strong> MET45 Trigger Path as obta<strong>in</strong>ed from <strong>the</strong> several samples we are us<strong>in</strong>g <strong>in</strong>this study. The plot below shows <strong>the</strong> ratio to <strong>the</strong> efficiency obta<strong>in</strong>ed with <strong>the</strong> HIGH PT MUON sample, whichwe consider our central reference. The yellow area displays <strong>the</strong> size of <strong>the</strong> uncerta<strong>in</strong>ty we quote on <strong>the</strong> triggerefficiency.of <strong>in</strong>terest is com<strong>in</strong>g from <strong>the</strong> Level 2 and Level 3 turn-on functions, <strong>the</strong> effect is negligible.We use <strong>the</strong> parameterization obta<strong>in</strong>ed from <strong>the</strong> HIGH PT MUON sample and <strong>the</strong> quoteduncerta<strong>in</strong>ty, to weight <strong>the</strong> MC events <strong>in</strong> <strong>the</strong> several regions under study.6.3 Monte Carlo Signal SamplesThe signal predictions are obta<strong>in</strong>ed by comput<strong>in</strong>g <strong>the</strong> acceptance us<strong>in</strong>g <strong>the</strong> PYTHIA [62] eventgenerator normalized to <strong>the</strong> NLO production cross section determ<strong>in</strong>ed with PROSPINO eventgenerator [61] and <strong>the</strong> CTEQ6M [64, 65] parton distribution functions.Several signal Monte Carlo samples are generated and passed through <strong>the</strong> detector simu-
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 81lation <strong>in</strong> order to cover <strong>the</strong> phase space under study as a function of <strong>the</strong> sbottom and glu<strong>in</strong>omasses. These samples are generated sett<strong>in</strong>g explicitly <strong>the</strong> SUSY parameters of <strong>the</strong> model,which only affects <strong>the</strong> masses of <strong>the</strong> <strong>in</strong>volved particles s<strong>in</strong>ce <strong>the</strong> production process is via <strong>the</strong>strong <strong>in</strong>teraction and all <strong>the</strong> decay branch<strong>in</strong>g ratio are set to 100%. The glu<strong>in</strong>o mass is variedbetween 240 GeV/c 2 and 400 GeV/c 2 and <strong>the</strong> sbottom masses from 150 GeV/c 2 to 350 GeV/c 2 .The neutral<strong>in</strong>o mass is fixed to 60 GeV/c 2 , while <strong>the</strong> squark mass is fixed to 500 GeV/c 2 .The po<strong>in</strong>ts generated are shown <strong>in</strong> <strong>the</strong> figure 6.2 along with <strong>the</strong> previous limit by a similaranalysis [63], <strong>the</strong> excluded region by <strong>the</strong> sbottom-pair production analysis made by DØ [94],and <strong>the</strong> region excluded by CDF Run I [95].)2Sbottom Mass (GeV/c350300250200150100Generated MC po<strong>in</strong>ts2M(∼χ) = 60 GeV/cM(~q) = 500 GeV/c1→ bb ~ g ~2k<strong>in</strong>ematically <strong>for</strong>bidden-1Run II 156 pbExcluded Limit-1DÊ Run II 310 pbSbottom Pair ProductionExcluded LimitCDF Run I excluded200 250 300 350 4002Glu<strong>in</strong>o Mass (GeV/c)Figure 6.2: SUSY po<strong>in</strong>ts (blue squares) generated with PYTHIA showed <strong>in</strong> <strong>the</strong> m(˜g)-m(˜b) plane. Previouslimit, <strong>the</strong> excluded region by <strong>the</strong> sbottom-pair production analysis made by DØ , and <strong>the</strong> region excluded by CDFRun I are shown.6.4 Background ProcessesSeveral SM processes, produced at Tevatron, have a f<strong>in</strong>al state that mimic <strong>the</strong> signal under study.Events selected <strong>in</strong> <strong>the</strong> analysis have as ma<strong>in</strong> characteristics: large / E T , large jet multiplicity,heavy flavor jets, and no leptons.
82 6.4. Background ProcessesDom<strong>in</strong>ant SM backgrounds are top-quark pair-production and s<strong>in</strong>gle top-quark production,electroweak boson and diboson production, heavy-flavor multijet production, and light-flavorjets falsely tagged as b jets (mistags). The latter two background contributions are estimatedfrom data. The PYTHIA event generator is used to estimate <strong>the</strong> rema<strong>in</strong><strong>in</strong>g backgrounds. For <strong>the</strong>event generation <strong>the</strong> CTEQ5L [96] parton distribution functions were used. Events are passedthrough <strong>the</strong> GEANT3-based [97] CDF II detector simulation and weighted by <strong>the</strong> probabilitythat <strong>the</strong>y would pass <strong>the</strong> trigger as determ<strong>in</strong>ed <strong>in</strong> <strong>in</strong>dependent data samples.In order to test <strong>the</strong> ability to model <strong>the</strong> backgrounds, and also to compute <strong>the</strong> data-drivenones, several control regions are def<strong>in</strong>e as described <strong>in</strong> section 6.5.6.4.1 Top ProductionTop-quark pair-production and s<strong>in</strong>gle top-quark production are considered as backgrounds <strong>in</strong>this analysis. Both contributions are measurable <strong>in</strong> <strong>the</strong> signal region. The top-quark productionis not only most significant because of its larger cross section, but ra<strong>the</strong>r, become one of <strong>the</strong>largest backgrounds because of its high jet multiplicity and <strong>the</strong> presence of two b quarks <strong>in</strong> <strong>the</strong>f<strong>in</strong>al state.The s<strong>in</strong>gle top-quark event yields are normalized to <strong>the</strong> <strong>the</strong>oretical cross sections [98]. Weuse <strong>the</strong> top-quark pair production cross section of σ t¯t = 7.3 ± 0.8 pb [99], as measured byCDF II <strong>in</strong> 2006.6.4.2 W/Z and Diboson ProductionW/Z and diboson events are negligible <strong>in</strong> <strong>the</strong> signal region after <strong>the</strong> requirement of high jetmultiplicity (3 or more jets). However, without this requirement, as it happens <strong>in</strong> one of <strong>the</strong>signal regions, <strong>the</strong>se processes become important and comparable with all <strong>the</strong> o<strong>the</strong>r sources ofbackground.The event yields <strong>for</strong> <strong>the</strong> electroweak boson samples are normalized to <strong>the</strong> lead<strong>in</strong>g order crosssection provided by PYTHIA, scaled by 1.4 to account <strong>for</strong> higher order (NLO) corrections. Dueto <strong>the</strong> limited ability of PYTHIA to simulate multijet environments, a 40% uncerta<strong>in</strong>ty [100] isassigned <strong>for</strong> <strong>the</strong> extracted yields of events with a W or Z boson and jets.The diboson event yields are normalized to <strong>the</strong> <strong>the</strong>oretical NLO cross sections [101, 102].
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 836.4.3 MistagsThe mistags are light-flavor jets falsely tagged as heavy flavor jets. Although <strong>the</strong> mistag efficiencyis two orders of magnitude smaller than <strong>the</strong> heavy flavor tagg<strong>in</strong>g efficiency, <strong>the</strong> largecross section of processes produc<strong>in</strong>g light flavor jets makes <strong>the</strong> mistag background one of <strong>the</strong>largest <strong>in</strong> <strong>the</strong> s<strong>in</strong>gle-tag data sample, and even <strong>in</strong> <strong>the</strong> double-tag data sample, <strong>for</strong> some k<strong>in</strong>ematicselections.The way <strong>in</strong> which <strong>the</strong> mistag matrix is computed and applied, is expla<strong>in</strong>ed <strong>in</strong> detail <strong>in</strong>section 5.2.6.4.4 Heavy-Flavor Multijet ProductionHeavy-flavor multijet events have a cross section which is several orders of magnitude largerthan any o<strong>the</strong>r background. These processes produce E / T if a heavy-flavor quark (b or c) producesa semi-leptonic decay. Mismeasured jets also produce imbalance <strong>in</strong> <strong>the</strong> total transverseenergy, caus<strong>in</strong>g <strong>the</strong> <strong>in</strong>clusion of <strong>the</strong>se events <strong>in</strong> <strong>the</strong> signal region. While <strong>the</strong> probability of amismeasurement is small, <strong>the</strong> large cross section of HF multijet events makes <strong>the</strong>m <strong>the</strong> ma<strong>in</strong>background.Due to <strong>the</strong> large cross section of <strong>the</strong> HF multijet production, <strong>the</strong> amount of MC simulatedevents needed to model <strong>the</strong> background is huge. To generate such a sample, a large amountof <strong>in</strong><strong>for</strong>matic resources should be used dur<strong>in</strong>g months. For this reason, a data driven methodbecomes mandatory to estimate this background.To estimate <strong>the</strong> HF multijet background from data, we have developed a multijet tag rateestimator (MUTARE) which is fully described <strong>in</strong> <strong>the</strong> next section 6.4.5.6.4.5 MUTARE MethodThe MUltijet TAg-Rate Estimator (MUTARE) is a method to estimate <strong>the</strong> HF multijet backgroundfrom data, explicitly created <strong>for</strong> this analysis but with a broad spectrum of usage.The method basel<strong>in</strong>e is well known <strong>in</strong> experimental physics. Based on <strong>the</strong> idea of a objectratebe<strong>in</strong>g constant among different samples, <strong>the</strong> key of <strong>the</strong> method is to select <strong>the</strong> appropriatesobjects (numerator) and proto-objects (denom<strong>in</strong>ator). The objects are, obviously a subsampleof <strong>the</strong> proto-objects. In <strong>the</strong> particular case of MUTARE <strong>the</strong> rate is def<strong>in</strong>e as:
84 6.4. Background ProcessesR =HF tagged jetsTaggable jets(6.1)where HF tagged jets are <strong>the</strong> objects we want to estimated from a proto-object population,taggable jets. The sample used to compute <strong>the</strong> rate has to pure enough <strong>in</strong> <strong>the</strong> desired events tocompute <strong>the</strong> rate with precision. As a sophistication of <strong>the</strong> simplest object-rate method, if <strong>the</strong>rate is parametrized on several variables, <strong>the</strong> rate becomes a matrix <strong>in</strong>stead of a s<strong>in</strong>gle factor.In summary, MUTARE parametrizes <strong>the</strong> probability of a taggable jet to become tagged.This probability is computed <strong>in</strong> high purity multijet sample (section 6.5) and applied <strong>in</strong> o<strong>the</strong>rsamples assum<strong>in</strong>g that <strong>the</strong> ratio, R mutare , does not change with<strong>in</strong> <strong>the</strong> samples.The practical implementation of MUTARE <strong>in</strong> <strong>the</strong> analysis is based on a three-dimensionaltag-rate matrix applied to each jet <strong>in</strong> an event follow<strong>in</strong>g a parametrization on E T , |η| and <strong>the</strong>scalar sum of E T of all jets <strong>in</strong> <strong>the</strong> event. Each element of <strong>the</strong> matrix is computed <strong>in</strong> a multijetenhanced sample as:R MUTARE = N tags − N mistags − N MCtagsN taggable − N MCtaggable(6.2)where N tags is <strong>the</strong> number of tagged jets, N mistags is <strong>the</strong> number of mistags, Ntags MC is <strong>the</strong> numberof tagged jets from non-multijet production computed from MC, N taggable is <strong>the</strong> number of taggablejets, and Ntaggable MC is <strong>the</strong> number of taggable jets from non-multijet production computedfrom MC. Jets are def<strong>in</strong>ed as taggable if ETraw >10 GeV, η
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 856.5 Control RegionsTo avoid potential biases when search<strong>in</strong>g <strong>for</strong> new physics we perfom a “bl<strong>in</strong>d search”. To besure about our predictions’ reliability, we test <strong>the</strong> various background contributions <strong>in</strong> dist<strong>in</strong>ctcontrol regions that are def<strong>in</strong>ed a priori, and <strong>in</strong> which <strong>the</strong> expectation <strong>for</strong> signal is negligiblewhen compared to <strong>the</strong> background and to <strong>the</strong> signal sample. The three control regions usedto check <strong>the</strong> SM prediction are denoted as HF multijet, lepton, and pre-optimization regions.All <strong>the</strong> basic selection cuts showed <strong>in</strong> Table 6.1 are required. In addiction, SecVtx algorithm isapplied requir<strong>in</strong>g s<strong>in</strong>gle and double b-tagged events <strong>in</strong> each region.The pre-optimization control region is def<strong>in</strong>ed as a signal-like region without optimizationcuts. Hence, this region is <strong>the</strong> benchmark <strong>for</strong> <strong>the</strong> optimization process. The o<strong>the</strong>r two regionsare def<strong>in</strong>ed to be orthogonal to <strong>the</strong> pre-optimization one. The HF multijet region is a multijetenrichedregion, requir<strong>in</strong>g <strong>the</strong> second lead<strong>in</strong>g jet to be aligned with <strong>the</strong> E / T . In this region,<strong>the</strong> MUTARE matrix is computed. The lepton region, <strong>in</strong> which at least one isolated leptonis required, is used to test <strong>the</strong> electroweak W/Z boson and top backgrounds, where <strong>the</strong>y areimportant contributions. The explicit cuts def<strong>in</strong><strong>in</strong>g each region are:• HF multijet control region: second lead<strong>in</strong>g E T jet (⃗j 2 ) aligned with <strong>the</strong> ⃗ / ET , wherealigned means ∆φ( ⃗ / ET ,⃗j 2 ) ≤ 0.4 rad.• Lepton control region: second lead<strong>in</strong>g E T jet not aligned with <strong>the</strong> ⃗ / ET (∆φ( ⃗ / ET ,⃗j 2 ) ≥0.7 rad) and at least one isolated lepton (as def<strong>in</strong>ed <strong>in</strong> section 4.2).• Pre-optimization control region: lead<strong>in</strong>g and second-lead<strong>in</strong>g E T jets not aligned with<strong>the</strong> ⃗ / ET , required lead<strong>in</strong>g jet E T > 50 GeV, and to have no identified leptons.Predicted total numbers of events and distributions of k<strong>in</strong>ematic variables such as jet E T , <strong>the</strong>track multiplicity, and <strong>the</strong> E / T have been studied and found to be <strong>in</strong> agreement with observations<strong>in</strong> <strong>the</strong> three control regions. As an example, <strong>the</strong> E / T and <strong>the</strong> first jet E T distributions <strong>in</strong> <strong>the</strong> threecontrol regions are shown <strong>in</strong> figure 6.3 <strong>for</strong> <strong>the</strong> s<strong>in</strong>gle b-tag analysis, and <strong>in</strong> figure 6.4 <strong>for</strong> <strong>the</strong>double b-tag analysis.The background contributions to <strong>the</strong> number of expected exclusive s<strong>in</strong>gle b-tagged and <strong>in</strong>clusivedouble b-tagged events and <strong>the</strong> observed events <strong>in</strong> <strong>the</strong> control regions are summarized<strong>in</strong> Table 6.3 and Table 6.4.
86 6.5. Control RegionsRegions Multijet Lepton Pre-optimizationElectroweak bosons 88 ± 37 152 ± 57 417 ± 162Top-quark 65 ± 16 405 ± 93 523 ± 119Light-flavor jets 5430 ± 2226 190 ± 78 919 ± 377HF Multijets 9741 ± 4870 195 ± 97 1660 ± 830Total expected 15325 ± 5355 943 ± 166 3520 ± 934Observed 15390 890 3525Table 6.3: Comparison of <strong>the</strong> total number of expected events with total uncerta<strong>in</strong>ties and observed s<strong>in</strong>gle b-tagged events <strong>in</strong> <strong>the</strong> control regions.Regions Multijet Lepton Pre-optimizationElectroweak bosons 10 ± 7 21 ± 14 33 ± 22Top-quark 19 ± 6 111 ± 34 146 ± 45Light-flavor jets 225 ± 49 8 ± 2 57 ± 12HF Multijets 839 ± 419 25 ± 12 270 ± 135Total expected 1093 ± 422 165 ± 39 506 ± 144Observed 1069 159 451Table 6.4: Comparison of <strong>the</strong> total number of expected events with total uncerta<strong>in</strong>ties and observed doubleb-tagged events <strong>in</strong> <strong>the</strong> control regions.
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 87Events/12 GeV18001600140012001000CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive MultijetsEvents/8 GeV410310210CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive Multijets80010600400120000 50 100 150 200 250 300 350 400 450E T,j1 (GeV)-1100 50 100 150 200 250 300 350 400E T(GeV)Events/12 GeV160140120100CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive MultijetsEvents/8 GeV21010CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive Multijets80601402000 50 100 150 200 250 300 350E T,j1 (GeV)-1100 50 100 150 200 250 300 350 400E T(GeV)CDF Run II-1∫L dt=2.5 fbCDF Run II-1∫L dt=2.5 fbEvents/12 GeV600500400300CDF DataEWK BosonsTOPMistagsInclusive MultijetsEvents/8 GeV310CDF Data21010EWK BosonsTOPMistagsInclusive Multijets200110000 50 100 150 200 250 300 350 400 450E T,j1 (GeV)-1100 50 100 150 200 250 300 350 400E T(GeV)Figure 6.3: Lead<strong>in</strong>g jet E T , and / E T <strong>in</strong> <strong>the</strong> HF multijet (top), lepton (middle) and pre-optimization (bottom)control regions with s<strong>in</strong>gle b-tagged events.
88 6.5. Control RegionsEvents/16 GeV18016014012010080604020CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive Multijets00 50 100 150 200 250 300 350 400 450E T,j1 (GeV)Events/8 GeV21010-1101CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive Multijets0 50 100 150 200 250 300 350 400E T(GeV)Events/16 GeV40353025CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive MultijetsEvents/8 GeV10CDF Run II-1∫L dt=2.5 fbCDF DataEWK BosonsTOPMistagsInclusive Multijets2015110500 50 100 150 200 250 300 350E T,j1 (GeV)-1100 50 100 150 200 250 300 350 400E T(GeV)CDF Run II-1∫L dt=2.5 fbCDF Run II-1∫L dt=2.5 fbEvents/16 GeV12010080CDF DataEWK BosonsTOPMistagsInclusive MultijetsEvents/8 GeV21010CDF DataEWK BosonsTOPMistagsInclusive Multijets604012000 50 100 150 200 250 300 350 400E T,j1 (GeV)-1100 50 100 150 200 250 300 350 400E T(GeV)Figure 6.4: Lead<strong>in</strong>g jet E T and / E T <strong>in</strong> <strong>the</strong> HF multijet (top), lepton (middle) and pre-optimization (bottom)control regions with double b-tagged events.
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 896.6 Signal OptimizationAn optimization process via two neural networks (NN) is made <strong>in</strong> order to reduce <strong>the</strong> backgroundcontribution and enhance <strong>the</strong> sensitivity to <strong>the</strong> signal. We choose two reference signalpo<strong>in</strong>ts based on values of ∆ m ≡ m(˜g) − m(˜b) and per<strong>for</strong>m <strong>the</strong> same optimization procedure.The two po<strong>in</strong>ts are chosen <strong>in</strong> a region not excluded by previous analyses and represent<strong>in</strong>g twodifferent k<strong>in</strong>ematic behaviors:• Large ∆m optimization ⇒ M(˜g) = 335 GeV/c 2 , M(˜b) = 260 GeV/c 2• Small ∆m optimization ⇒ M(˜g) = 335 GeV/c 2 , M(˜b) = 315 GeV/c 2The optimization process takes as benchmark <strong>the</strong> pre-optimization selection. In addictionto <strong>the</strong> cuts required <strong>in</strong> <strong>the</strong> pre-optimization region, <strong>for</strong> <strong>the</strong> large ∆m optimization a cut on <strong>the</strong>number of jets greater than two is applied. For <strong>the</strong> small ∆m optimization this cut is not appliedbecause of <strong>the</strong> small amount of momentum available <strong>in</strong> <strong>the</strong> glu<strong>in</strong>o decay, which translates <strong>in</strong>toa lower jet multiplicity <strong>in</strong> <strong>the</strong> f<strong>in</strong>al estate.Over this selection, two consecutive Neural Networks are applied and an event selection ismade by cutt<strong>in</strong>g on its outputs:• First Neural Network: called multijet-NN, is applied to dist<strong>in</strong>guish between glu<strong>in</strong>o signaland HF multijets background. This Neural Network is tra<strong>in</strong>ed with signal MC versustaggable jets (QCD-like) <strong>in</strong> <strong>the</strong> pre-optimization region with one exclusive tag <strong>in</strong> order tohave enough statistics.• Second Neural Network: called top-NN, is applied to remove <strong>the</strong> rema<strong>in</strong><strong>in</strong>g backgrounds,ma<strong>in</strong>ly top-pair production, and it is tra<strong>in</strong>ed with signal MC versus top pair MC also over<strong>the</strong> pre-optimization region with one exclusive tag after apply<strong>in</strong>g <strong>the</strong> cut on <strong>the</strong> previousmultijet-NN.The previous optimization process is applied over <strong>the</strong> two chosen signal po<strong>in</strong>ts requir<strong>in</strong>gone exclusive and two <strong>in</strong>clusive b-tagged events.The architecture used <strong>in</strong> both QCD multijet-NN and top-NN, <strong>the</strong> per<strong>for</strong>mace, and <strong>the</strong> resultsof each neural network is described <strong>in</strong> <strong>the</strong> follow<strong>in</strong>g sections. The output of each Neural Network,used as a dicrim<strong>in</strong>ant, is distributed with<strong>in</strong> an <strong>in</strong>terval of −1 to 1, where <strong>the</strong> backgroundpeaks at −1 and <strong>the</strong> signal peaks at 1.
