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1.4. Effective coupling between gluons and a Higgs in the limit of aheavy top quark 23R lim10CDF + D0 Run IIL=4.8-5.4 fb -1ObservedExpectedExpected ±1σExpected ±2σ1SM=1130 140 150 160 170 180 190 200m H(GeV)Figure 1.7: Combined CDF and D0 Higgs search results [58]. The sensitivity around2m W allows an exclusion region to develop around these masses. The exclusionoccurs where the observed line falls below the theoretical prediction.Over the next decade, as the LHC gathers a large enough data set, the Higgsboson will either be observed or excluded in the theoretically acceptable region.Like the Tevatron, the LHC will be more sensitive to a heavy Higgs [62], howeverit should gather a enough data to allow even very rare decays (but experimentallyfavourable) of light Higgs bosons such as H → γγ to be investigated.1.4 Effective coupling between gluons and a Higgsin the limit of a heavy top quark1.4.1 Effective LagrangianIn this section we introduce the effective Lagrangian which couples gluons to theHiggs boson [63–65]. Since the Higgs boson only couples to massive particles theinteraction proceeds predominantly through a top quark loop. The dependence onthe top mass quickly makes calculations extremely difficult, since at LO in the full
1.4. Effective coupling between gluons and a Higgs in the limit of aheavy top quark 24Tevatron Run II Preliminary, = 5.9 fb -195% CL Limit/SM101LEP ExclusionSM=1ExpectedObserved±1σ Expected±2σ ExpectedTevatronExclusionTevatron Exclusion July 19, 2010100 110 120 130 140 150 160 170 180 190 200m H(GeV/c 2 )Figure 1.8: Combined CDF and D0 results [61], the increased data set (relativeto [58]) has increased the exclusion limit around 2m W . The results are also beginningto approach the LEP lower limit on the Higgs mass.Figure 1.9: The Higgs-gluon coupling in the Standard Model proceeds through atop quark loop, at LO order in the full theory this is the only contributing diagram.
Page 7 and 8: Contentsvii1.4.1 Effective Lagrangi
Page 9 and 10: Contentsix4 One-loop Higgs plus fou
Page 11: ContentsxiB.2 Box Integral Function
Page 18 and 19: 1.1. The Standard Model of Particle
Page 20: 1.1. The Standard Model of Particle
Page 27 and 28: 1.2. Electroweak Symmetry Breaking
Page 33 and 34: 1.3. Higgs searches at colliders 18
Page 35 and 36: 1.3. Higgs searches at colliders 20
Page 37: 1.3. Higgs searches at colliders 22
Page 41 and 42: 1.4. Effective coupling between glu
Page 43 and 44: 1.5. Higgs plus two jets: Its pheno
Page 45 and 46: 1.5. Higgs plus two jets: Its pheno
Page 47 and 48: 2.1. Unitarity 32of two tree level
Page 49 and 50: 2.2. Quadruple cuts 34the rational
Page 51 and 52: 2.2. Quadruple cuts 360000000111111
Page 53 and 54: 2.2. Quadruple cuts 38We now must s
Page 55 and 56: 2.3. Forde’s Laurent expansion me
Page 61 and 62: 2.4. Spinor integration 46Here we h
Page 63 and 64: 2.4. Spinor integration 48The expli
Page 65 and 66: 2.4. Spinor integration 50with F z
Page 67 and 68: 2.5. MHV rules and BCFW recursion r
Page 69 and 70: 2.5. MHV rules and BCFW recursion r
Page 71 and 72: 2.6. The unitarity-bootstrap 56Next
Page 73 and 74: 2.6. The unitarity-bootstrap 58Figu
Page 75 and 76: 2.6. The unitarity-bootstrap 60of o
Page 77 and 78: 2.6. The unitarity-bootstrap 62rati
Page 79 and 80: 2.6. The unitarity-bootstrap 64Afte
Page 81 and 82: 2.8. Recent progress: One-loop auto
Page 83 and 84: 2.9. Summary 68cluding the recent c
Page 85 and 86: 3.2. The cut-constructible parts 70
Page 87 and 88: eplacemen3.2. The cut-constructible
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3.2. The cut-constructible parts 74
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3.3. The rational pieces 98m−1∑
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3.3. The rational pieces 100+m−1
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3.3. The rational pieces 102+R(4 +
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3.3. The rational pieces 104The cal
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3.4. Cross Checks and Limits 1063.4
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3.4. Cross Checks and Limits 108The
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3.4. Cross Checks and Limits 110The
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3.4. Cross Checks and Limits 112−
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3.5. Summary 114The rational terms
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Chapter 4One-loop Higgs plus four-g
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4.2. Cut-Constructible Contribution
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4.3. Rational Terms 124contains two
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4.4. Higgs plus four gluon amplitud
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4.4. Higgs plus four gluon amplitud
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4.6. Summary 130p µ 2 = (+0.344450
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Chapter 5The φqqgg- NMHV amplitude
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5.1. Introduction 134Figure 5.1: Sa
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5.1. Introduction 136H amplitude φ
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5.2. One-loop results 138A L 4 (φ,
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5.2. One-loop results 140with K 1 =
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5.2. One-loop results 142Relation f
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5.2. One-loop results 144+ 1s 123[
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5.4. Summary 146(φ, 1 −¯q , 2 +
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6.2. Improvements from the semi-num
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6.4. Tevatron results 150The W mass
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6.4. Tevatron results 152m H [GeV]
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6.5. LHC results 154Eq. (6.11) and
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6.5. LHC results 156m H [GeV] 120 1
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6.5. LHC results 158Figure 6.3: The
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6.5. LHC results 160of describing T
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6.5. LHC results 162Figure 6.6: p T
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6.6. Summary 164at LO and the effec
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6.6. Summary 166of Higgs masses, 15
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Chapter 7. Conclusions 168one can d
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Appendix ASpinor Helicity Formalism
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A.1. Spinor Helicity Formalism nota
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A.3. Pure QCD amplitudes 174Further
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Appendix BOne-loop Basis IntegralsI
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B.2. Box Integral Functions 178boxe
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B.2. Box Integral Functions 180L 2
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Bibliography 182[10] R. Feynman, Ma
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Bibliography 184[36] M. Bahr et. al
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Bibliography 186[63] M. Shifman, A.
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Bibliography 188[85] R. V. Harlande
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Bibliography 190[104] R. K. Ellis,
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Bibliography 192[125] G. Ossola, C.
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Bibliography 194[148] R. Boels and
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Bibliography 196[170] Z. Bern and A
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Bibliography 198anti-t + 2 jets at
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Bibliography 200[214] C. Anastasiou
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