Hadronic production of a Higgs boson in association with two jets at ...

More documents

Recommendations

Info

1.1. The Standard Model of Particle Physics 11Showers and jetsImmediately upon looking at an image of a high-energy collision one can spot acollection of hadrons which are grouped into a roughly cone sized area. Thesehadrons, which have travelled roughly collinear to each other, are known as jets.Therefore, to compare theory to experiment one needs a suitable jet algorithm todefine exactly what is meant by a jet and the properties it has. Several jet algorithmsexist [27–31], the one we will use in this thesis is known as the k T algorithm andworks in the following way [32]:• The algorithm begins with a set of preclusters, which for our theoretical calculationswith MCFM means partons. Each precluster is expressed in thefollowing form(E,p) = E(1, cosφsin θ, sin φ sin θ, cosθ) (1.23)where E is the precluster energy and φ and θ are the azimuthal and polarangles respectively.• For each precluster define the square of the transverse momenta and rapidity,d 2 i = p2 T,i , p2 T = p2 x + p2 y and y = 1 2 ln E + p zE − p z, (1.24)• For each pair (i, j) (i ≠ j) of preclusters define,d ij= min(p 2 T,i , p2 T,j )∆R2 ijD 2= min(p 2 T,i , p2 T,j )(y i − y j ) 2 + (φ i − φ j ) 2D 2 (1.25)where D ≈ 1 is a parameter of the jet algorithm.• Find the minimum of all the d i and d ij and call it d min .• If d min is a d ij remove preclusters i and j from the list and replace them witha new merged precluster (E ij , p ij ), given byE ij = E i + E jp ij = p i + p j (1.26)
1.2. Electroweak Symmetry Breaking 12• If d min is a d i then the precluster is not mergeable, remove precluster from thelist and define it as a jet.• Continue until no preclusters remain.We observe that the algorithm produces a list of jets which are separated by ∆R > Dand that this algorithm can be applied equally well to theoretical calculations orexperimental data.Perturbation theory naturally produces amplitudes containing a fixed number ofpartons, however the naive approximation that a jet is represented by a single hardparton (at higher orders in perturbation theory this is somewhat improved) is notreproduced in nature. The multiple emissions of partons in the soft and collinearregions (which then hadronise to form jets) are modeled theoretically by a partonshower 4 . Parton showers are a key element in Monte Carlo event generators, whichfor the most part merge [33] leading order matrix elements with parton showersand hadronisation to form a realistic prediction of particle physics collision. Somemodern examples are HERWIG [34–36], SHERPA [37,38] and PYTHIA [39,40].1.2 Electroweak Symmetry BreakingThe study of electroweak symmetry by spontaneously broken symmetries originallystarted in the 1960’s [41–45]. Yet the search for the Higgs is only now, nearly fiftyyears later, reaching its climax. In this section we introduce the main features ofthe Higgs mechanism and briefly review some Higgs phenomenology.1.2.1 Spontaneous breaking of O(N) symmetries, GoldstonebosonsIn this section we introduce the main aspects of a gauge theory which is spontaneouslybroken showing how within these theories gauge bosons naturally acquire a4 for an overview of parton showers see Chapter 5 of [7]
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 23 and 24: 1.1. The Standard Model of Particle
Page 25: 1.1. The Standard Model of Particle
Page 29 and 30: 1.2. Electroweak Symmetry Breaking
Page 31 and 32: 1.2. Electroweak Symmetry Breaking
Page 33 and 34: 1.3. Higgs searches at colliders 18
Page 39 and 40: 1.4. Effective coupling between glu
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
Page 89 and 90:
Page 91 and 92:
Page 93 and 94:
Page 95 and 96:
Page 97 and 98:
Page 99 and 100:
Page 101 and 102:
Page 103 and 104:
Page 105 and 106:
Page 107 and 108:
Page 109 and 110:
Page 111 and 112:
Page 113 and 114:
3.3. The rational pieces 98m−1∑
Page 115 and 116:
3.3. The rational pieces 100+m−1
Page 117 and 118:
3.3. The rational pieces 102+R(4 +
Page 119 and 120:
3.3. The rational pieces 104The cal
Page 121 and 122:
3.4. Cross Checks and Limits 1063.4
Page 123 and 124:
3.4. Cross Checks and Limits 108The
Page 125 and 126:
3.4. Cross Checks and Limits 110The
Page 127 and 128:
3.4. Cross Checks and Limits 112−
Page 129 and 130:
3.5. Summary 114The rational terms
Page 131 and 132:
Chapter 4One-loop Higgs plus four-g
Page 133 and 134:
4.2. Cut-Constructible Contribution
Page 135 and 136:
Page 137 and 138:
Page 139 and 140:
4.3. Rational Terms 124contains two
Page 141 and 142:
4.4. Higgs plus four gluon amplitud
Page 143 and 144:
4.4. Higgs plus four gluon amplitud
Page 145 and 146:
4.6. Summary 130p µ 2 = (+0.344450
Page 147 and 148:
Chapter 5The φqqgg- NMHV amplitude
Page 149 and 150:
5.1. Introduction 134Figure 5.1: Sa
Page 151 and 152:
5.1. Introduction 136H amplitude φ
Page 153 and 154:
5.2. One-loop results 138A L 4 (φ,
Page 155 and 156:
5.2. One-loop results 140with K 1 =
Page 157 and 158:
5.2. One-loop results 142Relation f
Page 159 and 160:
5.2. One-loop results 144+ 1s 123[
Page 161 and 162:
5.4. Summary 146(φ, 1 −¯q , 2 +
Page 163 and 164:
6.2. Improvements from the semi-num
Page 165 and 166:
6.4. Tevatron results 150The W mass
Page 167 and 168:
6.4. Tevatron results 152m H [GeV]
Page 169 and 170:
6.5. LHC results 154Eq. (6.11) and
Page 171 and 172:
6.5. LHC results 156m H [GeV] 120 1
Page 173 and 174:
6.5. LHC results 158Figure 6.3: The
Page 175 and 176:
6.5. LHC results 160of describing T
Page 177 and 178:
6.5. LHC results 162Figure 6.6: p T
Page 179 and 180:
6.6. Summary 164at LO and the effec
Page 181 and 182:
6.6. Summary 166of Higgs masses, 15
Page 183 and 184:
Chapter 7. Conclusions 168one can d
Page 185 and 186:
Appendix ASpinor Helicity Formalism
Page 187 and 188:
A.1. Spinor Helicity Formalism nota
Page 189 and 190:
A.3. Pure QCD amplitudes 174Further
Page 191 and 192:
Appendix BOne-loop Basis IntegralsI
Page 193 and 194:
B.2. Box Integral Functions 178boxe
Page 195 and 196:
B.2. Box Integral Functions 180L 2
Page 197 and 198:
Bibliography 182[10] R. Feynman, Ma
Page 199 and 200:
Bibliography 184[36] M. Bahr et. al
Page 201 and 202:
Bibliography 186[63] M. Shifman, A.
Page 203 and 204:
Bibliography 188[85] R. V. Harlande
Page 205 and 206:
Bibliography 190[104] R. K. Ellis,
Page 207 and 208:
Bibliography 192[125] G. Ossola, C.
Page 209 and 210:
Bibliography 194[148] R. Boels and
Page 211 and 212:
Bibliography 196[170] Z. Bern and A
Page 213 and 214:
Bibliography 198anti-t + 2 jets at
Page 215:
Bibliography 200[214] C. Anastasiou
show all

Hadronic production of a Higgs boson in association with two jets at ...

Create successful ePaper yourself

Delete template?

Save as template?