90 6.6. Signal Optimization6.6.1 Neural Networks ArchitectureThe Neural Networks used <strong>in</strong> <strong>the</strong> present analysis are tra<strong>in</strong>ed and tested us<strong>in</strong>g <strong>the</strong> TMVA package[103]. The same structure is used <strong>for</strong> all <strong>the</strong> Neural Networks, consist<strong>in</strong>g <strong>in</strong> two layers withN+1 and N nodes respectively, where N is <strong>the</strong> number of variables, and one output node. As anarchitecture example, figure 6.5 shows <strong>the</strong> multijet-NN <strong>in</strong> <strong>the</strong> large ∆m optimization.metleadjet_etsecondjet_etdphi_met_1jetdphi_met_2jetthirdjet_etdphi_met_3jethtBias nodeLayer 0 Layer 1 Layer 2 Layer 3Figure 6.5: neural network’s architecture used <strong>for</strong> tra<strong>in</strong><strong>in</strong>g. In particular <strong>for</strong> <strong>the</strong> multijet-NN <strong>in</strong> <strong>the</strong> large ∆moptimization.The same set of variables, all of <strong>the</strong>m related to <strong>the</strong> jet and E / T k<strong>in</strong>ematics, are used <strong>in</strong><strong>the</strong> multijet-NN and top-NN. Depend<strong>in</strong>g on <strong>the</strong> optimization, large or small ∆m, <strong>the</strong> set ofvariables is different due to <strong>the</strong> cut on number of jets applied <strong>in</strong> each selection. Table 6.5 shows<strong>the</strong> variables used <strong>in</strong> each optimization. All <strong>the</strong> variables are well modeled and are found as <strong>the</strong>ones provid<strong>in</strong>g <strong>the</strong> best separation power as is shown <strong>in</strong> appendix A.6.6.2 Multijet Neural NetworkApply<strong>in</strong>g to <strong>the</strong> pre-optimization region <strong>the</strong> multijet-NN we obta<strong>in</strong> <strong>the</strong> outputs showed <strong>in</strong> figure6.6 <strong>for</strong> <strong>the</strong> large ∆m optimization and <strong>for</strong> <strong>the</strong> small ∆m optimization (one exclusive tagand two <strong>in</strong>clusive tags).For all <strong>the</strong> cases showed <strong>in</strong> figure 6.6 we f<strong>in</strong>d 0.8 as an optimal value <strong>for</strong> <strong>the</strong> selection cut.This cut optimizes <strong>the</strong> sensitivity keep<strong>in</strong>g a reasonable amount of signal.
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 91Large ∆m optimization/⃗E TE T,j1Small ∆m optimization/ ⃗ETE T,j1E T,j2E T,j2E T,j3 ∆φ( ⃗ / ET ,⃗j 1 )∆φ( ⃗ / ET ,⃗j 1 ) ∆φ( ⃗ / ET ,⃗j 2 )∆φ( ⃗ / ET ,⃗j 2 ) M<strong>in</strong> ∆φ( ⃗ / ET ,⃗j i )∆φ( ⃗ / ET ,⃗j 3 )summed E T of all <strong>the</strong> jets <strong>in</strong> <strong>the</strong> eventsummed E T of all <strong>the</strong> jets <strong>in</strong> <strong>the</strong> eventTable 6.5: List of <strong>in</strong>put variables used <strong>in</strong> both multijet-NN and top-NN.6.6.3 Top Neural NetworkAt this stage of <strong>the</strong> optimization we apply <strong>the</strong> second neural network, based on top pair discrim<strong>in</strong>ation,to <strong>the</strong> events obta<strong>in</strong>ed after <strong>the</strong> cut on 0.8 on <strong>the</strong> multijet-NN output. The result ofapply<strong>in</strong>g <strong>the</strong> top-NN to this events is shown <strong>in</strong> figure 6.7 <strong>for</strong> <strong>the</strong> large ∆m optimization as wellas <strong>for</strong> <strong>the</strong> small ∆m optimization (one exclusive tag and two <strong>in</strong>clusive tags).We f<strong>in</strong>d 0.6 as an optimal selection cut <strong>in</strong> <strong>the</strong> large ∆m optimization and 0.8 <strong>in</strong> <strong>the</strong> small∆m optimization.Per<strong>for</strong>m<strong>in</strong>g <strong>the</strong> whole optimization process we obta<strong>in</strong> four f<strong>in</strong>al regions, depend<strong>in</strong>g on <strong>the</strong>tagg<strong>in</strong>g requirements, and <strong>the</strong> signal po<strong>in</strong>t used <strong>in</strong> <strong>the</strong> optimization. However, only <strong>the</strong> f<strong>in</strong>alregions requir<strong>in</strong>g two b-tagged jets are used as a f<strong>in</strong>al results due to <strong>the</strong>ir sensitivity. The oneb-tagged events regions are treated as additional control regions.As expected from a “bl<strong>in</strong>d search”, <strong>the</strong> optimization procedure is made over <strong>the</strong> predictions.CDF II data, as shown <strong>in</strong> <strong>the</strong> figures, is plotted once <strong>the</strong> process is f<strong>in</strong>ished.
92 6.6. Signal OptimizationN-Events1000800600CDF Run IIOne exclusive b-tag-1∫L dt=2.5 fb~Signal M(~g)=335, M( b)=260CDF DataEWK BOSONSTOPMistagsInclusive MultijetsN-Events1000800600CDF Run IIOne exclusive b-tag-1∫L dt=2.5 fb~Signal M(~g)=335, M( b)=315CDF DataEWK BOSONSTOPMistagsInclusive Multijets4004002002000-1.5 -1 -0.5 0 0.5 1 1.5NN Output0-1.5 -1 -0.5 0 0.5 1 1.5NN OutputN-Events14012010080CDF Run IITwo <strong>in</strong>clusive b-tags-1∫L dt=2.5 fb~Signal M(~g)=335, M( b)=260CDF DataEWK BOSONSTOPMistagsInclusive MultijetsN-Events14012010080CDF Run IITwo <strong>in</strong>clusive b-tags-1∫L dt=2.5 fb~Signal M(~g)=335, M( b)=315CDF DataEWK BOSONSTOPMistagsInclusive Multijets6060404020200-1.5 -1 -0.5 0 0.5 1 1.5NN Output0-1.5 -1 -0.5 0 0.5 1 1.5NN OutputFigure 6.6: Multijet-NN output plots <strong>for</strong> <strong>the</strong> large ∆m (left) and small ∆m (right) optimizations, requir<strong>in</strong>g oneb-tagged (top) or two b-tagged (bottom) events.
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 93N-Events20 CDF Run II -1L dt=2.5 fbOne exclusive b-tag18~ ~Signal M( g)=335, M( b)=26016CDF DataEWK BOSONS14 TOPMistags12 Inclusive Multijets∫N-Events302520CDF Run IIOne exclusive b-tag~ ~Signal M( g)=335, M( b)=315CDF DataEWK BOSONSTOPMistagsInclusive Multijets-1∫L dt=2.5 fb108156104250-1.5 -1 -0.5 0 0.5 1 1.5NN Output0-1.5 -1 -0.5 0 0.5 1 1.5NN OutputN-Events1086CDF Run IITwo <strong>in</strong>clusive b-tagsSignal M(~g)=335, M(CDF DataEWK BOSONSTOPMistagsInclusive Multijets~b)=260-1∫L dt=2.5 fbN-Events1086CDF Run IITwo <strong>in</strong>clusive b-tagsSignal M(~g)=335, M(CDF DataEWK BOSONSTOPMistagsInclusive Multijets~b)=315-1∫L dt=2.5 fb44220-1.5 -1 -0.5 0 0.5 1 1.5NN Output0-1.5 -1 -0.5 0 0.5 1 1.5NN OutputFigure 6.7: Top-NN output plots <strong>for</strong> <strong>the</strong> large ∆m (left) and small ∆m (right) optimizations, requir<strong>in</strong>g oneb-tagged (top) or two b-tagged (bottom) events.
94 6.7. Systematic Uncerta<strong>in</strong>ties6.7 Systematic Uncerta<strong>in</strong>tiesSystematic errors are <strong>the</strong> ma<strong>in</strong> source of uncerta<strong>in</strong>ty <strong>in</strong> this search. Some of <strong>the</strong>se errors affect<strong>the</strong> overall normalization of <strong>the</strong> signal or background templates. This k<strong>in</strong>d of systematic errors,so-called rate systematics, summarize effects that impact <strong>the</strong> number of events <strong>in</strong> <strong>the</strong> signal andbackground templates. However, <strong>the</strong> shapes of <strong>the</strong>se templates are not affected by <strong>the</strong>se sourcesof uncerta<strong>in</strong>ty.Contrarily, some o<strong>the</strong>r systematic uncerta<strong>in</strong>ties make <strong>the</strong> shapes of <strong>the</strong> templates to vary.This second k<strong>in</strong>d of systematic errors, named shape systematics, could also affect <strong>the</strong> overallnumber of events. These differences <strong>in</strong> shape are accounted <strong>for</strong> by produc<strong>in</strong>g sets of shiftedtemplates <strong>in</strong> parallel to <strong>the</strong> nom<strong>in</strong>al ones.The systematic uncerta<strong>in</strong>ties on <strong>the</strong> signal and <strong>the</strong> background predictions, tak<strong>in</strong>g <strong>in</strong>to accountcorrelated and uncorrelated uncerta<strong>in</strong>ties, are studied.• Jet Energy Scale [90]: A systematic error <strong>in</strong> <strong>the</strong> calorimeter energy scale affect <strong>the</strong> totaltransverse energy on <strong>the</strong> jets. The effect <strong>in</strong> <strong>the</strong> f<strong>in</strong>al regions varies <strong>in</strong> a range between 5%and 25% depend<strong>in</strong>g on <strong>the</strong> optimization.• b-tagg<strong>in</strong>g Scale Factor: The difference between data and MC <strong>in</strong> b-tagg<strong>in</strong>g efficiency( 5%) is taken as systematic uncerta<strong>in</strong>ty. The result<strong>in</strong>g uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> f<strong>in</strong>al regionsvaries between 1.5% and 5% depend<strong>in</strong>g on <strong>the</strong> optimization.• Mistag estimation: The systematic error assigned to <strong>the</strong> tag rate matrix is 4.8%.• Lum<strong>in</strong>osity: The systematic uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> lum<strong>in</strong>osity is taken to be 6%, affect<strong>in</strong>g to<strong>the</strong> normalization of all <strong>the</strong> MC estimated backgrounds.• ISR/FSR: The uncerta<strong>in</strong>ty associated with <strong>the</strong> <strong>in</strong>itial and f<strong>in</strong>al state radiation was evaluatedby generat<strong>in</strong>g sample with more/less ISR/FSR. The effect <strong>in</strong> <strong>the</strong> f<strong>in</strong>al regions varies<strong>in</strong> a range between 2% and 5% depend<strong>in</strong>g on <strong>the</strong> optimization.• PDF: The PDF uncerta<strong>in</strong>ty has been determ<strong>in</strong>ed to be 2% on <strong>the</strong> acceptance.• QCD Multijet Background: We assign a conservative 50% uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> predictionbased on <strong>the</strong> variation observed when matrix def<strong>in</strong>ition is changed.• Top-Pair Production cross section: We quote <strong>the</strong> uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> CDF measured value(11%) of <strong>the</strong> top-pair production cross section.
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 95• S<strong>in</strong>gle Top Production cross section: We quote <strong>the</strong> <strong>the</strong>oretical uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> s<strong>in</strong>gletopcross section (13%).• Diboson Production cross section: We quote <strong>the</strong> <strong>the</strong>oretical uncerta<strong>in</strong>ty be<strong>in</strong>g 10% <strong>in</strong> <strong>the</strong>WW and WZ cross sections and 20% <strong>for</strong> <strong>the</strong> ZZ process.• S<strong>in</strong>gle EWK Boson Production cross section: Although <strong>the</strong> cross section <strong>for</strong> Z and Wproduction are known to a high precision, we are us<strong>in</strong>g <strong>the</strong> <strong>in</strong>clusive processes <strong>in</strong> PYTHIAto per<strong>for</strong>m estimations of Z/W +multijet contributions s<strong>in</strong>ce PYTHIA parton shower<strong>in</strong>gdoes not properly reproduce <strong>the</strong> multijet spectrum, we estimate a 40% uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong>predictions.• Top quark mass: In <strong>the</strong> current analysis, <strong>the</strong> t¯t production background is estimated us<strong>in</strong>gMC with a top quark mass of 171.5 GeV/c 2 . S<strong>in</strong>ce our signal optimization is based ona Neural Network tra<strong>in</strong>ed with t¯t processes we <strong>in</strong>clude a systematic error due to <strong>the</strong> toppair neural network output dependence on <strong>the</strong> top quark mass. We compute this errormeasur<strong>in</strong>g <strong>the</strong> number of top-pair events <strong>in</strong> <strong>the</strong> f<strong>in</strong>al selection by us<strong>in</strong>g a top quark massof 174.5 GeV/c 2 . The effect <strong>in</strong> <strong>the</strong> f<strong>in</strong>al regions varies <strong>in</strong> a range between 0.3% and 17%depend<strong>in</strong>g on <strong>the</strong> optimization.6.8 ResultsThe signal region is analyzed after <strong>the</strong> background predictions are determ<strong>in</strong>ed. As describedabove, we f<strong>in</strong>d 0.8 as an optimal value <strong>for</strong> <strong>the</strong> selection cut <strong>for</strong> both multijet-NN outputs and0.6 (0.8) <strong>for</strong> <strong>the</strong> top-NN outputs <strong>in</strong> <strong>the</strong> large (small) ∆m optimization with<strong>in</strong> an <strong>in</strong>terval of −1to 1, where <strong>the</strong> background peaks at −1 and <strong>the</strong> signal peaks at 1. We observe 5 (2) events<strong>for</strong> <strong>the</strong> large (small) ∆m optimization region, where 4.7 ± 1.5 (2.4 ± 0.8) are expected frombackground, as summarized <strong>in</strong> Table 6.6.S<strong>in</strong>ce no significant deviation from <strong>the</strong> SM prediction is observed, <strong>the</strong> results are used tocalculate an exclusion limit <strong>for</strong> <strong>the</strong> cross section of <strong>the</strong> described glu<strong>in</strong>o process. We use aBayesian method to determ<strong>in</strong>e <strong>the</strong> 95% credibility level (C.L.) upper limit on <strong>the</strong> ˜g˜g cross section,assum<strong>in</strong>g a uni<strong>for</strong>m prior probability density. We treat <strong>the</strong> various correlated uncerta<strong>in</strong>tiesas nuisance parameters, which we remove by marg<strong>in</strong>alization, assum<strong>in</strong>g a Gaussian prior distribution.The obta<strong>in</strong>ed limit is such that no more than 8.0 (5.4) events are observed <strong>in</strong> <strong>the</strong> large(small) ∆m signal region. Figure 6.8 shows <strong>the</strong> expected and observed limits as a function of
96 6.8. ResultsOptimizations Large ∆m Small ∆mElectroweak bosons 0.17 ± 0.05 0.5 ± 0.3Top-quark 1.9 ± 1.0 0.6 ± 0.4Light-flavor jets 1.0 ± 0.3 0.6 ± 0.1HF Multijets 1.6 ± 0.8 0.7 ± 0.3Total expected SM 4.7 ± 1.5 2.4 ± 0.8Observed 5 2Optimized ˜g signal 14.9 ± 5.0 8.5 ± 2.8Table 6.6: Number of expected and observed events <strong>in</strong> <strong>the</strong> signal regions. Predictions <strong>for</strong> <strong>the</strong> signal po<strong>in</strong>ts arealso shown. Correlated and uncorrelated uncerta<strong>in</strong>ties <strong>in</strong> <strong>the</strong> total background and expected signal were treatedseparately <strong>in</strong> <strong>the</strong> analysis although <strong>the</strong>y are comb<strong>in</strong>ed here.m(˜g) <strong>for</strong> two values of <strong>the</strong> ˜b quark mass. The expected limit is computed by assum<strong>in</strong>g that <strong>the</strong>observed number of events matches <strong>the</strong> SM expectation <strong>in</strong> each signal region.The glu<strong>in</strong>o production cross section limit is nearly <strong>in</strong>dependent of <strong>the</strong> sbottom mass between250 and 300 GeV/c 2 , and is around 40 fb <strong>for</strong> m(˜g) = 350 GeV/c 2 . In addition, us<strong>in</strong>g <strong>the</strong>assumed model, a 95% C.L. limit is obta<strong>in</strong>ed <strong>in</strong> <strong>the</strong> parameter plane of <strong>the</strong> model. Figure 6.9shows <strong>the</strong> excluded region <strong>in</strong> <strong>the</strong> glu<strong>in</strong>o-sbottom mass plane, compared with <strong>the</strong> results fromprevious analyses [94, 95, 104, 63]. The limit obta<strong>in</strong>ed with <strong>the</strong> present analysis improves <strong>the</strong>results of previous searches us<strong>in</strong>g similar topology and also, under <strong>the</strong> assumptions discussedabove, sets a more str<strong>in</strong>gent limit on <strong>the</strong> sbottom and glu<strong>in</strong>o production than dedicated sbottomsearches <strong>in</strong> <strong>the</strong> region where those particles have similar masses.
Chapter 6. <strong>Search</strong> <strong>for</strong> Glu<strong>in</strong>o-mediated Bottom Squark 97Cross Section [pb]101-1-1CDF Run II (2.5 fb )295% CL limit (m[b ~ ]=250 GeV/c )Expected limit295% CL limit (m[b ~ ]=300 GeV/c )Expected limit~g →~b → b∼χ~bb (100% BR)0(100% BR)10-2pp→~g~g ats=1.96 GeVPROSPINO NLO (CTEQ6M)µ = µ = m(~g)R Fm(~q)=500 GeV/c2m(∼χ02)=60 GeV/c250 300 350 400m(~g) [GeV/c2]Figure 6.8: Observed (solid l<strong>in</strong>es) and expected (dashed l<strong>in</strong>es) 95% C.L. upper limit on <strong>the</strong> glu<strong>in</strong>o cross section(solid l<strong>in</strong>e with band) as a function of <strong>the</strong> glu<strong>in</strong>o mass <strong>for</strong> two assumed values of <strong>the</strong> sbottom mass. The shadedband denotes <strong>the</strong> uncerta<strong>in</strong>ty on <strong>the</strong> NLO ˜g˜g production due to <strong>the</strong> truncated higher-order terms and <strong>the</strong> partondistribution functions.
98 6.8. Results]2Sbottom Mass [GeV/c350-1CDF Run II (2.5 fb )30025020015095% CL limitExpected limitg ~ → bb ~ k<strong>in</strong>ematically <strong>for</strong>bidden-1CDF Run II 156 pbExcluded Region~ ~g → bb (100% BR)~ 0b → b∼χ (100% BR)02m( χ∼) = 60 GeV/c2m(~q) = 500 GeV/c-1D0 Run II 310 pbSbottom Pair ProductionExcluded RegionCDF Run I excluded100200 250 300 350 400Glu<strong>in</strong>o Mass [GeV/c2]Figure 6.9: Excluded region at 95% C.L. <strong>in</strong> <strong>the</strong> m(˜g)-m(˜b) plane <strong>for</strong> a m(˜χ 0 ) = 60 GeV/c 2 , m(˜q) =500 GeV/c 2 . The result is compared to <strong>the</strong> previous results from CDF <strong>in</strong> Run I [104], and Run II [63] anddirect sbottom production by DØ [94].
Chapter 7<strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>toCharm and Neutral<strong>in</strong>oThis chapter describes <strong>the</strong> second analysis presented <strong>in</strong> this <strong>the</strong>sis. We search <strong>for</strong> direct topsquarks (˜t) production, p¯p → ˜t˜t, where <strong>the</strong> stop decays to c˜χ 0 . The neutral<strong>in</strong>o is taken to be<strong>the</strong> Lightest Supersymetric particle (LSP) and R-parity conservation is assumed. There<strong>for</strong>e, <strong>the</strong>stop signature is 2 c-jets and miss<strong>in</strong>g transverse energy.The <strong>the</strong>oretical motivation is described <strong>in</strong> chapter 2, section 2.3.2. In <strong>the</strong> follow<strong>in</strong>g sections<strong>the</strong> analysis procedure, techniques, and result will be discussed.7.1 Dataset and Basic SelectionThe described analysis is based on 2.6 fb −1 of CDF Run II data collected between March 2003and April 2008.The data were collected with <strong>the</strong> three-level logic E / T +jets trigger. A sequence of cuts on <strong>the</strong>/E T is required at each level plus additional cuts requir<strong>in</strong>g two jets at level 2.Events computed <strong>in</strong> <strong>the</strong> analyisis are required to have a reconstructed vertex with z-positionwith<strong>in</strong> 60 cm of <strong>the</strong> nom<strong>in</strong>al <strong>in</strong>teraction po<strong>in</strong>t, / E T ≥ 50 GeV and track<strong>in</strong>g activity consistentwith <strong>the</strong> energy measured <strong>in</strong> <strong>the</strong> calorimeter to reject cosmics and beam-halo background. Twoor more jets are required to accept <strong>the</strong> event. Jets are def<strong>in</strong>ed us<strong>in</strong>g a cone-based algorithm [89]with radius 0.7 and required to have a transverse energy (E T ) above 25 GeV and a pseudorapidity|η| ≤ 2.4. At least one of <strong>the</strong> jets is required to be central (|η| ≤ 0.9) and <strong>the</strong> jet with99
100 7.2. Trigger Efficiency<strong>the</strong> highest transverse energy must satisfy E T ≥ 35 GeV. Table 7.1 shows <strong>the</strong> list of basic cutsapplied <strong>in</strong> <strong>the</strong> analysis.Basic cuts/E T quality cuts (section 4.5)At least 2 jetsE T,jets > 25 GeV|η jets | ≤ 2.4E T,j1 ≥ 35 GeV/E T > 50 GeV∆R(j 1 , j 2 ) > 0.1 radTable 7.1: Basic selection applied <strong>in</strong> <strong>the</strong> analysis.S<strong>in</strong>ce two c jets <strong>in</strong> <strong>the</strong> f<strong>in</strong>al state are expected, one of <strong>the</strong> jets is required to be orig<strong>in</strong>atedfrom a heavy-flavor quark. In order to identify this heavy-flavor jet, <strong>the</strong> loose SecVtx tagg<strong>in</strong>galgorithm is used.7.2 Trigger EfficiencyThis section describes <strong>the</strong> trigger efficiency of <strong>the</strong> MET+JETS path computed <strong>for</strong> <strong>the</strong> analysis.A secuence of cuts are required at each trigger level <strong>in</strong> <strong>the</strong> path under study. The resolutions of<strong>the</strong> quantities <strong>in</strong>volved <strong>in</strong>crease with <strong>the</strong> trigger decision level:• Level 1: E / T > 25 GeV• Level 2: (depend<strong>in</strong>g on <strong>the</strong> period)– L2 TWO JET10 L1 MET25– L2 CJET10 JET10 L1 MET25– L2 CJET10 JET10 L1 MET25 LUMI190– L2 CJET10 JET10 L1 MET25 DPS– L2 MET30 CJET20 JET15 DPS• Level 3: E / T > 35 GeV
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 101The trigger simulation <strong>for</strong> Monte Carlo events is not fully reliable, due to that, <strong>the</strong> triggerefficiency is computed <strong>in</strong> data samples used as reference. Monte Carlo events are weightedaccord<strong>in</strong>g to such efficiency which is a function of <strong>the</strong> k<strong>in</strong>ematic properties of <strong>the</strong> events.Thorough studies has been perfomed to parameterize <strong>the</strong> trigger efficiency <strong>for</strong> <strong>the</strong> datasetused <strong>in</strong> this analysis. This parameterization has been made <strong>in</strong> <strong>the</strong> appropriate variables <strong>for</strong> <strong>the</strong>several requirements of <strong>the</strong> trigger at all <strong>the</strong> levels and was validated us<strong>in</strong>g different referencesamples 7.2.Sample descriptionMuon sample with p T > 18 GeV requirementJet sample requir<strong>in</strong>g at least one jet with E T > 50 GeVJet sample requir<strong>in</strong>g at least one jet with E T > 20 GeV/E T requir<strong>in</strong>g 25 GeV and prescaledCDF nameHIGH PT MUONJET50JET20MET Back-upTable 7.2: Samples used <strong>for</strong> <strong>the</strong> MET+JETS path trigger studies.The f<strong>in</strong>al parameterization, obta<strong>in</strong>ed ma<strong>in</strong>ly us<strong>in</strong>g <strong>the</strong> HIGH-PT MUON sample, is directlyapplicable to <strong>the</strong> <strong>the</strong> analysis, s<strong>in</strong>ce <strong>the</strong> jet selection and E / T reconstruction are identical <strong>in</strong> bothcases. The uncerta<strong>in</strong>ty associated to <strong>the</strong> trigger efficiency has been estimated by cross-check<strong>in</strong>g<strong>the</strong> result<strong>in</strong>g parameterization with <strong>the</strong> jet samples.Regard<strong>in</strong>g <strong>the</strong> parameterization of <strong>the</strong> trigger efficiency, we have improved <strong>the</strong> precision of<strong>the</strong> calculations mak<strong>in</strong>g use of specific parameterizations <strong>in</strong> different k<strong>in</strong>ematic regions. This<strong>in</strong>troduces a bit of complication <strong>in</strong> <strong>the</strong> practical implementation of <strong>the</strong> weight<strong>in</strong>g of MC events,but it clearly allows <strong>the</strong> reduction of <strong>the</strong> uncerta<strong>in</strong>ties.The trigger efficiency consist on six different parameterizations <strong>in</strong> six different k<strong>in</strong>ematicregions, as shown <strong>in</strong> Table 7.3Figure. 7.1 shows one of <strong>the</strong> six trigger turn-on efficiencies as a function of E / T . The turnonefficiency is obta<strong>in</strong>ed multiply<strong>in</strong>g <strong>the</strong> fitted functions computed at each trigger level. Fourdifferent trigger turn-on functions are shown and <strong>the</strong> ratio of this functions to <strong>the</strong> central one(extracted from <strong>the</strong> muon sample).The effect of <strong>the</strong> uncerta<strong>in</strong>ty is small due to <strong>the</strong> k<strong>in</strong>ematic selection per<strong>for</strong>med <strong>in</strong> <strong>the</strong> analysisand to <strong>the</strong> improved parameterization of <strong>the</strong> turn-on applied to <strong>the</strong> MC events.
102 7.2. Trigger EfficiencyK<strong>in</strong>ematic regionsE T,j1 ≤ 50GeV +∆φ( ⃗ / ET ,⃗j 2 ) ≤ 0.4 rad50 ≤ E T,j1 ≤ 70GeV +∆φ( ⃗ / ET ,⃗j 2 ) ≤ 0.4 radE T,j1 ≥ 70GeV +∆φ( ⃗ / ET ,⃗j 2 ) ≤ 0.4 radE T,j1 ≤ 50GeV +∆φ( ⃗ / ET ,⃗j 2 ) ≥ 0.7 rad50 ≤ E T,j1 ≤ 70GeV +∆φ( ⃗ / ET ,⃗j 2 ) ≥ 0.7 radE T,j1 ≥ 70GeV +∆φ( ⃗ / ET ,⃗j 2 ) ≥ 0.7 radTable 7.3: K<strong>in</strong>ematic regions used <strong>in</strong> <strong>the</strong> MET+JETS path trigger parameterization.Efficiency10.8MET cuts: Global efficiency0.60.40.2Muon sampleJET-50 sampleJET-20 sampleMET-BACKUP sampleNot aligned, E >70 GeVT,j1Ratio1.41.2Ratio to <strong>the</strong> central prediction10.80.60 20 40 60 80 100 120 140E T[GeV]Figure 7.1: Total efficiency <strong>for</strong> <strong>the</strong> MET+JETS Trigger Path, as obta<strong>in</strong>ed from <strong>the</strong> several samples we areus<strong>in</strong>g <strong>in</strong> <strong>the</strong> study. This efficiency is one of <strong>the</strong> six trigger turn-on parametrizations used, <strong>in</strong> particular, <strong>the</strong> one<strong>for</strong> <strong>the</strong> region <strong>in</strong> which more signal is expected. The plot below shows <strong>the</strong> ratio to <strong>the</strong> efficiency obta<strong>in</strong>ed with<strong>the</strong> HIGH PT MUON sample, which we consider our central reference. The yellow area displays <strong>the</strong> size of <strong>the</strong>uncerta<strong>in</strong>ty we quote on <strong>the</strong> trigger efficiency.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 1037.3 Monte Carlo Signal SamplesThe signal predictions are obta<strong>in</strong>ed us<strong>in</strong>g <strong>the</strong> program PROSPINO [61] to compute <strong>the</strong> totalproduction cross section p¯p → ˜t˜t, and PYTHIA [62] to estimate <strong>the</strong> event acceptance <strong>in</strong> <strong>the</strong>detector and <strong>in</strong> <strong>the</strong> application of our selection cuts.Several signal Monte Carlo samples are generated with PYTHIA and passed through <strong>the</strong>detector simulation <strong>in</strong> order to cover <strong>the</strong> phase space under study as a function of <strong>the</strong> neutral<strong>in</strong>omass and stop mass. These samples are generated us<strong>in</strong>g <strong>the</strong> Tune AW [105] and sett<strong>in</strong>g explicitly<strong>the</strong> SUSY parameters of <strong>the</strong> model, which only affects <strong>the</strong> masses of <strong>the</strong> <strong>in</strong>volved particless<strong>in</strong>ce <strong>the</strong> production process is via <strong>the</strong> strong <strong>in</strong>teraction and all <strong>the</strong> decay branch<strong>in</strong>g ratio areset to 100%. The stop mass is varied between 90 GeV/c 2 to 195 GeV/c 2 and <strong>the</strong> neutral<strong>in</strong>o massfrom 60 GeV/c 2 to 125 GeV/c 2 .The generated signal po<strong>in</strong>ts are showed <strong>in</strong> <strong>the</strong> figure 6.2 with <strong>the</strong> previous limit obta<strong>in</strong>ed byCDF [106], DØ [107], and LEP [108].Neutral<strong>in</strong>o Mass (GeV/c2)1201008060m~= m + mt χ∼o c1m~= m + m b+ m oχ∼t W140oLEP θ = 56oLEP θ = 0-1CDF 295 pb-1DØ 995 pb60 80 100 120 140 160 1802Stop Mass (GeV/c)Figure 7.2: SUSY po<strong>in</strong>ts (blue squares) generated with PYTHIA showed <strong>in</strong> <strong>the</strong> m(˜χ 0 )-m(˜t) plane. Previouslimits by LEP, CDF, and DØ are shown.
104 7.4. Background Processes7.4 Background ProcessesSeveral SM processes, produced at Tevatron, have a f<strong>in</strong>al state that mimic <strong>the</strong> signal under study.Events selected <strong>in</strong> <strong>the</strong> analysis have as ma<strong>in</strong> charanteristics, large E / T , two jets with at least oneof <strong>the</strong>m orig<strong>in</strong>ated from a heavy-flavor quark, and no leptons.Part of <strong>the</strong> SM background <strong>in</strong> this analysis is predicted with MC simulation, <strong>in</strong> particularcontributions from Z and W production <strong>in</strong> association with jets, t¯t production, s<strong>in</strong>gle top anddiboson production. In <strong>the</strong> case of W/Z+ jets processes, ALPGEN [109] and PYTHIA MonteCarlo generators are used. The ALPGEN prediction is used as <strong>the</strong> nom<strong>in</strong>al estimation while<strong>the</strong> PYTHIA prediction is used as a cross check. Differences <strong>in</strong> shape between <strong>the</strong> two MonteCarlo estimations are taken as systematic uncerta<strong>in</strong>ties C. All <strong>the</strong> o<strong>the</strong>r background samples aregenerated with PYTHIA. Events are passed through <strong>the</strong> GEANT3-based [97] CDF II detectorsimulation and weighted by <strong>the</strong> probability that <strong>the</strong>y would pass <strong>the</strong> trigger as determ<strong>in</strong>ed <strong>in</strong><strong>in</strong>dependent data samples.tun<strong>in</strong>g parameters set described above, and processed <strong>in</strong> a similar way as <strong>the</strong> signal events.Background contributions from HF multijet production and light flavor jets falsely taggedas a heavy-falvour quark, are estimated from data.In order to test <strong>the</strong> ability to model <strong>the</strong> backgrounds, and also to compute <strong>the</strong> data-drivenbackgrounds, several control regions are def<strong>in</strong>ed, as described <strong>in</strong> section 7.5.7.4.1 Top ProductionTop-quark pair-production and s<strong>in</strong>gle top-quark production are considered as backgrounds <strong>in</strong>this analysis. Both contributions are measurable <strong>in</strong> <strong>the</strong> signal region. However, <strong>the</strong>y are <strong>the</strong>smallest background contributions taken <strong>in</strong>to account <strong>in</strong> <strong>the</strong> analysis. In contrast with <strong>the</strong> sbottomsearch, described <strong>in</strong> Chapter 6, where <strong>the</strong> top production is one of <strong>the</strong> largest backgrounds,<strong>in</strong> this analysis, due to <strong>the</strong> dijet selection and <strong>the</strong> one tag requirement, this contribution is highlysuppressed.The s<strong>in</strong>gle top-quark event yields are normalized to <strong>the</strong> <strong>the</strong>oretical cross sections [98]. Weuse <strong>the</strong> top-quark pair production cross section of σ t¯t = 7.02 ± 0.63 pb [110], as measured byCDF II <strong>in</strong> 2008.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 1057.4.2 W/Z and Diboson ProductionW/Z and diboson events are <strong>the</strong> dom<strong>in</strong>ant background <strong>in</strong> <strong>the</strong> signal region. The presence of<strong>the</strong>se event <strong>in</strong> <strong>the</strong> signal region, is ma<strong>in</strong>ly due to W+ jets production and Z+ jets, when <strong>the</strong> Wdecays <strong>in</strong>to lepton and neutr<strong>in</strong>o, and <strong>the</strong> Z boson decays <strong>in</strong>to neutr<strong>in</strong>os.As mention above, ALPGEN is <strong>the</strong> Monte Carlo generator used to compute <strong>the</strong> W/Z+ jetsprocesses. ALPGEN calculates <strong>the</strong> matrix elements <strong>for</strong> processes conta<strong>in</strong><strong>in</strong>g additional radiatedpartons and passes <strong>the</strong> color <strong>in</strong><strong>for</strong>mation to <strong>the</strong> shower<strong>in</strong>g algorithm. This should give a moreaccurate model<strong>in</strong>g of <strong>the</strong> k<strong>in</strong>ematics of <strong>the</strong> process than PYTHIA shower<strong>in</strong>g approximation,s<strong>in</strong>ce it <strong>in</strong>cludes proper matrix element calculations of <strong>the</strong> radiation process. ALPGEN alsocalculates <strong>the</strong> lead<strong>in</strong>g-order cross section of each <strong>in</strong>teraction it generates, which is useful <strong>for</strong>comb<strong>in</strong><strong>in</strong>g different processes. Once <strong>the</strong> events are generated <strong>the</strong>y are passed to PYTHIA <strong>for</strong>parton shower<strong>in</strong>g. This procedure generates <strong>in</strong>itial- and f<strong>in</strong>al-state gluon radiation <strong>for</strong> each eventand allows <strong>the</strong>m to decay to quark pairs, <strong>in</strong>creas<strong>in</strong>g <strong>the</strong> number of particles <strong>in</strong> <strong>the</strong> f<strong>in</strong>al state of<strong>the</strong> event. More particles may be added from effects of beam remnants or multiple <strong>in</strong>teractions.This gives <strong>the</strong> f<strong>in</strong>al set of particles that are passed to <strong>the</strong> hadronization rout<strong>in</strong>e.The way <strong>in</strong> which W/Z+ jets are generated <strong>in</strong> ALPGEN, us<strong>in</strong>g W/Z +i partons, <strong>in</strong>troducea complication because of <strong>the</strong> double count<strong>in</strong>g of events produced when a gluon, showered byPYTHIA, produces new partons <strong>in</strong> <strong>the</strong> f<strong>in</strong>al state. However, this issue is solved <strong>in</strong> ALPGENpackage with <strong>the</strong> so-called MLM, a sort of match<strong>in</strong>g between samples to decide which eventis kept when a double count<strong>in</strong>g occurs. The decision is made based on <strong>the</strong> angle between <strong>the</strong>partons.After <strong>the</strong> procedure described above, event yields are normalized to <strong>the</strong> NLO cross sectionsas computed by MCFM [111].An extra complication appears us<strong>in</strong>g samples <strong>in</strong>clud<strong>in</strong>g heavy flavor partons. In this case,<strong>the</strong> user is <strong>the</strong> one <strong>in</strong> charge of handle <strong>the</strong> double count<strong>in</strong>g issue, us<strong>in</strong>g a generalization of <strong>the</strong>MLM method used <strong>in</strong> <strong>the</strong> light flavor samples.The diboson event yields, estimated with PHYTIA, are normalized to <strong>the</strong> <strong>the</strong>oretical NLOcross sections [101, 102].
106 7.5. Control Regions7.4.3 MistagsThe mistags are light-flavor jets falsely tagged as heavy flavor jets. Although <strong>the</strong> mistag efficiencyis an order of magnitude smaller than <strong>the</strong> heavy flavor tagg<strong>in</strong>g efficiency, <strong>the</strong> large crosssection of processes that produce light flavor jets make <strong>the</strong> mistag background one of <strong>the</strong> largest<strong>in</strong> <strong>the</strong> signal region, and <strong>the</strong> dom<strong>in</strong>ant one be<strong>for</strong>e optimization.The way <strong>in</strong> which <strong>the</strong> mistag matrix is computed and applied, is expla<strong>in</strong>ed <strong>in</strong> detail <strong>in</strong>section 5.2.7.4.4 Heavy-Flavor Multijet ProductionThe HF multijet production has a very large cross section <strong>in</strong> comparison with <strong>the</strong> expectedsignal, however <strong>the</strong>se processes usually do not produce E / T <strong>in</strong> <strong>the</strong> f<strong>in</strong>al state. Events frommultijet production pass our selection if a jet mismeasurement or a semi-leptonic decay froma meson produces E / T . In both cases <strong>the</strong> E / T tends to be aligned with <strong>the</strong> first or second mostenergetic jet.Due to <strong>the</strong> large cross section of <strong>the</strong> process, <strong>the</strong> amount of MC simulated events neededto model <strong>the</strong> background is huge. To generate such a sample, a large amount of <strong>in</strong><strong>for</strong>matic resourcesshould be used dur<strong>in</strong>g months. For this reason, a data driven method become mandatoryto estimate this background.To estimate <strong>the</strong> HF multijet background from data, we have developed MUTARE, described<strong>in</strong> section 6.4.5.7.5 Control RegionsThe SM processes predicted with MC or data-driven methods are tested <strong>in</strong> control regions def<strong>in</strong>edas background-dom<strong>in</strong>ated samples <strong>in</strong> which <strong>the</strong> signal contribution is negligible. Tworegions are def<strong>in</strong>ed by revers<strong>in</strong>g <strong>the</strong> selection requirements <strong>in</strong>troduced to suppress specific backgroundprocesses. A third region is def<strong>in</strong>ed <strong>in</strong> order to check <strong>the</strong> analysis tools <strong>in</strong> a signal-likeenvironment, but avoid<strong>in</strong>g <strong>the</strong> application of cuts that would enhance <strong>the</strong> signal contribution toa measurable level. All <strong>the</strong> basic selection cuts showed <strong>in</strong> Table 6.1 are required. In addiction,loose SecVtx algorithm is applied requir<strong>in</strong>g s<strong>in</strong>gle HF-tagged events <strong>in</strong> each region.The pre-optimization control region is def<strong>in</strong>ed as a signal-like region without optimization
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 107cuts. Hence, this region is <strong>the</strong> benchmark <strong>for</strong> <strong>the</strong> optimization process. The o<strong>the</strong>r two regionsare def<strong>in</strong>ed orthogonally to <strong>the</strong> pre-optimization one. The HF multijet region is a multijet enrichedregion, requir<strong>in</strong>g <strong>the</strong> second lead<strong>in</strong>g E T aligned with <strong>the</strong> E / T , <strong>in</strong> which <strong>the</strong> MUTAREmatrix is computed. The lepton region, <strong>in</strong> which at least one lepton (def<strong>in</strong>ed <strong>in</strong> section 4.2)is required, is used to test <strong>the</strong> electroweak W/Z boson and top backgrounds, where <strong>the</strong>y aredom<strong>in</strong>ant contributions. The lepton control region is also a good place to check <strong>the</strong> MUTAREprediction <strong>in</strong> lepton environment, test<strong>in</strong>g <strong>the</strong> robustness of <strong>the</strong> method. The selection cuts def<strong>in</strong><strong>in</strong>geach region are:• HF multijet control region: second lead<strong>in</strong>g E T jet (⃗j 2 ) aligned with <strong>the</strong> ⃗ / ET , wherealigned means ∆φ( ⃗ / ET ,⃗j 2 ) ≤ 0.4 rad.• Lepton control region: second lead<strong>in</strong>g E T jet not aligned with <strong>the</strong> ⃗ / ET (∆φ( ⃗ / ET ,⃗j 2 ) ≥0.7 rad) and at least one isolated lepton (as def<strong>in</strong>ed <strong>in</strong> section 4.2).• Pre-optimization control region: lead<strong>in</strong>g and second-lead<strong>in</strong>g E T jets not aligned with<strong>the</strong> ⃗ / ET , and no identified isolated leptons.The first jet transverse energy and <strong>the</strong> E / T distributions <strong>for</strong> <strong>the</strong> multijet, lepton, and preoptimizationcontrol regions, are shown <strong>in</strong> figure 7.3, figure 7.4, and figure 7.5. Good agreementbetween data and SM predictions is obta<strong>in</strong>ed <strong>in</strong> all control regions. Table 7.4 shows <strong>the</strong> variousbackgrounds contributions compare to data <strong>in</strong> each region.Due to <strong>the</strong> <strong>in</strong>tr<strong>in</strong>sic properties of <strong>the</strong> MUTARE method we do not expect an accurate predictionof <strong>the</strong> normalization <strong>in</strong> regions where <strong>the</strong> fraction of heavy flavor to <strong>the</strong> total multijetcontent is different to <strong>the</strong> one <strong>in</strong> which <strong>the</strong> parametrization was computed. For this reason <strong>the</strong>HF multijet prediction is normalized to data <strong>in</strong> <strong>the</strong> lepton control region <strong>for</strong> comparison of <strong>the</strong>k<strong>in</strong>ematic distribution.
108 7.5. Control RegionsEvents/12 GeV18000160001400012000100008000600040002000CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons00 50 100 150 200 250 300 350 400 450E T,j1 [GeV]Events/12 GeV510410310210101-1CDF Run II Prelim<strong>in</strong>ary-1L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons100 50 100 150 200 250 300 350 400 450E T,j1 [GeV]∫Events/8 GeV600005000040000300002000010000CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons00 50 100 150 200 250 300 350 400E T[GeV]Events/8 GeV510410310210101-1CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons100 50 100 150 200 250 300 350 400E T[GeV]Figure 7.3: Lead<strong>in</strong>g jet E T and / E T <strong>in</strong> l<strong>in</strong>ear (left) and logarithmic (right) scales <strong>in</strong> <strong>the</strong> HF multijet control region.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 109CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/12 GeV350CDF Data300250HF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/12 GeV310210CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons2001015010015000 50 100 150 200 250 300 350E T,j1 [GeV]10-10 50 100 150 200 250 300 350E T,j1 [GeV]CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/8 GeV350CDF Data300250200HF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/8 GeV21010CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons15010015000 50 100 150 200 250 300 350 400E T[GeV]10-10 50 100 150 200 250 300 350 400E T[GeV]Figure 7.4: Lead<strong>in</strong>g jet E T and / E T <strong>in</strong> l<strong>in</strong>ear (left) and logarithmic (right) scales <strong>in</strong> <strong>the</strong> lepton control region.
110 7.5. Control RegionsCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/12 GeV4000CDF Data350030002500HF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/12 GeV310210CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons20001015001000150000 50 100 150 200 250 300 350 400 450E T,j1 [GeV]10-10 50 100 150 200 250 300 350 400 450E T,j1 [GeV]CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/8 GeV1000080006000CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/8 GeV410310210CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons4000102000100 50 100 150 200 250 300 350 400E T[GeV]10-10 50 100 150 200 250 300 350 400E T[GeV]Figure 7.5: Lead<strong>in</strong>g jet E T and / E T <strong>in</strong> l<strong>in</strong>ear (left) and logarithmic (right) scales <strong>in</strong> <strong>the</strong> pre-optimization controlregion.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 111CDF Run II Prelim<strong>in</strong>ary 2.6 fb −1Regions Multijet Lepton Pre-optimizationW/Z + jets production 457 ± 190 375 ± 156 1551 ± 644Diboson production 17 ± 2 45 ± 5 118 ± 13Top pair production 188 ± 21 547 ± 60 870 ± 96S<strong>in</strong>gle top production 11 ± 2 71 ± 10 130 ± 19HF QCD Multijets 75407 ± 23376 268 ± 83 12935 ± 4010Light-flavour contam<strong>in</strong>ation 65839 ± 8427 720 ± 92 7741 ± 991Total expected 141919 ± 24849 2026 ± 208 23345 ± 4182Observed 143441 2026 22792Table 7.4: Comparison of <strong>the</strong> total number of expected events with total uncerta<strong>in</strong>ties and observed s<strong>in</strong>gle taggedevents <strong>in</strong> <strong>the</strong> control regions.
112 7.6. Signal Optimization7.6 Signal OptimizationIn order to <strong>in</strong>crease <strong>the</strong> signal over background ratio <strong>in</strong> <strong>the</strong> analysis, an optimization processwas per<strong>for</strong>med tak<strong>in</strong>g <strong>the</strong> pre-optimization selection as benchmark. The optimization processconsists on <strong>the</strong> application of k<strong>in</strong>ematic cuts and a Neural Network to reduce <strong>the</strong> HF multijetbackground, and f<strong>in</strong>ally a flavor separator to enhance <strong>the</strong> c jet contribution <strong>in</strong> <strong>the</strong> f<strong>in</strong>al state.7.6.1 Heavy-Flavor Multijet Removal CutsAs a first step <strong>in</strong> <strong>the</strong> optimization process, we select events with only two jets, as it is expectedfrom <strong>the</strong> signal under optimization, and fulfill<strong>in</strong>g <strong>the</strong> condition ∆φ( E / T , Track E / T ) < π/2.This variable takes <strong>in</strong>to account <strong>the</strong> angular difference between <strong>the</strong> “standard” E / T from <strong>the</strong>calorimeter and <strong>the</strong> Track E / T calculated with tracks. When <strong>the</strong> E / T <strong>in</strong> <strong>the</strong> event is real, <strong>the</strong>setwo quantities are usually aligned <strong>in</strong> φ. However, when <strong>the</strong> E / T comes from calorimetry mismeasurements,as HF multijet events (with no real E / T ) populat<strong>in</strong>g <strong>the</strong> E / T sample, <strong>the</strong> angulardifference between <strong>the</strong> two quantities is more randomly distributed. The application of <strong>the</strong>secuts allow us to reduce drastically <strong>the</strong> HF multijet contribution <strong>in</strong> a simple way and also preventus to tra<strong>in</strong> <strong>the</strong> neural network with <strong>the</strong>se HF multijet events that are clearly different from <strong>the</strong>signal.These two variables, number of jets, and ∆φ( E / T , Track E / T ) <strong>in</strong> which we are apply<strong>in</strong>g <strong>the</strong>cuts, are shown <strong>in</strong> figure 7.6.7.6.2 Heavy-Flavor Multijet Neural NetworkA Neural Network is applied as second step <strong>in</strong> <strong>the</strong> optimization process. The goal of this neuralnetwork is to remove HF multijet events.After choos<strong>in</strong>g <strong>the</strong> set of variables used as <strong>in</strong>put <strong>for</strong> <strong>the</strong> neural network, a tra<strong>in</strong><strong>in</strong>g andtest evaluations have been per<strong>for</strong>med with <strong>the</strong> framework of <strong>the</strong> TMVA package [103], us<strong>in</strong>gtaggable jets (HF multijet like) as background and stop (m(˜t) = 125 GeV/c 2 , m(˜χ 0 ) = 70 GeV/c 2 )MC as signal. The architecture of <strong>the</strong> neural network consists <strong>in</strong> two layers with N+1 andN nodes respectively, where N is <strong>the</strong> number of variables, and one output node as shown <strong>in</strong>figure 7.7. The variables used dur<strong>in</strong>g <strong>the</strong> tra<strong>in</strong><strong>in</strong>g and test process are listed <strong>in</strong> Table 7.5. All<strong>the</strong>se variables are well modeled and are found as <strong>the</strong> ones prov<strong>in</strong>g <strong>the</strong> best dist<strong>in</strong>ction powerbetween signal and background, as shown <strong>in</strong> appendix B.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 113N-Events120001000080006000400020000CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsSignal-125 (x10)Signal-135 (x10)Signal-115 (x10)0 2 4 6 8 10 12Number of JetsN-Events1800CDF Data1600140012001000800600400200CDF Run II Prelim<strong>in</strong>aryHF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsSignal-125 (x10)Signal-135 (x10)Signal-115 (x10)00 20 40 60 80 100 120 140 160 180∆φ(E,TrackE T ) [Deg]T-1∫L dt=2.6 fbFigure 7.6: Number of jets (left) and ∆φ(met, Track / E T ) (right) distributions <strong>in</strong> <strong>the</strong> Pre-optimization region.The plots show <strong>the</strong> background prediction, data and stop signals with m(˜t) = 115, 125, and 135 GeV/c 2 and m(˜χ 0 )= 70 GeV/c 2 .metleadjet_etsecondjet_etleadjet_etasecondjet_etadphi_1jet_2jetm<strong>in</strong>_dphi_met_jetshttrackmettrackmetphiBias nodeLayer 0 Layer 1 Layer 2 Layer 3Figure 7.7: Neural network’s architecture used <strong>for</strong> <strong>the</strong> tra<strong>in</strong><strong>in</strong>g. The background is taggable jets from data(QCD-like) and <strong>the</strong> signal is stop MC with m(˜t) = 125 GeV/c 2 and m(˜χ 0 ) = 70 GeV/c 2 .7.6.3 Neural Network ResultsThe neural network output obta<strong>in</strong>ed is distributed between -1 (backgroud like) and 1 (signallike). We select <strong>the</strong> events <strong>in</strong> <strong>the</strong> region between 0 and 1, apply<strong>in</strong>g a cut <strong>in</strong> <strong>the</strong> selection process,as shown <strong>in</strong> figure 7.8. S<strong>in</strong>ce <strong>the</strong> key po<strong>in</strong>t of <strong>the</strong> optimization is <strong>the</strong> application of <strong>the</strong> flavorseparator, this cut on 0 may not have <strong>the</strong> best S/B ratio, but tries not to loose signal acceptance
114 7.6. Signal OptimizationHF multijet-NN variables/ ⃗ETE T,j1E T,j2η j1Track / ⃗ ETm<strong>in</strong>∆φ( / ⃗ ET , jets)η j2 ∆φ( ⃗ / ET , Track ⃗ / ET )∑ Nj ets∆φ(⃗j 1 ,⃗j 2 ) i=1 E T,jiTable 7.5: List of <strong>in</strong>put variables used <strong>in</strong> HF multijet-NN.to exploit to <strong>the</strong> maximum <strong>the</strong> per<strong>for</strong>mance of fur<strong>the</strong>r optimizations.From this po<strong>in</strong>t on, we expect most of our sensitivity to <strong>the</strong> signal com<strong>in</strong>g from <strong>the</strong> (0,1)output region, so we get a control region look<strong>in</strong>g at <strong>the</strong> events <strong>in</strong> <strong>the</strong> (-1,0) <strong>in</strong>terval. In fact,we are us<strong>in</strong>g this region (HF multijet enriched) to normalize <strong>the</strong> HF multijet prediction to datas<strong>in</strong>ce we already know that our HF multijet prediction is slightly over-estimated <strong>in</strong> <strong>the</strong> preoptimizationregion.Events700600500400-1CDF Run II Prelim<strong>in</strong>ary ∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons~Signal m( t)=125, m(∼χ)=70(x10)~Signal m( t)=135, m(∼~χ)=70(x10)Signal m( t)=115, m(∼χ)=70(x10)3002001000-1 -0.5 0 0.5 1NN OutputFigure 7.8: Output of <strong>the</strong> multijet-NN to reject HF multijet background. The arrow <strong>in</strong>dicates <strong>the</strong> cut applied <strong>in</strong><strong>the</strong> analysis.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 1157.6.4 Charm-jet Selection with CHAOSThe f<strong>in</strong>al stage <strong>in</strong> <strong>the</strong> stop signal optimization is <strong>the</strong> application of a flavor separator to enhance<strong>the</strong> sample with c jets. For this purpose, we develop CHAOS, a Charm Hadron AnalysisOriented Separator explicitly built <strong>for</strong> this analysis (described <strong>in</strong> section 5.3).CHAOS is applied over <strong>the</strong> events already selected, cutt<strong>in</strong>g on <strong>the</strong> HF multijet-NN, with oneheavy flavor tagged jet (loose SecVtx). The sum of <strong>the</strong> CHAOS outputs is distributed between 0and 2 (c flavor). We select <strong>the</strong> events <strong>in</strong> <strong>the</strong> region between 1.65 and 1, apply<strong>in</strong>g a cut as shown<strong>in</strong> figure 7.9.A scale factor on top of <strong>the</strong> SecVtx tagger is needed, <strong>for</strong> MC predictions, to take <strong>in</strong>to account<strong>the</strong> differences <strong>in</strong> efficiency between data and MC. This scale factor is calculated explicitly <strong>for</strong><strong>the</strong> cut we are apply<strong>in</strong>g <strong>in</strong> <strong>the</strong> analysis at 1.65 <strong>in</strong> <strong>the</strong> sum of <strong>the</strong> outputs, as shown <strong>in</strong> figure 7.9.The scale factors and efficiencies <strong>for</strong> b and c jets are described <strong>in</strong> section 5.4.• SF CHAOSb = 1.14 ± 0.22• SF CHAOSc = 1.01 ± 0.15The application of CHAOS to data and MC is straight <strong>for</strong>ward. However, obta<strong>in</strong><strong>in</strong>g <strong>the</strong> HFmultijet and mistags prediction via MUTARE and mistag matrices after CHAOS is not possible.These two matrices are applied over taggable jets to obta<strong>in</strong> <strong>the</strong>ir predictions, never<strong>the</strong>less, toapply CHAOS tagged jets are needed.To overcome this problem, we per<strong>for</strong>m <strong>the</strong> follow<strong>in</strong>g procedure. The amount of MUTAREand mistag prediction right be<strong>for</strong>e CHAOS application (Table 7.6) is known, so as far as weknow <strong>the</strong> flavor efficiency of CHAOS cutt<strong>in</strong>g at 1.65 we apply this efficiency assum<strong>in</strong>g <strong>the</strong>MUTARE as b-jets and <strong>the</strong> mistags as light-jets.PredictionsMUTARE 279.6Mistags 658.3Table 7.6: MUTARE and mistags prediction right be<strong>for</strong>e CHAOS.The procedure used to compute <strong>the</strong> CHAOS’ efficiencies is fully expla<strong>in</strong>ed <strong>in</strong> section 5.4In order to check <strong>the</strong> flavor composition of <strong>the</strong> MUTARE and mistags predictions <strong>in</strong> thisregion we per<strong>for</strong>m a flavor-based template fit to data us<strong>in</strong>g <strong>the</strong> mass of <strong>the</strong> vertex variable. Us<strong>in</strong>g
116 7.6. Signal OptimizationFraction of objects [%]1614121086Sum of network outputsCharmBottomLight+Taus4200.8 1 1.2 1.4 1.6 1.8 2Sum of outputsFigure 7.9: Sum of <strong>the</strong> CHAOS outputs <strong>in</strong> 1D apply<strong>in</strong>g <strong>the</strong> NN to <strong>the</strong> samples used <strong>for</strong> tra<strong>in</strong><strong>in</strong>g. The arrow<strong>in</strong>dicates <strong>the</strong> cut applied on <strong>the</strong> analysis to enhance <strong>the</strong> contribution of charm-jets.<strong>the</strong> data distribution of <strong>the</strong> vertex mass subtract<strong>in</strong>g all <strong>the</strong> backgrounds com<strong>in</strong>g from MC weobta<strong>in</strong> <strong>the</strong> distribution of HF-multijet+mistags from data, right be<strong>for</strong>e <strong>the</strong> CHAOS application.Fitt<strong>in</strong>g flavor templates to <strong>the</strong> mass of <strong>the</strong> vertex extracted <strong>in</strong> this way we obta<strong>in</strong> <strong>the</strong> follow<strong>in</strong>gamount of flavor contributions as is shown <strong>in</strong> figure 7.10.• b jets from <strong>the</strong> fit = 388.2• c jets from <strong>the</strong> fit ≈ 0• light jets from <strong>the</strong> fit = 492.4From <strong>the</strong> fit we conclude that <strong>the</strong> amount of c jets is negligible at this po<strong>in</strong>t, <strong>the</strong>re<strong>for</strong>e <strong>the</strong>procedure apply<strong>in</strong>g to <strong>the</strong> MUTARE prediction <strong>the</strong> b jet efficiency <strong>in</strong> CHAOS is a reasonableapproach. The differences between <strong>the</strong> predictions and <strong>the</strong> numbers obta<strong>in</strong>ed from <strong>the</strong> fit aretaken <strong>in</strong>to account as systematics as expla<strong>in</strong>ed <strong>in</strong> section 7.7.One way to know if our light flavor template has a reasonable shape, is to compare it with <strong>the</strong>distribution obta<strong>in</strong>ed from negative tags from data. This comparison, <strong>for</strong> <strong>the</strong> mass of <strong>the</strong> vertex
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 1171000]Jets [×0.160.140.120.1Data-MC Pre CHAOSDataLightCharm0.08Bottom0.060.040.0200 1 2 3 4 5 6Vertex mass [GeV/c2]Figure 7.10: Mass of <strong>the</strong> vertex after multijet-NN cut <strong>in</strong> data subtract<strong>in</strong>g all <strong>the</strong> backgrounds com<strong>in</strong>g from MC.The colored histograms are flavor templates fitted to <strong>the</strong> data distribution.and CHAOS sum of <strong>the</strong> outputs, is shown <strong>in</strong> figure 7.11. The agreement between negative tagsand <strong>the</strong> template is quite good.The values <strong>for</strong> CHAOS flavor efficiency cutt<strong>in</strong>g on 1.65 are:• b-jets efficiency = 7.3%• c-jets efficiency = 34.6%• light-jets efficiency = 4.9%Where <strong>the</strong> b-jet and c-jet efficiency comes from data (as is expla<strong>in</strong> <strong>in</strong> section 5.4) and <strong>the</strong>light-jet efficiency comes from MC.After <strong>the</strong> optimization process described <strong>in</strong> this section we come out with <strong>the</strong> f<strong>in</strong>al regionas is shown <strong>in</strong> section 7.8, where <strong>the</strong> f<strong>in</strong>al numbers <strong>for</strong> data and predictions are summarized <strong>in</strong>Table 7.7.As expected from a “bl<strong>in</strong>d search”, <strong>the</strong> optimization procedure is made over <strong>the</strong> predictions.CDF II data, as shown <strong>in</strong> <strong>the</strong> figures, is plotted once <strong>the</strong> process is f<strong>in</strong>ished.
118 7.6. Signal OptimizationJets (arbitrary units)100MC light-flavourNeg. tags8060Jets (arbitrary units)60MC light-flavourNeg. tags (default)50Neg. tags (reverse)40304020201000 0.5 1 1.5 2 2.5 3 3.5 42Vertex Mass [GeV/c]00.8 1 1.2 1.4 1.6 1.8 2CHAOS Output <strong>for</strong> c-jetsFigure 7.11: Light template from MC and negative tags from data <strong>in</strong> <strong>the</strong> vertex mass distribution (left) andCHAOS sum of <strong>the</strong> outputs (right).
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 1197.7 Systematic Uncerta<strong>in</strong>tiesSystematic errors are <strong>the</strong> ma<strong>in</strong> source of uncerta<strong>in</strong>ty <strong>in</strong> this search. Some of <strong>the</strong>se errors affect<strong>the</strong> overall normalization of <strong>the</strong> signal or background templates. This k<strong>in</strong>d of systematic errors,so-called rate systematics, summarize effects that impact <strong>the</strong> number of events <strong>in</strong> <strong>the</strong> signal andbackground templates. However, <strong>the</strong> shapes of <strong>the</strong>se templates are not affected by <strong>the</strong>se sourcesof uncerta<strong>in</strong>ty.Contrarily, some o<strong>the</strong>r systematic uncerta<strong>in</strong>ties make <strong>the</strong> shapes of <strong>the</strong> templates to vary.This second k<strong>in</strong>d of systematic errors, named shape systematics, could also affect <strong>the</strong> overallnumber of events. These differences <strong>in</strong> shape are accounted <strong>for</strong> by produc<strong>in</strong>g sets of shiftedtemplates <strong>in</strong> parallel to <strong>the</strong> nom<strong>in</strong>al ones.S<strong>in</strong>ce <strong>the</strong> shape of <strong>the</strong> various backgrounds is used to extract <strong>the</strong> f<strong>in</strong>al exclusion limit, <strong>the</strong>shape uncerta<strong>in</strong>ties <strong>in</strong> this analysis are as relevant as <strong>the</strong> rate uncerta<strong>in</strong>ties.The systematic uncerta<strong>in</strong>ties on <strong>the</strong> signal and <strong>the</strong> background predictions, tak<strong>in</strong>g <strong>in</strong>to accountcorrelated and uncorrelated uncerta<strong>in</strong>ties, are studied.• Jet Energy Scale [90]: A systematic error <strong>in</strong> <strong>the</strong> calorimeter energy scale affect <strong>the</strong> totaltransverse energy on <strong>the</strong> jets. The effect <strong>in</strong> <strong>the</strong> f<strong>in</strong>al region is negligible.• Tagg<strong>in</strong>g Scale Factor: The difference between data and MC <strong>in</strong> c-tagg<strong>in</strong>g efficiency ( 10%)is taken as systematic uncerta<strong>in</strong>ty. The result<strong>in</strong>g uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> f<strong>in</strong>al region is 3.6%.• CHAOS Scale Factor: The difference between data and MC is taken as systematic uncerta<strong>in</strong>ty.The result<strong>in</strong>g uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> f<strong>in</strong>al region is 9.2%.• Mistag estimation: The systematic error assigned to <strong>the</strong> tag rate matrix is 4.8%.• Lum<strong>in</strong>osity: The systematic uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> lum<strong>in</strong>osity is taken to be 6%, affect<strong>in</strong>g to<strong>the</strong> normalization of all <strong>the</strong> MC estimated backgrounds.• ISR/FSR: The uncerta<strong>in</strong>ty associated with <strong>the</strong> <strong>in</strong>itial and f<strong>in</strong>al state radiation was evaluatedby generat<strong>in</strong>g sample with more/less ISR/FSR. The effect <strong>in</strong> <strong>the</strong> f<strong>in</strong>al region is 1.7%.• PDF: The PDF uncerta<strong>in</strong>ty has been determ<strong>in</strong>ed to be 3.8% on <strong>the</strong> acceptance.• HF QCD Multijet Background: We assign a conservative 30% uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> predictionbased on <strong>the</strong> variation observed when matrix def<strong>in</strong>ition is changed.
120 7.8. Results• Top-Pair Production cross section: We quote <strong>the</strong> uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> CDF measured value(11%) of <strong>the</strong> top-pair production cross section.• S<strong>in</strong>gle Top Production cross section: We quote <strong>the</strong> <strong>the</strong>oretical uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> s<strong>in</strong>gletopcross section (13%).• Diboson Production cross section: We quote <strong>the</strong> <strong>the</strong>oretical uncerta<strong>in</strong>ty be<strong>in</strong>g 10% <strong>in</strong> <strong>the</strong>WW and WZ cross sections and 20% <strong>for</strong> <strong>the</strong> ZZ process.• S<strong>in</strong>gle EWK Boson Production cross section: Although <strong>the</strong> cross section <strong>for</strong> Z and Wproduction are known to a high precision, we are us<strong>in</strong>g <strong>the</strong> heavy flavor processes <strong>in</strong> ALP-GEN to per<strong>for</strong>m estimations of Z/W +multijet processes. Because of this, we estimate a40% uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> predictions.• Top quark mass: In <strong>the</strong> current analysis, <strong>the</strong> t¯t production background is estimated us<strong>in</strong>gMC with a top quark mass of 175 GeV/c 2 . S<strong>in</strong>ce our signal optimization is based on aNeural Network tra<strong>in</strong>ed with t¯t processes we <strong>in</strong>clude a systematic error due to <strong>the</strong> top pairNN output dependence on <strong>the</strong> top quark mass. We compute this error measur<strong>in</strong>g <strong>the</strong> numberof top-pair events <strong>in</strong> <strong>the</strong> f<strong>in</strong>al selection by us<strong>in</strong>g a top quark mass of 172.5 GeV/c 2 .• Differences <strong>in</strong> shape between ALPGEN and PYTHIA: We <strong>in</strong>clude a shape systematicuncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong> f<strong>in</strong>al selections due to <strong>the</strong> differences between ALPGEN and PYTHIAgenerators used to estimate <strong>the</strong> Z/W + jets processes.• HF QCD Multijet and mistag estimation after CHAOS: We quote <strong>the</strong> uncerta<strong>in</strong>ty <strong>in</strong> <strong>the</strong>f<strong>in</strong>al region due to this estimations of 3.6% and 8.2% respectively.7.8 ResultsIn <strong>the</strong> f<strong>in</strong>al signal region <strong>the</strong> number of observed events is <strong>in</strong> good agreement with <strong>the</strong> expectationsfrom <strong>the</strong> SM processes, as summarized <strong>in</strong> Table 7.7. The uncerta<strong>in</strong>ty on <strong>the</strong> total expectednumber of events was computed tak<strong>in</strong>g <strong>in</strong>to account <strong>the</strong> anti-correlations among <strong>the</strong> several/background contributions. K<strong>in</strong>ematic distributions <strong>in</strong> <strong>the</strong> signal region are checked. E T , E T,j1 ,E T,j2 , and η j1 distributions are shown <strong>in</strong> figure 7.13.S<strong>in</strong>ce no significant deviation from <strong>the</strong> SM prediction is observed, <strong>the</strong> result is used tocalculate an exclusion limit <strong>for</strong> <strong>the</strong> cross section of <strong>the</strong> described stop process. We f<strong>in</strong>d <strong>the</strong>
CDF Run II Prelim<strong>in</strong>ary 2.6 fb −1 SignalChapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 121RegionW/Z + jets production 60.9 ± 26.6Diboson production 10.7 ± 1.9Top pair production 4.6 ± 1.3S<strong>in</strong>gle top production 3.2 ± 0.8HF QCD Multijets 20.4 ± 15.2Light-flavour contam<strong>in</strong>ation 32.2 ± 12.7Total expected 132.0 ± 24.4Observed 115Signal m(˜t)=125, m(˜χ 0 )=70 90.2 ± 23.9Signal m(˜t)=135, m(˜χ 0 )=70 78.0 ± 20.7Signal m(˜t)=115, m(˜χ 0 )=70 82.4 ± 21.8Table 7.7: Number of expected and observed events <strong>in</strong> <strong>the</strong> signal region. Predictions <strong>for</strong> <strong>the</strong> signal po<strong>in</strong>ts arealso shown. Correlated and uncorrelated uncerta<strong>in</strong>ties <strong>in</strong> <strong>the</strong> total background and expected signal were treatedseparately <strong>in</strong> <strong>the</strong> analysis although <strong>the</strong>y are comb<strong>in</strong>ed here.output of <strong>the</strong> multijet-NN, <strong>in</strong> <strong>the</strong> region (0,1), after apply<strong>in</strong>g CHAOS (figure 7.12), as <strong>the</strong> bestdiscrim<strong>in</strong>ant to extract a limit us<strong>in</strong>g shapes. We per<strong>for</strong>m a likelihood fit to set a 95% C.L.limit <strong>in</strong> <strong>the</strong> production cross section as it is shown <strong>in</strong> figure 7.14, as a function of <strong>the</strong> stop-pairproduction cross section <strong>for</strong> given value of <strong>the</strong> neutral<strong>in</strong>o mass.For <strong>the</strong> assumed model, <strong>the</strong> sensitivity of <strong>the</strong> analysis is able to exclude ˜t masses up to180 GeV/c 2 at 95 % C.L. In addition, us<strong>in</strong>g <strong>the</strong> assumed model, a 95% C.L. limit was obta<strong>in</strong>ed<strong>in</strong> <strong>the</strong> mass parameter plane of <strong>the</strong> model. Figure 7.15 shows <strong>the</strong> excluded region <strong>in</strong> <strong>the</strong> stopneutral<strong>in</strong>omass plane of <strong>the</strong> analysis, compared with results from previous analyses [107, 106].Currently <strong>the</strong> limit obta<strong>in</strong>ed with <strong>the</strong> present analysis clearly improves <strong>the</strong> results of previoussearches us<strong>in</strong>g similar topology.
122 7.8. ResultsEvents45 CDF Run II Prelim<strong>in</strong>ary -1L dt=2.6 fb4035302520∫CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons~Signal m( t)=125, m(∼χ)=70~Signal m( t)=135, m(∼χ)=70~Signal m( t)=115, m(∼χ)=701510500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1NN OutputFigure 7.12: Observed f<strong>in</strong>al discrim<strong>in</strong>ant used to extract <strong>the</strong> limits from <strong>the</strong> shapes comparison.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 123Events/8 GeV302520CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/12 GeV30CDF Data2520CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons151510105500 50 100 150 200 250E T[GeV]00 50 100 150 200 250 300E T,j1 [GeV]CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/12 GeV50CDF Data4030HF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents252015CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons201010500 50 100 150 200 250[GeV]E T,j20-3 -2 -1 0 1 2 3ηj1Figure 7.13: / E T , first jet E T , second jet E T , and first jet η <strong>in</strong> <strong>the</strong> f<strong>in</strong>al region.
124 7.8. ResultsCross Section [pb]10210CDF Run II Prelim<strong>in</strong>ary~95% Exclusion limit from t χ∼1→ c∫∼2Observed [m( χ )=80 GeV/c ]Expected (±1σ)-1L dt=2.6 fb0101o + m χ ∼11PROSPINO NLO (CTEQ6M)µR~= µ = m( t 1)Fm t ~≥ m W + m b90 100 110 120 130 140 150 160 170~m(t 1 ) [GeV/c2]Figure 7.14: Observed 95% C.L. limit <strong>in</strong> terms of cross section <strong>for</strong> a m(˜χ 0 ) = 80 Gev/c 2 (black l<strong>in</strong>e) andexpected limit (red l<strong>in</strong>e) with 1σ uncerta<strong>in</strong>ty band. The region where <strong>the</strong> branch<strong>in</strong>g ratio assumed <strong>for</strong> <strong>the</strong> analysisis no longer valid is also shown.
Chapter 7. <strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to Charm and Neutral<strong>in</strong>o 125]CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fb2Neutral<strong>in</strong>o Mass [GeV/c1201008060Observed Limit (95% CL)Expected Limit (±1σ)m t ~= m χ∼o1+ m cm t ~= m W+ m b+ m oχ∼140oLEP θ = 56-1CDF 295 pboLEP θ = 0-1DØ 995 pb60 80 100 120 140 160 180Stop Mass [GeV/c2]Figure 7.15: Excluded region at 95% C.L. <strong>in</strong> <strong>the</strong> m(˜χ 0 )-m(˜t) plane assum<strong>in</strong>g R-parity conservation. The resultis compared to <strong>the</strong> previous results from CDF [106], DØ [107], and LEP [108].
126 7.8. Results
Chapter 8ConclusionsTwo different searches <strong>for</strong> third generation squarks <strong>in</strong> <strong>the</strong> E / T plus jet sample have been per<strong>for</strong>med.S<strong>in</strong>ce no significant deviation from <strong>the</strong> SM prediction is observed, <strong>the</strong> results havebeen used to calculate 95% C.L. exclusion limits <strong>for</strong> <strong>the</strong> cross section of <strong>the</strong> two SUSY processes.The sensitivity achieved by <strong>the</strong>se analyses is based on <strong>the</strong> robustness of <strong>the</strong> backgrounddescriptions and <strong>the</strong> strength of <strong>the</strong> signal optimization techniques. In <strong>the</strong>se two aspects, specialcredit is due to <strong>the</strong> MUTARE method, to estimate <strong>the</strong> heavy flavor multijet background fromdata, and <strong>the</strong> CHAOS flavor separator. Developed <strong>for</strong> <strong>the</strong> analyses presented <strong>in</strong> this <strong>the</strong>ses, <strong>the</strong>setools have moreover a broad spectrum of application <strong>in</strong> searches and measurements among <strong>the</strong>physics program.The only experiment, up to now, capable of per<strong>for</strong>m<strong>in</strong>g comparable searches is DØ . Thestop search was per<strong>for</strong>med by DØ achiev<strong>in</strong>g a sensitivity that provides a smaller excludedregion, due partially to <strong>the</strong> smaller dataset used.The Tevatron SUSY search program will be crucial <strong>in</strong> <strong>the</strong> next years, even with <strong>the</strong> beg<strong>in</strong>n<strong>in</strong>gof <strong>the</strong> LHC program <strong>in</strong> <strong>the</strong> <strong>in</strong>com<strong>in</strong>g months. In particular, scenarios where <strong>the</strong> thirdgeneration squarks are assumed to be very light, as <strong>the</strong> ones presented <strong>in</strong> this <strong>the</strong>ses, rema<strong>in</strong> importantat <strong>the</strong> Tevatron energy scale. However, <strong>the</strong> conquest of <strong>the</strong> Terascale with <strong>the</strong> imm<strong>in</strong>entLHC, will be <strong>the</strong> biggest challenge <strong>in</strong> <strong>the</strong> com<strong>in</strong>g years. The work presented <strong>in</strong> this <strong>the</strong>ses ismade with two <strong>in</strong>tentions: explor<strong>in</strong>g <strong>the</strong> Tevatron’s energy frontier search<strong>in</strong>g <strong>for</strong> new physics,and keep improv<strong>in</strong>g <strong>the</strong> analysis techniques to get ready <strong>for</strong> <strong>the</strong> LHC data. Both <strong>in</strong>tentions becomereal as described <strong>in</strong> <strong>the</strong> present <strong>the</strong>ses, sett<strong>in</strong>g world best exclusion limits <strong>in</strong> <strong>the</strong> per<strong>for</strong>medsearches, and successfully develop<strong>in</strong>g and implement<strong>in</strong>g new analysis techniques.127
128
Appendix APer<strong>for</strong>mance of <strong>the</strong> NN <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong>Glu<strong>in</strong>o-mediated Bottom SquarkTwo different neural networks are used dur<strong>in</strong>g <strong>the</strong> optimization process <strong>in</strong> <strong>the</strong> search <strong>for</strong> glu<strong>in</strong>omediatedbottom squark. One of <strong>the</strong>m is made to remove <strong>the</strong> HF multijet background and <strong>the</strong>o<strong>the</strong>r one to remove <strong>the</strong> top par production background.The same set of variables are used <strong>in</strong> <strong>the</strong> multijet-NN and top-NN. Depend<strong>in</strong>g on <strong>the</strong> optimization,large or small ∆m, <strong>the</strong> set of variables is different due to <strong>the</strong> cut on number of jetsapplied <strong>in</strong> each selection. All <strong>the</strong> variables are well modeled and are found as <strong>the</strong> ones provid<strong>in</strong>g<strong>the</strong> best separation power.A.1 Multijet Neural NetworkThe variable used dur<strong>in</strong>g <strong>the</strong> tra<strong>in</strong><strong>in</strong>g of <strong>the</strong> multijet-NN <strong>for</strong> <strong>the</strong> large and small ∆m optimizationare shown <strong>in</strong> figures A.1 and A.2 compar<strong>in</strong>g <strong>the</strong> signal and background.The output of <strong>the</strong> neural networks <strong>for</strong> <strong>the</strong> two optimizations is shown <strong>in</strong> figure A.3 withtra<strong>in</strong><strong>in</strong>g and test events.129
130 A.1. Multijet Neural NetworkNormalisedNormalisedTMVA Input Variable: met0.06 SignalBackground0.050.040.030.020.010100 150 200 250 300 350 400metTMVA Input Variable: dphi_met_1jet1.61.41.210.80.60.40.201 1.5 2 2.5 3dphi_met_1jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedNormalisedTMVA Input Variable: leadjet_et0.0140.0120.010.0080.0060.0040.00200.90.80.70.60.50.40.30.20.10100 150 200 250 300 350 400 450leadjet_etTMVA Input Variable: dphi_met_2jet1 1.5 2 2.5 3dphi_met_2jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedNormalisedTMVA Input Variable: secondjet_et0.0220.020.0180.0160.0140.0120.010.0080.0060.0040.00200.0450.040.0350.030.0250.020.0150.010.005050 100 150 200 250 300secondjet_etTMVA Input Variable: thirdjet_et40 60 80 100 120 140 160 180 200thirdjet_etU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Figure A.1: Input variables used <strong>for</strong> <strong>the</strong> multijet-NN tra<strong>in</strong><strong>in</strong>g <strong>in</strong> <strong>the</strong> large ∆m optimization. Signal is plotted <strong>in</strong>blue and background (taggable jets) <strong>in</strong> red.
Appendix A. Per<strong>for</strong>mance of <strong>the</strong> NN <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong> Sbottom 131NormalisedTMVA Input Variable: met0.05 SignalBackground0.040.030.020.010100 150 200 250 300 350 400metTMVA Input Variable: dphi_met_1jetNormalised1.81.61.41.210.80.60.40.201 1.5 2 2.5 3dphi_met_1jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedTMVA Input Variable: leadjet_et0.0180.0160.0140.0120.010.0080.0060.0040.0020100 150 200 250 300 350 400 450leadjet_etTMVA Input Variable: dphi_met_2jetNormalised0.90.80.70.60.50.40.30.20.101 1.5 2 2.5 3dphi_met_2jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedNormalisedTMVA Input Variable: secondjet_et0.030.0250.020.0150.010.005050 100 150 200 250 300 350secondjet_etTMVA Input Variable: m<strong>in</strong>_dphi_met_jets2.42.221.81.61.41.210.80.60.40.200 0.5 1 1.5 2 2.5 3m<strong>in</strong>_dphi_met_jetsU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Figure A.2: Input variables used <strong>for</strong> <strong>the</strong> multijet-NN tra<strong>in</strong><strong>in</strong>g <strong>in</strong> <strong>the</strong> small ∆m optimization. Signal is plotted <strong>in</strong>blue and background (taggable jets) <strong>in</strong> red.NormalizedTMVA overtra<strong>in</strong><strong>in</strong>g check <strong>for</strong> classifier: MLP20Signal (test sample)Signal (tra<strong>in</strong><strong>in</strong>g sample)18 Background (test sample) Background (tra<strong>in</strong><strong>in</strong>g sample)16 Kolmogorov-Smirnov test: signal (background) probability = 0.991 (0.967)14121086420-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8MLP responseU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalizedTMVA overtra<strong>in</strong><strong>in</strong>g check <strong>for</strong> classifier: MLP16 Signal (test sample)Background (test sample)Signal (tra<strong>in</strong><strong>in</strong>g sample)Background (tra<strong>in</strong><strong>in</strong>g sample)14Kolmogorov-Smirnov test: signal (background) probability = 1 (0.0989)121086420-1.5 -1 -0.5 0 0.5 1MLP responseU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Figure A.3: Multijet-NN tra<strong>in</strong><strong>in</strong>g and test output <strong>for</strong> <strong>the</strong> large ∆m optimization (left) and small ∆m optimization(right).
132 A.2. Top Neural NetworkA.2 Top Neural NetworkThe variable used dur<strong>in</strong>g <strong>the</strong> tra<strong>in</strong><strong>in</strong>g of <strong>the</strong> top-NN <strong>for</strong> <strong>the</strong> large and small ∆m optimizationare shown <strong>in</strong> figures A.4 and A.5 compar<strong>in</strong>g <strong>the</strong> signal and background.The output of <strong>the</strong> neural networks <strong>for</strong> <strong>the</strong> two optimizations is shown <strong>in</strong> figure A.3 withtra<strong>in</strong><strong>in</strong>g and test events.NormalisedNormalisedTMVA Input Variable: met0.0140.0120.010.0080.0060.0040.002SignalBackground0100 150 200 250 300 350 400metTMVA Input Variable: dphi_met_1jet10.80.60.40.201 1.5 2 2.5 3dphi_met_1jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedNormalisedTMVA Input Variable: leadjet_et0.0140.0120.010.0080.0060.0040.00200.70.60.50.40.30.20.10100 150 200 250 300 350 400 450leadjet_etTMVA Input Variable: dphi_met_2jet1 1.5 2 2.5 3dphi_met_2jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedTMVA Input Variable: secondjet_et0.020.0180.0160.0140.0120.010.0080.0060.0040.002Normalised0.030.0250.020.0150.010.0050050 100 150 200 250 300secondjet_etTMVA Input Variable: thirdjet_et40 60 80 100 120 140 160thirdjet_etU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Figure A.4: Input variables used <strong>for</strong> <strong>the</strong> top-NN tra<strong>in</strong><strong>in</strong>g <strong>in</strong> <strong>the</strong> large ∆m optimization. Signal is plotted <strong>in</strong> blueand background (top pair production) <strong>in</strong> red.
Appendix A. Per<strong>for</strong>mance of <strong>the</strong> NN <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong> Sbottom 133NormalisedTMVA Input Variable: met0.0140.0120.010.0080.0060.0040.0020SignalBackground100 150 200 250 300 350 400 450TMVA Input Variable: dphi_met_1jetmetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedTMVA Input Variable: leadjet_et0.0120.010.0080.0060.0040.0020100 150 200 250 300 350 400 450leadjet_etTMVA Input Variable: dphi_met_2jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedTMVA Input Variable: secondjet_et0.0160.0140.0120.010.0080.0060.0040.002050 100 150 200 250 300 350secondjet_etTMVA Input Variable: m<strong>in</strong>_dphi_met_jetsU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised1.210.80.60.40.201 1.5 2 2.5 3U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised0.70.60.50.40.30.20.101 1.5 2 2.5 3U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised0.80.70.60.50.40.30.20.100.5 1 1.5 2 2.5 3U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%dphi_met_1jetdphi_met_2jetm<strong>in</strong>_dphi_met_jetsFigure A.5: Input variables used <strong>for</strong> <strong>the</strong> top-NN tra<strong>in</strong><strong>in</strong>g <strong>in</strong> <strong>the</strong> small ∆m optimization. Signal is plotted <strong>in</strong> blueand background (top pair production) <strong>in</strong> red.TMVA overtra<strong>in</strong><strong>in</strong>g check <strong>for</strong> classifier: MLPTMVA overtra<strong>in</strong><strong>in</strong>g check <strong>for</strong> classifier: MLPNormalized32.5Signal (test sample)Signal (tra<strong>in</strong><strong>in</strong>g sample)Background (test sample) Background (tra<strong>in</strong><strong>in</strong>g sample)Kolmogorov-Smirnov test: signal (background) probability = 0.996 (0.625)Normalized9 Signal (test sample)Signal (tra<strong>in</strong><strong>in</strong>g sample)8Background (test sample) Background (tra<strong>in</strong><strong>in</strong>g sample)Kolmogorov-Smirnov test: signal (background) probability = 0.352 ( 0.99)721.510.50-0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1 1.2U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%6543210-1 -0.5 0 0.5 1U/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%MLP responseMLP responseFigure A.6: Top-NN tra<strong>in</strong><strong>in</strong>g and test output <strong>for</strong> <strong>the</strong> large ∆m optimization (left) and small ∆m optimization(right).
134 A.2. Top Neural Network
Appendix BPer<strong>for</strong>mance of <strong>the</strong> NN <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong>Scalar Top Decay<strong>in</strong>g <strong>in</strong>to c + ˜χ 0A neural network is used dur<strong>in</strong>g <strong>the</strong> optimization process <strong>in</strong> <strong>the</strong> search <strong>for</strong> scalar top decay<strong>in</strong>g<strong>in</strong>to charm and neutral<strong>in</strong>o. The neural network is made to remove <strong>the</strong> HF multijet background.All <strong>the</strong> variables are well modeled and are found as <strong>the</strong> ones provid<strong>in</strong>g <strong>the</strong> best separationpower, as shown <strong>in</strong> figure B.2.The output of <strong>the</strong> neural network is shown <strong>in</strong> figure B.1 with tra<strong>in</strong><strong>in</strong>g and test events.TMVA overtra<strong>in</strong><strong>in</strong>g check <strong>for</strong> classifier: MLPNormalized1.8 Signal (test sample)Signal (tra<strong>in</strong><strong>in</strong>g sample)Background (test sample) Background (tra<strong>in</strong><strong>in</strong>g sample)1.6Kolmogorov-Smirnov test: signal (background) probability = 0.973 (0.963)1.41.210.80.60.40.20-1 -0.5 0 0.5 1MLP responseU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Figure B.1: Multijet-NN tra<strong>in</strong><strong>in</strong>g and test output.135
136NormalisedTMVA Input Variable: met0.070.060.050.040.030.020.01SignalBackground060 80 100 120 140 160 180 200 220 240metTMVA Input Variable: leadjet_etaU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.1)%NormalisedTMVA Input Variable: leadjet_et0.0240.0220.020.0180.0160.0140.0120.010.0080.0060.0040.002050 100 150 200 250 300leadjet_etTMVA Input Variable: secondjet_etaU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%NormalisedTMVA Input Variable: secondjet_et0.060.050.040.030.020.01040 60 80 100 120 140 160 180 200secondjet_etTMVA Input Variable: dphi_1jet_2jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised0.60.50.40.30.20.10-2 -1.5 -1 -0.5 0 0.5 1 1.5 2leadjet_etaU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised0.50.40.30.20.10-2 -1.5 -1 -0.5 0 0.5 1 1.5 2secondjet_etaU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised0.70.60.50.40.30.20.100.5 1 1.5 2 2.5 3dphi_1jet_2jetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%TMVA Input Variable: m<strong>in</strong>_dphi_met_jetsTMVA Input Variable: htTMVA Input Variable: trackmetNormalised0.70.60.50.40.30.20.101 1.5 2 2.5 3m<strong>in</strong>_dphi_met_jetsU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised0.0120.010.0080.0060.0040.0020100 150 200 250 300 350 400 450 500htU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Normalised0.0250.020.0150.010.00500 20 40 60 80 100 120 140 160 180trackmetU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%TMVA Input Variable: trackmetphiNormalised2.521.510.500 0.2 0.4 0.6 0.8 1 1.2 1.4trackmetphiU/O-flow (S,B): (0.0, 0.0)% / (0.0, 0.0)%Figure B.2: Input variables used <strong>for</strong> <strong>the</strong> tra<strong>in</strong><strong>in</strong>g of <strong>the</strong> multijet-NN
Appendix CAlpgen vs Pythia Comparison <strong>in</strong> <strong>the</strong><strong>Search</strong> <strong>for</strong> Scalar Top Decay<strong>in</strong>g <strong>in</strong>to c + ˜χ 0The search <strong>for</strong> scalar top decay<strong>in</strong>g <strong>in</strong>to charm and neutral<strong>in</strong>o is per<strong>for</strong>m us<strong>in</strong>g ALPGEN generatorto predict <strong>the</strong> W/Z+ jets background, as described <strong>in</strong> Chapter 7. However, we also run <strong>the</strong>whole analysis us<strong>in</strong>g PYTHIA event generator. The ALPGEN prediction is used as <strong>the</strong> nom<strong>in</strong>alestimation while <strong>the</strong> PYTHIA prediction is used as a cross check. Differences <strong>in</strong> shape between<strong>the</strong> two Monte Carlo estimations are taken as systematic uncerta<strong>in</strong>ties.This comparison between Monte Carlo generators is made with <strong>the</strong> analysis selection andis not <strong>in</strong>tended to compare <strong>the</strong> two Monte Carlo <strong>the</strong>mselves. The goal of this comparison is tosee how sensitive we are to differences between both generators.The figures <strong>in</strong> this appendix are <strong>the</strong> same as <strong>the</strong> ones shown <strong>in</strong> Chapter 7 but us<strong>in</strong>g PYTHIA<strong>in</strong>stead of ALPGEN <strong>for</strong> <strong>the</strong> W/Z+ jets prediction. This means that <strong>the</strong> differences are onlypresent <strong>in</strong> <strong>the</strong> red histogram labeled as Electroweak bosons.Figures C.1,C.2, and C.3 show <strong>the</strong> lead<strong>in</strong>g jet E T and E / T <strong>in</strong> <strong>the</strong> three control regions def<strong>in</strong>ed<strong>in</strong> <strong>the</strong> analysis.Figure C.4 shows <strong>the</strong> output of <strong>the</strong> multijet-NN, and figure C.5 shows <strong>the</strong> neural networkoutput <strong>in</strong> <strong>the</strong> region (0,1) after CHAOS application. The latter plot is used to extract a shapesystematic uncerta<strong>in</strong>ty used to compute <strong>the</strong> f<strong>in</strong>al limit.137
138Events/12 GeV18000160001400012000100008000600040002000CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons00 50 100 150 200 250 300 350 400 450E T,j1 [GeV]Events/12 GeV510410310210101-1CDF Run II Prelim<strong>in</strong>ary-1L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons100 50 100 150 200 250 300 350 400 450E T,j1 [GeV]∫Events/8 GeV600005000040000300002000010000CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons00 50 100 150 200 250 300 350 400E T[GeV]Events/8 GeV510410310210101-1CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons100 50 100 150 200 250 300 350 400E T[GeV]Figure C.1: Lead<strong>in</strong>g jet E T and / E T <strong>in</strong> l<strong>in</strong>ear (left) and logarithmic (right) scales <strong>in</strong> <strong>the</strong> HF multijet controlregion.
Appendix C. Alpgen vs Pythia Comparison <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong> Stop 139CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/12 GeV350CDF Data300250HF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/12 GeV310210CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons2001015010015000 50 100 150 200 250 300 350E T,j1 [GeV]10-10 50 100 150 200 250 300 350E T,j1 [GeV]CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/8 GeV350300250200CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/8 GeV21010CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons15010015000 50 100 150 200 250 300 350 400E T[GeV]10-10 50 100 150 200 250 300 350 400E T[GeV]Figure C.2: Lead<strong>in</strong>g jet E T and / E T <strong>in</strong> l<strong>in</strong>ear (left) and logarithmic (right) scales <strong>in</strong> <strong>the</strong> lepton control region.
140CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/12 GeV4000CDF Data350030002500HF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/12 GeV310210CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons20001015001000150000 50 100 150 200 250 300 350 400 450E T,j1 [GeV]10-10 50 100 150 200 250 300 350 400 450E T,j1 [GeV]CDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbCDF Run II Prelim<strong>in</strong>ary-1∫L dt=2.6 fbEvents/8 GeV1000080006000CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosonsEvents/8 GeV410310210CDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons4000102000100 50 100 150 200 250 300 350 400E T[GeV]10-10 50 100 150 200 250 300 350 400E T[GeV]Figure C.3: Lead<strong>in</strong>g jet E T and / E T <strong>in</strong> l<strong>in</strong>ear (left) and logarithmic (right) scales <strong>in</strong> <strong>the</strong> pre-optimization controlregion.
Appendix C. Alpgen vs Pythia Comparison <strong>in</strong> <strong>the</strong> <strong>Search</strong> <strong>for</strong> Stop 141Events700600500400-1CDF Run II Prelim<strong>in</strong>ary ∫L dt=2.6 fbCDF DataHF MultijetsLight-flavor jetsTop-quarkElectroweak bosons~Signal m( t)=125, m(∼χ)=70(x10)~Signal m( t)=135, m(∼~χ)=70(x10)Signal m( t)=115, m(∼χ)=70(x10)3002001000-1 -0.5 0 0.5 1OutputFigure C.4: Output of <strong>the</strong> NN to reject HF multijet background. The arrow <strong>in</strong>dicates <strong>the</strong> cut applied <strong>in</strong> <strong>the</strong>analysis.N-Events45 CDF Run II Prelim<strong>in</strong>ary -1L dt=2.6 fb4035302520∫HF MultijetsLight-flavor jetsTop-quarkElectroweak bosons~Signal m( t)=125, m(∼χ)=70~Signal m( t)=135, m(∼χ)=70~Signal m( t)=115, m(∼χ)=701510500 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1OutputFigure C.5: Observed f<strong>in</strong>al discrim<strong>in</strong>ant used to extract <strong>the</strong> limits from <strong>the</strong> shapes.
142
Appendix DResumen en castellanoEl Modelo Estándar (ME) de las partículas elementales ha demostrado ser una de las descripcionesmás precisas de la Naturaleza. El modelo, <strong>in</strong>cluye las <strong>in</strong>teracciones electromagnética,débil y fuerte, construyendo el Lagrangiano para describirlas desde pr<strong>in</strong>cipios de simetría.En el marco del Modelo Estándar hay dos tipos de constituyentes fundamentales de la naturaleza:bosones y fermiones. Los bosones son las partículas responsables de <strong>in</strong>tercambiar las<strong>in</strong>teracciones entre los fermiones, que son los constituyentes de la materia. Los fermiones sedividen en seis quarks y seis leptones, <strong>for</strong>mando una estructura de tres familias. Cada fermióny bosón así def<strong>in</strong>ido, tiene ademas su antipartícula.A pesar del su éxito, varias dificultades apuntan a que el Modelo Estándar es una teoríaválida a baja escala de energías. Sus limitaciones <strong>in</strong>cluyen la dificultad de <strong>in</strong>troducir la gravedady la falta de justificación para el ajuste f<strong>in</strong>o de algunas correcciones perturbativas. Ademas,algunos aspectos de la teoría no están entendidos, como el espectro de masas o el mecanismode rotura de la simetría electrodébil.Como respuesta a las carencias del Modelo Estándar nace la Supersimetría (SUSY), unnuevo marco teórico que solventa los citados problemas, manteniendo <strong>in</strong>tacto el poder predictivode la teoría. La SUSY <strong>in</strong>troduce una nueva simetría que relaciona un nuevo bosón con cadafermión del ME y un nuevo fermión con cada bosón del ME. De esta <strong>for</strong>ma, para cada bosónexistente en el ME, debería existir un súper compañero fermiónico (denotado con el sufijo <strong>in</strong>o),y de la misma <strong>for</strong>ma, para cada fermión existente en el ME, debería existir un súper compañerobosónico (denotado con el prefijo s). Además, se suele <strong>in</strong>troducir otra simetría, llamada paridadR para prevenir <strong>in</strong>teracciones con violación de numero bariónico y leptónico. Asumiendo conservaciónde paridad R, las súper partículas solo pueden ser producidas en pares y no pueden143
144des<strong>in</strong>tegrarse completamente en partículas del ME. Este último punto implica la existencia dela partícula supersimétrica más ligera, que proporciona un candidato para materia oscura, comosugieren datos astrofísicos.Tevatron es un colisionador hadrónico situado en Fermilab, EEUU. Este acelerador producecolisiones protón-antiprotón con una energía en el centro de masas de √ s=1.96 TeV. En uno delos dos puntos de colisión del Tevatron, se encuentra CDF, un detector construido para analizarlas colisiones producidas por el acelerador.Introducción teóricaEl Modelo Estándar de las partículas es un teoría cuántica de campos que ha demostrado describirmuchos resultados experimentales con un nivel de precisión s<strong>in</strong> precedentes.Basada en varias simetrías de grupos, el Modelo Estándar <strong>in</strong>cluye las <strong>in</strong>teracciones electromagnética,débil y fuerte. Los constituyentes básicos de la Naturaleza, de acuerdo con elModelo Estándar, son un conjunto de fermiones y bosones. Los fermiones son los responsablesde la materia, mientras que los bosones son los mediadores de las <strong>in</strong>teracciones.El sector fermiónico agrupa seis quarks, seis leptones y sus respectivas antipartículas, divididosen tres familias. Los miembros de esas familias son idénticos en todos los observablesexcepto por la masa. Nuestro mundo más <strong>in</strong>mediato está hecho con partículas de la primerafamilia: el quark u y d que <strong>for</strong>man los protones y neutrones de los núcleos y los electrones, ysus neutr<strong>in</strong>os asociados, como se mustra en la Tabla D.1. Las partículas de las otras dos familiasson mas masivas y se des<strong>in</strong>tegran rápidamente en partículas de la primera familia.quarksleptons1 st <strong>Generation</strong> 2 nd <strong>Generation</strong> 3 rd <strong>Generation</strong>Up (u) Charm (c) Top (t)1.5-3.0 MeV/c 2 1.25±0.09 GeV/c 2 173.1±1.3 GeV/c 2Down (d) Strange (s) Bottom (b)3.0-7.0 MeV/c 2 95±25 MeV/c 2 4.20±0.07 GeV/c 2Electron neutr<strong>in</strong>o (ν e ) Muon neutr<strong>in</strong>o (ν µ ) Tau neutr<strong>in</strong>o (ν τ )< 2 eV/c 2 < 0.19 MeV/c 2 < 18.2 MeV/c 2Electron (e) Muon (µ) Tau (τ)0.511 MeV/c 2 105.66 MeV/c 2 1776.99 +0.29−0.26 MeV/c2Table D.1: El sector fermiónico del Modelo Estándar.
Appendix D. Resumen en castellano 145Las <strong>in</strong>teracciones de los fermiones están mediadas por los constituyentes bosónicos delModelo Estándar. Estos bosones llevan las fuerzas fundamentales derivadas de las simetrías,como se resume en la Tabla D.2.Interacción Partícula Masaelectromagnética fotón, γ 0fuerte gluón, g 0débilW ± 80.403±0.029 GeV/c 2Z 0 91.188±0.002 GeV/c 2Table D.2: Los bosones de gauge del Modelo Estándar y sus <strong>in</strong>teracciones.S<strong>in</strong> embargo, <strong>in</strong>cluso si la gravedad es la <strong>in</strong>teracción que ha sido conocida por mayor tiempoy es la más cercana a nuestra vida cotidiana, todavía no ha sido <strong>in</strong>cluida satisfactoriamente enel marco del Modelo Estándar. Este es uno de los mayores argumentos en contra del ModeloEstándar como una teoría del todo, sugiriéndose de esta manera que debería existir unateoría más general. Esta nueva teoría debería <strong>in</strong>cluir todas las simetrías del Modelo Estándar ysimultáneamente aceptar esta cuarta <strong>in</strong>teracción.Incluso aceptando las peculiaridades del Modelo Estándar, este contiene por lo menos 19parámetros libres, como acoplos, masas y mezclas, los cuales no están predichos pero deben sermedidos por los experimentos. Además, más parámetros serían necesarios si uno quiere acomodarobservaciones que no proceden de la física de aceleradores, como la asimetría bariónicaen cosmología, las masas de los neutr<strong>in</strong>os y sus mezclas.El Modelo Estándar deja además varias cuestiones s<strong>in</strong> responder como por qué hay tres generaciones,dimensiones espaciales o colores, como entender las oscilaciones de los neutr<strong>in</strong>os,por qué son las cargas eléctricas del protón y del electrón exactamente opuestas o si el mecanismode Higgs es realmente el proceso que a través del cual se produce la rotura electrodébil dela simetría. Además, el modelo no puede explicar cuales son los mecanismos para producir laasimetría de materia anti-materia observada en el universo, o cual es la relación entre las fuerzasfuerte y electrodébil. Quizás, la propiedad más sorprendente del Modelo Estándar es su precisadescripción de las <strong>in</strong>teracciones entre partículas con masas 17 ordenes de magnitud menoresque la escala de la masa Planck.Para dar solución a estos problemas uno de los modelos más populares es el conocido comoSupersimetría, un nuevo marco teórico que solventa los citados problemas, manteniendo <strong>in</strong>tacto
146el poder predictivo de la teoría. La SUSY <strong>in</strong>troduce una nueva simetría que relaciona un nuevobosón con cada fermión del ME y un nuevo fermión con cada bosón del ME. De esta <strong>for</strong>ma, paracada bosón existente en el ME, debería existir un súper compañero fermiónico (denotado con elsufijo <strong>in</strong>o), y de la misma <strong>for</strong>ma, para cada fermión existente en el ME, debería existir un súpercompañero bosónico (denotado con el prefijo s). Además, se suele <strong>in</strong>troducir otra simetría,llamada paridad R para prevenir <strong>in</strong>teracciones con violación de numero bariónico y leptónico.Asumiendo conservación de paridad R, las súper partículas solo pueden ser producidas en paresy no pueden des<strong>in</strong>tegrarse completamente en partículas del ME. Este último punto implica laexistencia de la partícula supersimétrica más ligera, que proporciona un candidato para materiaoscura, como sugieren datos astrofísicos.Esta tesis presenta dos búsquedas de squarks de la tercera familia. En el marco de la Superimetríay en particular en su mínima extensión, el MSSM, se espera una gran mezcla de losestados de masa dependiendo de ciertos parámetros de la teoría: tanβ y A t,b .En particular para el caso del ˜b, la masa de este squark podría ser significativamente máspequeña que la masa de los otros squarks:m 2˜b1,2 = 1 2 [m2˜bL + m 2˜bR ±√(m 2˜bL − m 2˜bR ) 2 + 4m 2 b (A b − µtanβ) 2 ] (D.1)Además, la sección eficaz de producción de glu<strong>in</strong>o es casi un orden de magnitud mayor quela del sbottom de una masa similar. A las energías alcanzadas en Tevatron, los glu<strong>in</strong>os se producenpr<strong>in</strong>cipalmente a través de aniquilación quark-antiquark y fusión de gluones, figure D.1.Si el sbottom es sufientemente ligero, entonces la des<strong>in</strong>tegración a dos cuerpos ˜g → b˜b estaríac<strong>in</strong>emáticamente permitida.q g ~ g ~qq~g~gg~_q_qg~gg~Figure D.1: Mecanismos de producción de glu<strong>in</strong>os a primer orden a la energía de centro de masas de Tevatron.En la región de <strong>in</strong>terés para este análisis (m t , m˜χ + > m˜b> m˜χ 0), la des<strong>in</strong>tegración dom<strong>in</strong>antees sbottom a bottom quark y neutral<strong>in</strong>o ˜b → b˜χ 0 , con n<strong>in</strong>guna otra des<strong>in</strong>tegración posible,puesto que exigimos que m˜b< m t , m˜χ +. Por lo tanto, asumimos un tasa de des<strong>in</strong>tegración del
Appendix D. Resumen en castellano 147100% para el ˜b → b˜χ 0 . La cadena completa de des<strong>in</strong>tegración del glu<strong>in</strong>o se muestra en lafigura D.2.~g~bbb~χ 0Figure D.2: Des<strong>in</strong>tegración del glu<strong>in</strong>o en quark bottom y sbottom.En el caso del stop, dada la gran masa del quark top, la separación entre estados de masaaparece de <strong>for</strong>ma natural:m 2˜t 1,2= 1 2 [m2˜t L+ m 2˜t R±√(m 2˜t L− m 2˜t R) 2 + 4m 2 t(A t − µcotβ) 2 ] (D.2)Asumiendo conservación de paridad-R, los quarks stop se producen en pares, como se muestraen la figura D.3 y la partícula supersimétrica más ligera debe ser estable. Si además no tienecolor y es neutra, escapará a la detección produciendo momento trasnverso neto en el estadof<strong>in</strong>al.g~tq~tg~- tg~- tq-~- tg~tFigure D.3: Mecanismos de producción de stop a primer orden a la energía en el centro de masas del Tevatron.Este escenario es accesible en el rango m˜t 1< m b +m˜χ + y m˜t 1< m W +m b +m˜χ 0 en el cual,la des<strong>in</strong>tegración dom<strong>in</strong>ante de ˜t 1 es el proceso de cambio de sabor ˜t 1 → c˜χ 0 que típicamentese asume como un 100%, tal y como se muestra en la figura D.4. La des<strong>in</strong>tegración ˜t 1 → t˜χ 0está c<strong>in</strong>ematicamente prohibida por encima del rango de masas del ˜t 1 accesible a día de hoy enel Tevatron. Por otro lado, la des<strong>in</strong>tegración a tres cuerpos ˜t 1 → bff ′˜χ 0 es despreciable. En
148este caso particular, el estado f<strong>in</strong>al consiste en dos c-jets y momento transverso neto procedentedel ˜χ 0 .~tb~χ +Wc~χ 0Figure D.4: Des<strong>in</strong>tegración de stop en charm y neutral<strong>in</strong>o.Dispositivo experimentalEl acelerador Tevatron situado en el Fermi National Accelerator Laboratory (Fermilab) enBatavia (Ill<strong>in</strong>ois, EEUU) es un colisionador protón-antiprotón con una energía en el centro demasas de 1.96 TeV. Estas <strong>in</strong>stalaciones tienen c<strong>in</strong>co aceleradores y anillos de almacenamientousados en etapas sucesivas para acelerar las partículas hasta 980 GeV.El ciclo de aceleración empieza con la producción de protones a partir de hidrógeno ionizado,que se aceleran hasta 750 KeV por un Cockroft-Walton. Estos iones preacelerados se<strong>in</strong>yectan en el L<strong>in</strong>ac donde se aceleran hasta 400 GeV. Al f<strong>in</strong>al de este proceso, los iones pasana través de una hoja de carbono para arrancar sus electrones y producir protones. Dentro delBooster los protones se agrupan en paquetes y se aceleran hasta una energía de 8 GeV. En elMa<strong>in</strong> Injector, estos protones se aceleran hasta 150 GeV y se <strong>in</strong>yectan en el paso f<strong>in</strong>al en elTevatron.La producción de antiprotones es significativamente más complicada. El ciclo empieza conla extracción de protones a 120 GeV del Ma<strong>in</strong> Injector y su posterior colisión contra un blancode acero <strong>in</strong>oxidable. Este proceso produce una amplia variedad de partículas entre las que seencuentran los antiprotones. Las partículas emergen del blanco con diferentes ángulos y sonfocalizadas hacia la l<strong>in</strong>ea de aceleración. Con el objetivo de seleccionar solo antiprotones, elhaz de partículas se envía a través de un imán pulsado que actúa como expectrómetro. Losantiprotones asi producidos son <strong>in</strong>yectados en el Debuncher, un acelerador que aumenta suenergía hasta 8 GeV. Después de este proceso, el haz de antiprotones se dirige al Accumulator,
Appendix D. Resumen en castellano 149un anillo de almacenamiento. Desde ahí, los antiprotones son f<strong>in</strong>almente <strong>in</strong>yectados en el Ma<strong>in</strong>Injector y acelerados hasta 150 GeV, desde donde se <strong>in</strong>yectan al Tevatron de la misma maneraque los protones.El detector CDF II se encuentra en operación desde 2001. Es un detector multipropósitoque comb<strong>in</strong>a varios subdetectores dispuestos de <strong>for</strong>ma cilíndrica y concentrica respecto al ejede del haz de partículas. CDF II, mostrado en la figura D.5, está <strong>for</strong>mado por:• Un sistema de identificación de trazas que proporciona la medida del momento de laspartículas cargadas, la posición del vértice primario de la <strong>in</strong>teracción en el eje z, y permite,a su vez, reconstruir vértices secundarios.• Un calorímetro cuyo propósito es medir la energía de las partículas cargadas producidasen la <strong>in</strong>teracción.• Cámaras de deriva y centelleadores para la detección de muones.Figure D.5: Vista del detector CDF Run II.En los siguientes párrafos se llevará a cabo una breve <strong>in</strong>troducción a cada uno de los subdetectoresempezando por los más cercanos a la tubería del haz y siguiendo hacia el exterior endirección radial.
150Los sistemas de identificación de trazas se encuentran dentro de un solenoide superconductorde 1.5 m de radio y 4.8 m de longitud que genera un campo magnético de 1.4 T paraleloal eje del haz de partículas. La parte más <strong>in</strong>terna del sistema de identificación de trazas es undetector de microtiras de silicio resistente a la radiación. Se extiende desde un radio de 1.2 cmhasta 28 cm, cubriendo las regiones centrales del detector.La capa más <strong>in</strong>terna de silicio se conoce como L00 y está <strong>for</strong>mada por microtiras activassolo por uno de sus lados. Las siguientes c<strong>in</strong>co capas de silicio después del L00, constituyenel SVXII. F<strong>in</strong>almente, las dos capas más externas <strong>for</strong>man el ISL. Las siete capas que <strong>for</strong>man elSVXII y el ISL contienen material sensible por los dos lados y proporcionan <strong>in</strong><strong>for</strong>mación de laposición de las partículas con una precisión de 9 micras en el mejor de los casos.Rodeando el detector de silicio se encuentra la Central Outer Tracker (COT), la pieza fundamentaldel sistema de detección de trazas de CDF II. La COT es una cámara de deriva cilíndricade 3.1 m de longitud, que cubre en la zona radial una región desde los 40 a los 137 cm. Esta<strong>for</strong>mada por 96 capas de hilos sensibles que están agrupados de <strong>for</strong>ma radial en 8 supercapas.El número total de hilos sensibles de la COT es 30240. Aproximadamente la mitad de estoshilos van en la dirección z y la otra mitad están <strong>in</strong>cl<strong>in</strong>ados un pequeño ángulo (2 grados) conrespecto a la dirección z. La comb<strong>in</strong>ación de estos dos tipos de hilos permite la medida deposiciones en z.El sistema de calorímetros de CDF II se encuentra rodeando el sistema de detección detrazas en la parte exterior del solenoide. Los dist<strong>in</strong>tos calorímetros que componen el sistemason detectores basados en centelleadores segmentados en torres proyectivas que apuntan a laregión de <strong>in</strong>teracción.El calorímetro está dividido en dos regiones: la región central y el “plug”. Cada una deestas regiones esta dividida en parte electromagnética y hadrónica. La parte electromagnéticaproporciona <strong>in</strong><strong>for</strong>mación para reconstruir objetos como electrones o fotones, mientras que laparte hadrónica se usa para la reconstrucción de jets.Por último, en la parte más externa de CDF II se encuentran las cámaras de muones. Elsistema de detección de muones consiste en un conjunto de cámaras de deriva y centelleadoresque están <strong>in</strong>stalados en la parte exterior del calorímetro.Como complemento a los sistemas de detección, CDF II cuenta con un complejo sistema deadquisición de datos. La tasa media de <strong>in</strong>teracciones en el Tevatron es de 2,53 Mhz. Esta tasade <strong>in</strong>teracción es órdenes de magnitud superior a la máxima tasa que el sistema de adquisiciónde datos puede soportar. Además, la mayoría de las colisiones producidas son de un <strong>in</strong>terés nulo
Appendix D. Resumen en castellano 151para el análisis de datos. Por estos motivos, CDF cuenta con un sistema automático de selecciónde sucesos a tiempo real, trigger. El trigger decide si el correspondiente suceso medido por eldetector va a ser almacenado en c<strong>in</strong>ta para su posterior análisis o descartado def<strong>in</strong>itivamente.El sistema de trigger de CDF consiste en tres niveles de decisión. Los dos primeros nivelesestán basados en hardware y el tercero consiste en una granja de procesadores. Las decisionestomadas por el sistema están basadas en <strong>in</strong><strong>for</strong>mación de los sucesos con complejidad creciente.El nivel 1 del trigger es un sistema síncrono que lee sucesos y toma decisiones cada vez que seproduce un cruce de protones y antiprotones. El nivel 1 del trigger reduce la tasa de sucesos de2,53 MHz a menos de 50 kHz. El hardware de este nivel 1 consiste en tres l<strong>in</strong>eas paralelas deprocesado que alimentan a la unidad global de decisión de nivel 1. Una de las l<strong>in</strong>eas se encargade encontrar objetos basados en medidas del calorímetro, L1 CAL, otra encuentra muones,L1 MUON, mientras que la tercera encuentra trazas en la COT, L1 TRACK. Puesto que losmuones y electrones necesitan la presencia de una traza apuntando al correspondiente detector,la <strong>in</strong><strong>for</strong>mación de estas trazas se envía a las l<strong>in</strong>eas de calorímetro, muones y trazas.F<strong>in</strong>almente, la unidad global de decisión de nivel 1 toma una decisión basada en los objetosde <strong>in</strong>terés encontrados por diferentes procesos del nivel 1.Como segundo paso en sistema de decisión tenemos el nivel 2 del trigger que es un sistemaasíncrono que procesa sucesos recibidos desde el nivel 1. Después del nivel 2, la tasa de sucesosse reduce a 1 kHz.Una vez que el suceso es aceptado a nivel 2, tiene que ser procesado completamente contoda la <strong>in</strong><strong>for</strong>mación disponible en el detector. Esta operación tiene lugar en el granjas de procesadoresa nivel 3. El nivel 3 reconstruye el suceso utilizando algoritmos que usan toda la <strong>in</strong><strong>for</strong>macióndisponible en el detector y mejoran la resolución utilizada en los niveles anteriores.Esto <strong>in</strong>cluye una reconstrucción tridimensional de las trazas, el emparejamiento entre trazasy calorímetro o sistema de muones. Los sucesos que pasan satisfactoriamente los requisitosdel nivel 3 son transferidos al sistema de almacenado en c<strong>in</strong>ta magnética. La tasa media deprocesado a nivel 3 por suceso es de unos pocos segundos. La tasa de sucesos cumpliendo losrequisitos de nivel 3 se reduce a 50 Hz.
152Reconstrucción de sucesosPara realizar un analis de datos, la <strong>in</strong><strong>for</strong>mación obtenida del detector tiene que ser procesadacon el objetivo de reconstruir observables. Esta reconstrucción implica algoritmos matemáticosy def<strong>in</strong>iciones muy relacionadas con el detector en si mismo.Los análisis descritos en esta tesis están basados en jets, momento transverso neto y de<strong>for</strong>ma <strong>in</strong>directa, electrones y muones.De especial relevancia es la reconstrucción del vértice primario de <strong>in</strong>teracción. El vérticeno es un objeto de análisis como tal, s<strong>in</strong> embargo, es la referencia <strong>in</strong>icial para la reconstrucciónde cualquier otro objeto f<strong>in</strong>al.En los análisis presentados en este trabajo no se esperan leptones en el estado f<strong>in</strong>al. Por lotanto, durante los procesos de optimización de señal se aplica un rechazo de este tipo de objetos.Esta condición de rechazo implica la identificación de dicho objeto.Para la identificación de electrones se requiere, básicamente, una deposición de energíaaislada en el calorímetro central de más de 10 GeV/c. Por su parte, los muones candidatos hande tener una traza en las cámaras de deriva con momento transverso de más de 10 GeV/c y s<strong>in</strong>n<strong>in</strong>guna condición en las cámaras de muones.De especial <strong>in</strong>terés para nuestros estudios son los sucesos que después de la <strong>in</strong>teracción dequarks y gluones producen chorros de partículas conocidos como jets. Estos jets son reconociblespor sus deposiciones de energía en el calorímetro.Existen varios algoritmos para la reconstrucción de jets. La mayoría de ellos están basadosen <strong>in</strong><strong>for</strong>mación puramente calorimétrica, s<strong>in</strong> embargo, también se pueden encontrar algoritmosque <strong>in</strong>corporan <strong>in</strong><strong>for</strong>mación de trazas. La identificación de jets usada en estas búsquedas sebasa por completo en el algoritmo JETCLU.Este algoritmo comienza buscando una torre en el calorímetro con energía superior a 1 GeV,luego por agrupación de torres adyacentes dentro de un radio dado desde la torre de mayorenergía a la de menor energía se construye un pre-jet. Una torre puede estar asignada a unoy solo un pre-jet. En el siguiente paso, se calcula el centro de cada pre-jet y se def<strong>in</strong>e unnuevo cono <strong>in</strong>cluyendo torres con energía superior a 100 MeV. Si el centro del nuevo pre-jetcambia, el cono es redef<strong>in</strong>ido y se añaden nuevas torres de <strong>for</strong>ma iterativa. Cuando se encuentrauna solución estable, se evita el solapamiento entre objetos uniéndolos o separándolos pre-jetscontiguos y de esta <strong>for</strong>ma se def<strong>in</strong>e el objeto f<strong>in</strong>al, jet.Por último, la energía del jet se corrige por la dependencia del calorímetro con la pseudo-
Appendix D. Resumen en castellano 153rapidez y la energía procedente de <strong>in</strong>teracciones múltiples.El último de los objetos def<strong>in</strong>idos es el momento transverso neto. La presencia de partículas<strong>in</strong>detectables en un suceso es <strong>in</strong>ferida por la medida de momento transverso no nulo en eldetector. Esta cantidad se reconstruye basandose por completo en <strong>in</strong><strong>for</strong>mación del calorímetro.Algoritmos de tagg<strong>in</strong>gEl hecho de que la mayoría de los sucesos de procesos considerados fondos contengan soloquarks ligeros en sus estados f<strong>in</strong>ales, hace al tagg<strong>in</strong>g de sabores pesados una de las herramientasmás poderosas a la hora de elim<strong>in</strong>ar fondos. Diferentes algoritmos y separadores de sabor seusan de <strong>for</strong>ma extensiva en la física de partículas.Los hadrones B en jets prov<strong>in</strong>ientes de la fragmentación de quarks b, tienen de media unadistancia de vuelo de unas 500 micras, produciendo vértices secundarios con respecto al puntode <strong>in</strong>teracción. Estos hadrones viajan alejandose del vértice primario y des<strong>in</strong>tegrandose a travésde una cascada de partículas. Los productos cargados de esta des<strong>in</strong>tegración se pueden reconstruirgeneralmente como trazas desplazadas. La <strong>in</strong>tersección de estas trazas <strong>for</strong>ma vérticessecundarios en el punto donde los hadrones se habian des<strong>in</strong>tegrado.El algoritmo SecVtx busca trazas desplazadas comb<strong>in</strong>ando trazas dentro de un jet “taggable”.Los jets son taggable si la ETraw >10 GeV, η
154identificado como un quark pesado, un quark b, o un quark c. Dependiendo del sabor del partónorig<strong>in</strong>al, el tagged jet y su vértice secundario tienen diferentes características, pr<strong>in</strong>cipalmenterelacionadas con las trazas.Usando propiedades de las trazas que <strong>for</strong>man el vértice secundario y las trazas del jet en unared neuronal, CHAOS nos permite aumentar la presencia de c-jets en nuestro estado f<strong>in</strong>al.CHAOS es una red neuronal basada en SNNS. La estructura <strong>in</strong>cluye tres capas, una capade entrada con 22 nodos, una capa oculta con 22 nodos y una capa de salida con 2 nodosproduciendo una salida bidimensional. La red neuronal utiliza un conjunto de 22 variables,relacionadas en su mayoría con propiedades de las trazas. Estas variables se pueden encontraren la Tabla D.3 y han sido seleccionadas de <strong>for</strong>ma cuidadosa para estar bien reproducidas porla simulación y para tener un comportamiento estable, evitando dependencias con la c<strong>in</strong>ematicade los jets.Mass of <strong>the</strong> vertexCharge of <strong>the</strong> vertexVariables de entrada del CHAOSAverage |d 0 | of good tracksAverage |d 0 significance| of good tracksL xy significance Fraction of good tracks with |d 0 significance| >1Number of pass−1 tracksNumber of good tracksFraction of good tracks with |d 0 significance| >3Number of vertex ′ s tracksNumber of good tracksFraction of good tracks with |d 0 significance| >5∑pT (good tracks)PE, where E T is <strong>the</strong> jet E TT T E T, where P T is <strong>the</strong> P T of <strong>the</strong> secondary vertex∑z t = ∑ pT (pass−1 tracks)pT (good tracks)Fraction of vertex p T <strong>in</strong> <strong>the</strong> lead<strong>in</strong>g trackFraction of vertex p T <strong>in</strong> <strong>the</strong> second lead<strong>in</strong>g trackr vtx = p T of <strong>the</strong> vertex∑pT (good tracks)Signed d 0 of <strong>the</strong> lead<strong>in</strong>g vertex trackSigned d 0 of <strong>the</strong> second lead<strong>in</strong>g vertex trackSigned d 0 significance of <strong>the</strong> lead<strong>in</strong>g vertex trackSigned d 0 significance of <strong>the</strong> second lead<strong>in</strong>g vertex trackφ jetη jetTable D.3: Listas de variables usadas en el CHAOS.La salida bidimensional de la red neuronal permite la separacion de tres sabores diferentes.Cortando en esta salida se puede seleccionar el sabor deseado. En nuestro caso particular utilizamosel CHAOS para seleccionar jets c, como se muestra en la figura D.6.Las eficiencias de selección para jets b y c se resumen en la Tabla D.4. Los números presentadosson obtenidos para un corte en el CHAOS de 1.65.
Appendix D. Resumen en castellano 155Fraction of objects [%]6050403020Network Output <strong>for</strong> Node 0CharmBottomLight+TausFraction of objects [%]6050403020Network Output <strong>for</strong> Node 1CharmBottomLight+TausFraction of objects [%]16141210864Sum of network outputsCharmBottomLight+Taus1010200 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1SNNS Output 0 (anti-light)00 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1SNNS Output 1 (anti-bottom)00.8 1 1.2 1.4 1.6 1.8 2Sum of outputsFigure D.6: Figuras de salida del CHAOS en 1-D.c jets b jetsEficiencia (Datos) 0.346 ± 0.052 0.073 ± 0.014Factor de escala CHAOS 1.01 ± 0.15 1.14 ± 0.22Table D.4: Eficiencia de selección de c y b tagged jets y factores de escala (SF CHAOS ) para un corte en elCHAOS de 1.65.Búsqueda de sbottom producido a través de glu<strong>in</strong>osEl primero de los análisis de datos presentado en este trabajo es la búsqueda de sbottom quarks através de la des<strong>in</strong>tegración de glu<strong>in</strong>os. Asumiendo paridad R, los glu<strong>in</strong>os se producen en pares,des<strong>in</strong>tegrándose cada uno de ellos en bottom quark y sbottom quark. A su vez, cada sbottom sedes<strong>in</strong>tegra en bottom quark y neutral<strong>in</strong>o. Como resultando un estado f<strong>in</strong>al con cuatro b-jets ymomento transverso neto procedente de los neutral<strong>in</strong>os, que escapan a la detección. Se asumeen que la cadena de des<strong>in</strong>tegración descrita ocurre en un 100 % de las veces.Con un estado f<strong>in</strong>al semejante, el uso de herramientas como el “tagg<strong>in</strong>g” es obligatorio parauna optimización adecuada. El primer paso en cualquier análisis es la correcta estimación delos fondos. Varios procesos del Modelo Estándar, producidos en el Tevatron, tienen un estadof<strong>in</strong>al que similar a nuestra señal de sbottom. Los sucesos seleccionados en el análisis tienencomo pr<strong>in</strong>cipales características: un momento transverso neto elevado, gran multiplicidad dejets, jets procedentes de quarks pesados y la ausencia de leptones.Los fondos del Modelo Estándar que tienen estas características son:
156• Producción e quark top• Producción de dibosones• Producción de W/Z + jets• Producción de multijes• Producción de multijes ligerosEl mayor desafío del análisis es, s<strong>in</strong> duda, la estimación de uno de los fondos mayoritarios,la producción de multijets, a partir de los datos. Puesto que la simulación de este fondo mediantemétodos de Monte Carlo supondría un gasto <strong>in</strong>gente de recursos <strong>in</strong><strong>for</strong>máticos, se ha estimadola contribución como un cociente de “tagged jets” sobre proto-“tagged jets”, en una muestrarepresentativa y parametrizado con respecto a varias variables. El método que se ha desarrolladorecibe el nombre de MUTARE. La <strong>for</strong>ma precisa de obtener la estimacion del MUTARE es lasiguiente:R MUTARE = N tags − N mistags − N MCtagsN taggable − N MCtaggable(D.4)donde N tags es el número de tagged jets, N mistags es el numero de jets procedentes de quarksligeros identificados de <strong>for</strong>ma erronea como jets procedentes de quarks pesados, Ntags MC es elnúmero de tagged jets procedentes de procesos no-multijet estimados a partir de Monte Carlo,N taggable es el número de taggable jets, y Ntaggable MC es el número de taggable jets procedentes deprocesos no-multijet estimados a partir de Monte Carlo.La predicción f<strong>in</strong>al se obtiene después de sustraer la contribución de sabores pesados procedentesde procesos no-multijet.HF multijetNevents= R(Ntaggable data − NMC taggable )(D.5)Una vez demostrado que los fondos son reproducibles en regiones de control def<strong>in</strong>idas“a priori”, se lleva a cabo una optimización de la señal de sbottom usando dos redes neuronalesen dos regiones c<strong>in</strong>emáticas dist<strong>in</strong>tas. La primera de las redes neuronales se utiliza para laelim<strong>in</strong>ación de multijets, el fondo dom<strong>in</strong>ante antes de cualquier optimización y la segunda redneuronal se utiliza para ellim<strong>in</strong>ar la producción de t¯t, el fondo dom<strong>in</strong>ante en el estado f<strong>in</strong>al.El proceso descrito se lleva a cabo para dos señales de sbotton dist<strong>in</strong>tas para tener en cuentados regiones c<strong>in</strong>emáticas bien diferenciadas. Estas dos regiones se caracterizan por la diferencia
Appendix D. Resumen en castellano 157de masas entre el glu<strong>in</strong>o y el sbottom. Los valores particulares elegidos para las optimizacionesson los siguientes:• Optimización con gran ∆m ⇒ M(˜g) = 335 GeV/c 2 , M(˜b) = 260 GeV/c 2• Optimización con pequeño ∆m ⇒ M(˜g) = 335 GeV/c 2 , M(˜b) = 315 GeV/c 2Como resultado de esta búsqueda no se ha encontrado n<strong>in</strong>guna desviación de la prediccióndel Modelo Estándar en el espacio de fases estudiado y se ha procedido a extraer un límite en lasección eficaz de producción del sbottom con un 95% de nivel de confianza, como se muestraen la figura D.7.Cross Section [pb]101-1-1CDF Run II (2.5 fb )295% CL limit (m[b ~ ]=250 GeV/c )Expected limit295% CL limit (m[b ~ ]=300 GeV/c )Expected limit~g →~b → b∼χ~bb (100% BR)0(100% BR)10-2pp→~g~g ats=1.96 GeVPROSPINO NLO (CTEQ6M)µ = µ = m(~g)R F~2 02m( q)=500 GeV/c m(∼χ )=60 GeV/c250 300 350 4002m(~g) [GeV/c]Figure D.7: Límites con un 95% de nivel de confianza en la sección eficaz de producción, observado (l<strong>in</strong>easolida) y esperado (l<strong>in</strong>ea de puntos).
158Búsqueda de stop des<strong>in</strong>tegrandose en charm y neutral<strong>in</strong>oEl segundo análisis llevado a cabo como parte de la presente tesis, es la búsqueda de quarkstop des<strong>in</strong>tegrandose en quark charm y neutral<strong>in</strong>o. Puesto que el stop se produce en paresasumiendo paridad R, el estado f<strong>in</strong>al está compuesto por dos charm jets y momento transversoneto procedente de los neutral<strong>in</strong>os. Este análisis es en muchos aspectos similar al descritoanteriormente por lo que la estimación de los fondos se lleva a cabo practicamente de la misma<strong>for</strong>ma.En este caso, los sucesos seleccionados en el análisis tienen como pr<strong>in</strong>cipales características:un momento transverso neto moderado, jets procedentes de c quarks y la ausencia de leptones.Los fondos del Modelo Estándar que tienen estas características son los mismos que se handescrito en análisis anterior pero con una proporción diferente:• Producción e quark top• Producción de dibosones• Producción de W/Z + jets• Producción de multijes• Producción de multijes ligerosS<strong>in</strong> embargo, el mayor reto en este caso es enriquecer la muestra en su estado f<strong>in</strong>al concharm jets, algo no trivial con los algoritmos de “tagg<strong>in</strong>g” estándar usados en CDF II. Por estemotivo se ha tenido que desarrollar un separador de sabor para jets, basado en una red neuronalcon nodo de salida en dos dimensiones que permite dist<strong>in</strong>guir el sabor de los jets separándolosen charm, bottom y jets ligeros (u,d,s). El anteriormente mencionado CHAOS.El proceso de optimización se ha llevado a cabo utilizando una señal de stop con las siguientescaracterísticas:• m(˜t) = 125 GeV/c 2 , m(˜χ 0 ) = 70 GeV/c 2El primer paso en la optimización es la elim<strong>in</strong>ación de gran parte del fondo de multijets medianteuna red neuronal entrenada para dist<strong>in</strong>guir la señal de stop y la producción de multijets.Una vez seleccionados los sucesos aplicando un corte en el discrim<strong>in</strong>ante de la red neuronal, se
Appendix D. Resumen en castellano 159aplica el CHAOS para aumentar la contribucion de jets c en el estado f<strong>in</strong>al. Aplicando nuevamenteun corte, esta vez en el CHAOS a 1.65, se obtiene la región f<strong>in</strong>al.No se ha encontrado n<strong>in</strong>guna desviación de la predicción del Modelo Estándar en el espaciode fases estudiado y se ha procedido a extraer un límite en la sección eficaz de producción delsbottom con un 95 % de nivel de confianza.Cross Section [pb]10210-1CDF Run II Prelim<strong>in</strong>ary L dt=2.6 fb~ 095% Exclusion limit from t χ∼1→ c∫02Observed [m(∼χ )=80 GeV/c ]Expected (±1σ)11o + m χ ∼11PROSPINO NLO (CTEQ6M)~µ = µ = m( t 1)RFm t ~≥ m W + m b90 100 110 120 130 140 150 160 170~2m(t 1 ) [GeV/c]Figure D.8: Límite observado con un 95% de nivel de confianza en term<strong>in</strong>os de sección eficaz para unam(˜χ 0 ) = 80 Gev/c 2 (l<strong>in</strong>ea negra) y límite esperado (l<strong>in</strong>ea roja) con una banda de <strong>in</strong>certidumbre de 1σ.
160Errores sistemáticosEn los dos análisis descritos se han llevado a cabo detallados estudios de los errores sistemáticos.En esta sección describiremos los errores procedentes de la búsqueda de stop des<strong>in</strong>tegrandoseen charm y neutral<strong>in</strong>o, ya que <strong>in</strong>cluyen errores en la <strong>for</strong>ma además de los errores que afectan ala normalización.Los errores sistemáticos son la mayor fuente de <strong>in</strong>certidumbre en cualquiera de las dosbúsquedas presentandas en esta tesis. Algunos de ellos afectan a la normalización de la señalo los fondos. Esta clase de errores tiene un impacto directo en el número de suscesos. S<strong>in</strong>embargo, la <strong>for</strong>ma de las predicciones no está afectada por este tipo de errores.Por el contrario, algunos errores sistematicos producen una variación en la <strong>for</strong>ma de laspredicciones. Esta segunda clase de errores sistemáticos se conoce como errores de <strong>for</strong>ma ypuede afectar a su vez al numero de sucesos predichos.Dado que la <strong>for</strong>ma de los fondos es utilizada para la extracción de los límites de exclusión,este tipo de errores de <strong>for</strong>ma son especialmente importantes.Los errores sistemáticos en señal y fondos han sido estudiados teniendo en cuenta correlacionesy anticorrelaciones entre ellos.• Escala de Energía de los Jets: Un error sistemático en la escala de energía del calorímetroafecta a la energía transversa total de los jets. El efecto en la región f<strong>in</strong>al es despreciable.• Factor de Escala del Tagg<strong>in</strong>g: Las diferencias entre datos y Monte Carlo en eficiencia detagg<strong>in</strong>g son tenidas en cuenta como un error sistemático. El error resultante en la regiónf<strong>in</strong>al es de un 3.6%.• Factor de Escala del CHAOS: La diferancia entre datos y Monte Carlo es tomada comoun error sistemático. El error resultante en la región f<strong>in</strong>al es del 9.2%.• Estimación de Mistags: El error asignado es del 4.8%.• Lum<strong>in</strong>osidad: El error sistemático debido a la lum<strong>in</strong>osidad es del 6%.• ISR/FSR: La <strong>in</strong>certidumbre asociada a los estados <strong>in</strong>icial y f<strong>in</strong>al de radiación ha sidoevaluado generando muestras con mayor y menor ISR/FSR. El efecto en la región f<strong>in</strong>ales del 1.7%.• PDF: El error en las PDF ha sido determ<strong>in</strong>ado como un 3.8% en la aceptancia.
Appendix D. Resumen en castellano 161• Fondo de Multijet (MUATRE): Asignamos una <strong>in</strong>certidumbre del 30%.• Sección eficaz de producción de t¯t: Se cita una <strong>in</strong>certidumbre del 11%.• Sección eficaz de producción de top: La <strong>in</strong>certidumbre en este proceso es del 13%.• Sección eficaz de producción de dibosones: Citamos una <strong>in</strong>certidumbre del 10% en WWy WZ y un 20% para los procesos ZZ.• Sección eficaz de producción de procesos electrodébiles: Asignamos un 40% de <strong>in</strong>certidumbreen la predicción de estos procesos.• Masa del quark top: En el presente análisis, la producción de t¯t se estima usando métodosde Monte Carlo con una masa del quark top de 175 GeV/c 2 . Puesto que nuestra optimizaciónde señal está basada en una red neuronal entrenada con procesos de t¯t, <strong>in</strong>cluimosun error sistemático debido a las dependencia de la red neuronal con la masa utilizada.Calculamos este error midiendo el número de sucesos de top en selección f<strong>in</strong>al usandouna masa para el quark top de 172.5 GeV/c 2 .• Diferencias de <strong>for</strong>ma entre ALPGEN y PYTHIA: Incluimos un sistemático en la <strong>for</strong>ma enlas selecciones f<strong>in</strong>ales debido a las diferencias entre los generadores ALPGEN y PYTHIAusados para estimar los procesos de Z/W + jets.• Estimación de multijets y mistags después del CHAOS: Citamos una <strong>in</strong>certidumbre en laregión f<strong>in</strong>al del 3.6% y 8.2% respectivamente.ConclusionesDos búsquedas de squarks de la tercera familia en la muestra de jets y momento transversoneto han sido llevadas a cabo. Puesto que no se han encontrado desviaciones significativascon respecto a las predicciones del Modelo Estándar, los resultados han sido utilizados paraextraer límites con un 95% de nivel de confianza en la sección eficaz de producción de estosdos procesos de SUSY.La sensibilidad alcanzada por estos análisis está basada en la robustez de la descripciónde los fondos y en el poder de la técnicas de optimización de la señal. En estos dos últimosaspectos, merece un crédito especial el método MUTARE, para la estimación del fondo demultijets a partir de datos y el CHAOS. Estas dos herramientas, desarrolladas para la realización
162de estos dos análisis tienen además un amplio espectro de aplicación a lo largo del programa defísica.El único experimento, a día de hoy, capaz de realizar unas búsquedas semejantes es D0. Labúsqueda de stop ha sido llevada a cabo por D0, alcanzando una sensibilidad que proporcionauna región de exclusión menor, en parte debido a la menor cantidad de datos usados.El programa de búsqueda de SUSY en Tevatron será crucial en los próximos años, <strong>in</strong>clusodespués del <strong>in</strong>icio del LHC en los próximos meses. En particular, escenarios en los que lossquarks de la tercera familia se asumen como ligeros, como los mostrados en la presente tesis,segiran siendo importantes a la escala de energías de Tevatron. S<strong>in</strong> embargo, la conquista de laescala del TeV en el LHC, será s<strong>in</strong> duda el mayor de los retos en los años venideros. El trabajorealizado en esta tesis se ha hecho con dos claras <strong>in</strong>tenciones: explorar las frontera energéticade Tevatron buscando nueva físisca y desarrollar técnicas de análisis en preparación para losnuevos datos del LHC.Ambas <strong>in</strong>tenciones se han hecho realidad en la presente tesis, en primer lugar fijando losmejores limites de exclusión del mundo para los análisis llevados a cabo y por últimos desarrollandoe implementando de <strong>for</strong>ma satisfactoria nuevas técnicas de análisis.
Bibliography[1] D. N. Spergel et al. Wilk<strong>in</strong>son microwave anisotropy probe (wmap) three year results:Implications <strong>for</strong> cosmology. Astrophys.J.Suppl., 170:377, 2007.[2] Mary K. Gaillard, Paul D. Grannis, and Frank J. Sciulli. The standard model of particlephysics. Rev. Mod. Phys., 71:S96–S111, 1999.[3] A.D. Mart<strong>in</strong> F. Halzen. Quarks and Leptons: An Introductory Course <strong>in</strong> Modern ParticlePhysics. Wiley Text Books, 1984.[4] David Griffiths. Introduction to Elementary Particles. Wiley, 1987.[5] W. M. Yao et al. Review of particle physics. J. Phys., G33:1–1232, 2006.[6] CDF and DØ Collaborations. Comb<strong>in</strong>ation of cdf and DØ results on <strong>the</strong> mass of <strong>the</strong> topquark. hep-ex/0903.2503, 2009.[7] R. P. Feynman. Ma<strong>the</strong>matical <strong>for</strong>mulation of <strong>the</strong> quantum <strong>the</strong>ory of electromagnetic<strong>in</strong>teraction. Phys. Rev., 80:440–457, 1950.[8] R. Keith Ellis, W. James Stirl<strong>in</strong>g, and B. R. Webber. Qcd and collider physics. Camb.Monogr. Part. Phys. Nucl. Phys. Cosmol., 8:1–435, 1996.[9] G. Dissertori, I. G. Knowles, and M. Schmell<strong>in</strong>g. High energy experiments and <strong>the</strong>ory.Ox<strong>for</strong>d, UK: Clarendon (2003) 538 p.[10] A. D. Mart<strong>in</strong>, W. J. Stirl<strong>in</strong>g, R. S. Thorne, and G. Watt. Update of partondistributions at nnlo. Phys. Lett., B652:292–299, 2007. MRST Webpage,http://durpdg.dur.ac.uk/hepdata/mrs.html.[11] H. L. Lai et al. Improved parton distributions from global analysis of recent deep <strong>in</strong>elasticscatter<strong>in</strong>g and <strong>in</strong>clusive jet data. Phys. Rev., D55:1280–1296, 1997. CTEQ Webpage,http://www.phys.psu.edu/∼cteq/.163
164 Bibliography[12] D. Stump et al. Uncerta<strong>in</strong>ties of predictions from parton distribution functions. i: Thelagrange multiplier method. Phys. Rev., D65:014012, 2002.[13] J. Pumpl<strong>in</strong> et al. Uncerta<strong>in</strong>ties of predictions from parton distribution functions. ii: Thehessian method. Phys. Rev., D65:014013, 2002.[14] E. Fermi. An attempt of a <strong>the</strong>ory of beta radiation. 1. Z. Phys., 88:161–177, 1934.[15] S. L. Glashow. Partial symmetries of weak <strong>in</strong>teractions. Nucl. Phys., 22:579–588, 1961.[16] Abdus Salam and John Clive Ward. Electromagnetic and weak <strong>in</strong>teractions. Phys. Lett.,13:168–171, 1964.[17] Steven We<strong>in</strong>berg. A model of leptons. Phys. Rev. Lett., 19:1264–1266, 1967.[18] L. D. Faddeev and V. N. Popov. Feynman diagrams <strong>for</strong> <strong>the</strong> yang-mills field. Phys. Lett.,B25:29–30, 1967.[19] G. Arnison et al. Experimental observation of lepton pairs of <strong>in</strong>variant mass around95 GeV/c 2 at <strong>the</strong> CERN SPS collider. Phys. Lett., B126:398–410, 1983.[20] G. Arnison et al. Experimental observation of isolated large transverse energy electronswith associated miss<strong>in</strong>g energy at √ s = 540 GeV. Phys. Lett., B122:103–116, 1983.[21] H. Georgi, Helen R. Qu<strong>in</strong>n, and Steven We<strong>in</strong>berg. Hierarchy of <strong>in</strong>teractions <strong>in</strong> unifiedgauge <strong>the</strong>ories. Phys. Rev. Lett., 33:451–454, 1974.[22] Leonard Sussk<strong>in</strong>d. Dynamics of spontaneous symmetry break<strong>in</strong>g <strong>in</strong> <strong>the</strong> we<strong>in</strong>berg- salam<strong>the</strong>ory. Phys. Rev., D20:2619–2625, 1979.[23] Stephen P. Mart<strong>in</strong>. A supersymmetry primer. 1997.[24] Hitoshi Murayama. Supersymmetry phenomenology. 2000.[25] Rudolf Haag, Jan T. Lopuszanski, and Mart<strong>in</strong> Sohnius. All possible generators of supersymmetriesof <strong>the</strong> s matrix. Nucl. Phys., B88:257, 1975.[26] Robert Nyden Hill and Edward H. Kerner. Unique canonical representation of <strong>the</strong> <strong>in</strong>homogeneouslorentz group <strong>in</strong> relativistic particle dynamics. Phys. Rev. Lett., 17:1156,1966.
Bibliography 165[27] Joseph Polch<strong>in</strong>ski and Leonard Sussk<strong>in</strong>d. Break<strong>in</strong>g of supersymmetry at <strong>in</strong>termediateenergy.Phys. Rev., D26:3661, 1982.[28] Edward Witten. Dynamical break<strong>in</strong>g of supersymmetry. Nucl. Phys., B188:513, 1981.[29] Romesh K. Kaul. Gauge hierarchy <strong>in</strong> a supersymmetric model. Phys. Lett., B109:19,1982.[30] Ugo Amaldi, Wim de Boer, and Hermann Furstenau. Comparison of grand unified<strong>the</strong>ories with electroweak and strong coupl<strong>in</strong>g constants measured at lep. Phys. Lett.,B260:447–455, 1991.[31] Ugo Amaldi, Wim de Boer, Paul H. Frampton, Hermann Furstenau, and James T. Liu.Consistency checks of grand unified <strong>the</strong>ories. Phys. Lett., B281:374–383, 1992.[32] Paul Langacker and M<strong>in</strong>g-x<strong>in</strong>g Luo. Implications of precision electroweak experiments<strong>for</strong> m t , ρ 0 , s<strong>in</strong> 2 θ W and grand unification. Phys. Rev., D44:817–822, 1991.[33] John R. Ellis, S. Kelley, and Dimitri V. Nanopoulos. Prob<strong>in</strong>g <strong>the</strong> desert us<strong>in</strong>g gaugecoupl<strong>in</strong>g unification. Phys. Lett., B260:131–137, 1991.[34] F. Gliozzi, Joel Scherk, and David I. Olive. Supersymmetry, supergravity <strong>the</strong>ories and<strong>the</strong> dual sp<strong>in</strong>or model. Nucl. Phys., B122:253–290, 1977.[35] S. He<strong>in</strong>emeyer, W. Hollik, D. Stock<strong>in</strong>ger, A. M. Weber, and G. Weigle<strong>in</strong>. Precise prediction<strong>for</strong> m(w) <strong>in</strong> <strong>the</strong> mssm. JHEP, 08:052, 2006.[36] H. E. Haber, (ed. ) Harvey, Jeffrey A., and (ed. ) Polch<strong>in</strong>ski, J. Recent directions <strong>in</strong>particle <strong>the</strong>ory: From superstr<strong>in</strong>gs and black holes to <strong>the</strong> standard model. proceed<strong>in</strong>gs,<strong>the</strong>oretical advanced study <strong>in</strong>stitute <strong>in</strong> elementary particle physics, boulder, usa, june1-26, 1992. pages 589–686. S<strong>in</strong>gapore, S<strong>in</strong>gapore: World Scientific (1993) 827 p.[37] David J. Gross and R. Jackiw. Effect of anomalies on quasirenormalizable <strong>the</strong>ories. Phys.Rev., D6:477–493, 1972.[38] C. Bouchiat, J. Iliopoulos, and P. Meyer. An anomaly free version of we<strong>in</strong>berg’s model.Phys. Lett., B38:519–523, 1972.[39] Luis Alvarez-Gaume and Edward Witten. Gravitational anomalies. Nucl. Phys.,B234:269, 1984.
166 Bibliography[40] John F. Gunion, Howard E. Haber, Gordon L. Kane, and Sally Dawson. The higgshunter’s guide. SCIPP-89/13.[41] S. Dawson. The mssm and why it works. 1997.[42] Savas Dimopoulos and Howard Georgi. Softly broken supersymmetry and su(5). Nucl.Phys., B193:150, 1981.[43] N. Sakai. Naturalness <strong>in</strong> supersymmetric guts. Zeit. Phys., C11:153, 1981.[44] P. Fayet. Spontaneously broken supersymmetric <strong>the</strong>ories of weak, electromagnetic andstrong <strong>in</strong>teractions. Phys. Lett., B69:489, 1977.[45] Pierre Fayet. Relations between <strong>the</strong> masses of <strong>the</strong> superpartners of leptons and quarks,<strong>the</strong> goldst<strong>in</strong>o coupl<strong>in</strong>gs and <strong>the</strong> neutral currents. Phys. Lett., B84:416, 1979.[46] Steven We<strong>in</strong>berg. Supersymmetry at ord<strong>in</strong>ary energies. 1. masses and conservation laws.Phys. Rev., D26:287, 1982.[47] N. Sakai and Tsutomu Yanagida. Proton decay <strong>in</strong> a class of supersymmetric grand unifiedmodels. Nucl. Phys., B197:533, 1982.[48] Savas Dimopoulos, Stuart Raby, and Frank Wilczek. Proton decay <strong>in</strong> supersymmetricmodels. Phys. Lett., B112:133, 1982.[49] John R. Ellis, Dimitri V. Nanopoulos, and Serge Rudaz. Guts 3: Susy guts 2. Nucl. Phys.,B202:43, 1982.[50] Glennys R. Farrar and Pierre Fayet. Phenomenology of <strong>the</strong> production, decay, and detectionof new hadronic states associated with supersymmetry. Phys. Lett., B76:575–579,1978.[51] F. Zwirner. Observable delta b=2 transitions without nucleon decay <strong>in</strong> a m<strong>in</strong>imal supersymmetricextension of <strong>the</strong> standard model. Phys. Lett., B132:103–106, 1983.[52] Lawrence J. Hall and Mahiko Suzuki. Explicit r-parity break<strong>in</strong>g <strong>in</strong> supersymmetric models.Nucl. Phys., B231:419, 1984.[53] John R. Ellis, G. Gelm<strong>in</strong>i, C. Jarlskog, Graham G. Ross, and J. W. F. Valle. Phenomenologyof supersymmetry with broken r-parity. Phys. Lett., B150:142, 1985.
Bibliography 167[54] Graham G. Ross and J. W. F. Valle. Supersymmetric models without r-parity. Phys. Lett.,B151:375, 1985.[55] Sally Dawson. R-parity break<strong>in</strong>g <strong>in</strong> supersymmetric <strong>the</strong>ories. Nucl. Phys., B261:297,1985.[56] Savas Dimopoulos and Lawrence J. Hall. Lepton and baryon number violat<strong>in</strong>g collidersignatures from supersymmetry. Phys. Lett., B207:210, 1988.[57] Carl E. Carlson, Probir Roy, and Marc Sher. New bounds on r-parity violat<strong>in</strong>g coupl<strong>in</strong>gs.Phys. Lett., B357:99–104, 1995.[58] Gautam Bhattacharyya. R-parity-violat<strong>in</strong>g supersymmetric yukawa coupl<strong>in</strong>gs: A m<strong>in</strong>ireview.Nucl. Phys. Proc. Suppl., 52A:83–88, 1997.[59] D. J. H. Chung, L. L. Everett, G.L. Kane, S. F. K<strong>in</strong>g, J. Lykken, and L. Wang. The softsupersymmetry break<strong>in</strong>g lagrangian: Theory and applications. Phys. Rept., 407, 2005.[60] A. Bartl, W. Majerotto, and W. Porod. Squark and glu<strong>in</strong>o decays <strong>for</strong> large tan beta.Z.Phys.C, C64:499–508, 1994. Erratum-ibid.C68:518,1995.[61] W. Beenakker et al. Squark and glu<strong>in</strong>o production at hadron colliders. Nucl. Phys.,B492:51–103, 1997.[62] Torbjorn Sjostrand, Leif Lonnblad, and Stephen Mrenna. PYTHIA 6.2: Physics andmanual. 2001.[63] A. Abulencia et al. A search <strong>for</strong> scalar bottom quarks from glu<strong>in</strong>o decays <strong>in</strong> p anti-pcollisions at √ s = 1.96 tev. Phys. Rev. Lett., 96:171802, 2006.[64] J. Pumpl<strong>in</strong> et al. New generation of parton distributions with uncerta<strong>in</strong>ties from globalQCD analysis. J. High Energy Phys., 0207:012, 2002.[65] D. Stump et al. Inclusive Jet Production, Parton Distributions, and <strong>the</strong> <strong>Search</strong> <strong>for</strong> NewPhysics. 2003.[66] Fermilab Beam Division. http://www-bd.fnal.gov.[67] Fermilab Beam Division. Run II Handbook. http://www-bd.fnal.gov/runII/<strong>in</strong>dex.html.
168 Bibliography[68] R. Blair et al. The CDF II detector: Technical design report. Technical report, FNAL,1996. FERMILAB-PUB-96/390-E.[69] A. Sill. CDF Run II silicon track<strong>in</strong>g projects. Nucl. Instrum. Meth., A447:1–8, 2000.[70] Anthony Allen Affolder et al. CDF central outer tracker. Nucl. Instrum. Meth.,A526:249–299, 2004.[71] CDF Track<strong>in</strong>g Group. see http://www-cdf.fnal.gov/<strong>in</strong>ternal/detectors/parameters.htmland http://www-cdf.fnal.gov/cdfsim/validation/cot/cotVal.html.[72] C. Paus et al. Design and per<strong>for</strong>mance tests of <strong>the</strong> CDF time of flight system. Nucl.Instrum. Meth., A461:579–581, 2001.[73] C. Grozis et al. A time of flight detector <strong>for</strong> CDF. Int. J. Mod. Phys., A16S1C:1119–1121, 2001.[74] C. Grozis et al. The time of flight detector at CDF. Nucl. Phys. Proc. Suppl., 93:344–347,2001.[75] L. Balka et al. The CDF central electromagnetic calorimeter. Nucl. Instrum. Meth.,A267:272, 1988.[76] S. Bertolucci et al. The CDF central and endwall hadron calorimeter. Nucl. Instrum.Meth., A267:301, 1988.[77] M. G. Albrow et al. The CDF plug upgrade electromagnetic calorimeter: Test beamresults. Nucl. Instrum. Meth., A480:524–546, 2002.[78] C. M. G<strong>in</strong>sburg. CDF Run II muon system. Eur. Phys. J., C33:s1002–s1004, 2004.[79] D. Acosta et al. The CDF Cherenkov lum<strong>in</strong>osity monitor. Nucl. Instrum. Meth.,A461:540–544, 2001.[80] D. Acosta et al. The per<strong>for</strong>mance of <strong>the</strong> CDF lum<strong>in</strong>osity monitor. Nucl. Instrum. Meth.,A494:57–62, 2002.[81] F. Abe et al. Measurement of <strong>the</strong> ¯pp total cross-section at √ s = 546 GeV and 1800 GeV.Phys. Rev., D50:5550–5561, 1994.
Bibliography 169[82] S. Klimenko, J. Konigsberg, and Tony M. Liss. Averag<strong>in</strong>g of <strong>the</strong> <strong>in</strong>elastic cross sectionsmeasured by <strong>the</strong> CDF and <strong>the</strong> E811 experiments. FERMILAB-FN-0741.[83] S. Jundariani et al. Lum<strong>in</strong>osity uncerta<strong>in</strong>ty <strong>for</strong> Run II up until August 2004.CDF/ANA/7446, 2005.[84] H.J. Frisch and P.J. Wilson. Trigger tower organization and summ<strong>in</strong>g <strong>in</strong> η − φ space <strong>for</strong>Run II and beyond. CDF/DOC/TRIGGER/CDFR/2045, 2001.[85] The XFT system webpage. http://www.physics.ohio-state.edu/∼hughes/xft/.[86] The XTRP webpage. http://web.hep.uiuc.edu/eng<strong>in</strong>/cdf/xtrp/.[87] I. Vila. Per<strong>for</strong>mance and first physics results of <strong>the</strong> SVT trigger at CDF II. 2003. hepph/0307165.[88] The Trigger and Datasets Work<strong>in</strong>g Group. Run II trigger table and datasets plan.CDF/PHYS/TRIGGER/CDFR/4718, 2001.[89] F. Abe et al. Phys. Rev., D45:1448–1458, 1992.[90] A. Bhatti et al. Nucl. Instrum. Methods, A566:2, 2006.[91] D. Acosta et al. Measurement of <strong>the</strong> t¯t production cross section <strong>in</strong> p¯p collisions at√ s = 1.96 tev us<strong>in</strong>g lepton + jets events with secondary vertex b-tagg<strong>in</strong>g. Phys. Rev.,D71:052003, 2005.[92] A. Zell et al. Stuttgart neural network simulator. http://www.ra.cs.unitueb<strong>in</strong>gen.de/SNNS/contact.html.[93] T. Aaltonen et al. <strong>Search</strong> <strong>for</strong> glu<strong>in</strong>o-mediated bottom squark production <strong>in</strong> p¯p collisionsat √ s = 1.96 tev. Phys. Rev. Lett., 102:221801, 2009.[94] V.M. Abazov et al. <strong>Search</strong> <strong>for</strong> pair production of scalar bottom quarks <strong>in</strong> p¯p collisions at√ s = 1.96 tev. Phys. Rev. Lett, 97:171806, 2006.[95] T. Affolder et al. <strong>Search</strong> <strong>for</strong> scalar top and scalar bottom quarks <strong>in</strong> p¯p collisions at√ s = 1.8 tev. Phys. Rev. Lett., 84:5704, 2000.[96] H. L. Lai et al. Global QCD analysis of parton structure of <strong>the</strong> nucleon: CTEQ5 partondistributions. Eur. Phys. J., C12:375–392, 2000.
170 Bibliography[97] R. Brun et al. GEANT 3 manual, CERN Program Library Long Writeup. 1994.[98] B. H. Harris et al. The fully differential s<strong>in</strong>gle top quark cross-section <strong>in</strong> next to lead<strong>in</strong>gorder qcd. Phys. Rev. D, 66:2002, 054024.[99] CDF Collaboration. Comb<strong>in</strong>ation of top pair production cross-section with 760pb −1 .CDF/PHYS/TOP/PUBLIC/8148, 2006.[100] T. Aaltonen et al. <strong>Search</strong> <strong>for</strong> <strong>the</strong> higgs boson <strong>in</strong> events with miss<strong>in</strong>g transverse energyand b quark jets produced <strong>in</strong> proton-antiproton collisions at √ s = 1.96 tev. Phys. Rev.Lett., 100:211801, 2008.[101] M. Cacciari. The t anti-t cross-section at 1.8-tev and 1.96-tev: A study of <strong>the</strong> systematicsdue to parton densities and scale dependence. J. High Energy Phys., 0404:068, 2004.[102] J. R. Campbell. An update on vector boson pair production at hadron colliders. Phys.Rev. D, 60:113006, 1999.[103] A. Hocker et al. TMVA - Toolkit <strong>for</strong> Multivariate Data Analysis. arXiv:physics/0703039.[104] T. Affolder et al. <strong>Search</strong> <strong>for</strong> glu<strong>in</strong>os and scalar quarks <strong>in</strong> p¯p collisions at √ s = 1.8 tevus<strong>in</strong>g <strong>the</strong> miss<strong>in</strong>g energy plus multijets signature. Phys. Rev. Lett., 88:041801, 2002.[105] R.D. Field. Contribution to <strong>the</strong> APS/DPF/DPB Summer Study on <strong>the</strong> Future of ParticlePhysics (Snowmass 2001), Snowmass, Colorado, 30 June 21 July 2001 [hepph/0201192];CDF Note 6403; R.D. Field (CDF Collaboration), presentations at <strong>the</strong> <strong>the</strong>’Matrix Element and Monte Carlo Tun<strong>in</strong>g Workshop’, Fermilab, 4 October 2002 and2930 April 2003, talks available from webpage http://cepa.fnal.gov/psm/MCTun<strong>in</strong>g/; R.Field and R. C. Group (CDF Collaboration), hep-ph/0510198; R.D. Field (CDF Collaboration),fur<strong>the</strong>r recent talks available from webpage http://www.phys.ufl.edu/rfield/cdf/.[106] T. Aaltonen et al. <strong>Search</strong>es <strong>for</strong> direct pair production of supersymmetric top and supersymmetricbottom quarks <strong>in</strong> p¯p collisions at √ s = 1.96 tev. Phys. Rev. D, 79:072010,2007.[107] V.M. Abazov et al. <strong>Search</strong> <strong>for</strong> scalar top quarks <strong>in</strong> <strong>the</strong> acoplanar charm jets and miss<strong>in</strong>gtransverse energy f<strong>in</strong>al state <strong>in</strong> p¯p collisions at √ s = 1.96 tev. Phys. Lett. B, 665:1, 2008.[108] LEPSUSYWG/04-07.1. http://lepsusy.web.cern.ch/lepsusy/.
Bibliography 171[109] M.L. Mangano et al. Alpgen, a generator <strong>for</strong> hard multiparton processes <strong>in</strong> hadroniccollisions. J. High Energy Phys., 0307:001, 2003.[110] CDF Collaboration. Top quark pair production cross section and <strong>for</strong>ward-backwardasymmetry at <strong>the</strong> tevatron. arXiv:0810.3350, 2008.[111] J. Campbell and K. Ellis. MCFM - Monte Carlo <strong>for</strong> FeMtobarn processes.