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

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Chapter 7. Conclusions 169licly available, performs the NLO calculation of cross-sections. The user can definecuts for the external particles as required. Using this program we performed somephenomenology relevant for the Tevatron and the LHC. We observed that whenexperimentalists choose exclusive final states with specific numbers of jets, such asCDF have done in their recent gg → H → WW ∗ studies . [215], one naturallyencounters H + 2 jets. Higgs production through gluon fusion has been calculatedthrough to NNLO [78,79,81], but when one explicitly selects two jets in the eventit is inappropriate to use NNLO α S running and PDF’s. Rather, one should matchthese to the order in which the amplitude has been calculated in perturbation theory.In our case this is NLO therefore, we were able to improve the LO scale uncertainty[214]. We also studied some phenomenology at the LHC. We compared the gluonandvector-boson fusion cross sections before and after VBF cuts finding that theratio between the cross sections (after the cuts have been applied) shrinks as thecentre of mass energy grows. We also studied the scale variation and minimum jetp T dependence at the LHC. Finally we investigated the role of dynamic and fixedscales, finding that dynamic scales preserve the shape of leading order distributions.We observed, however, that this preservation in the high-p T region may actually beundesirable since it is in this region that the effective theory LO distributions showdeviations in shape due to top-mass effects.It is hoped that the code will be of use to experimentalists as we enter an excitingperiod in the hunt for the Higgs.
Appendix ASpinor Helicity Formalism andTree-level AmplitudesA.1 Spinor Helicity Formalism notation and conventionsA.1.1Spinor notationsThroughout this thesis we define kinematic invariants associated with sums of gluonmomenta as follows,s ij = (p i + p j ) 2 , s ijk = (p i + p j + p k ) 2 , s i,j = (p i + p i+1 + · · · + p j ) 2 etc.(A.1.1)Sums of external momenta are also written using the following shorthand notation,p i + p j + p k = P ijk(A.1.2)We will express helicity amplitudes using the notation of the spinor-helicity formalism,〈ij〉 = u − (k i )u + (k j ), (A.1.3)[ij] = u + (k i )u − (k j ),(A.1.4)where u ± (k i ) represents a massless Dirac spinor associated with either positive ornegative helicity (and a momentum k i ). Spinor products are related to kinematic170
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Contentsvii1.4.1 Effective Lagrangi
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Contentsix4 One-loop Higgs plus fou
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ContentsxiB.2 Box Integral Function
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1.1. The Standard Model of Particle
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1.2. Electroweak Symmetry Breaking
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1.3. Higgs searches at colliders 18
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1.4. Effective coupling between glu
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1.4. Effective coupling between glu
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1.5. Higgs plus two jets: Its pheno
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1.5. Higgs plus two jets: Its pheno
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2.1. Unitarity 32of two tree level
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2.2. Quadruple cuts 34the rational
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2.2. Quadruple cuts 360000000111111
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2.2. Quadruple cuts 38We now must s
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2.4. Spinor integration 46Here we h
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2.4. Spinor integration 48The expli
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2.4. Spinor integration 50with F z
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2.5. MHV rules and BCFW recursion r
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2.5. MHV rules and BCFW recursion r
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2.6. The unitarity-bootstrap 56Next
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2.6. The unitarity-bootstrap 58Figu
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2.6. The unitarity-bootstrap 60of o
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2.6. The unitarity-bootstrap 62rati
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2.6. The unitarity-bootstrap 64Afte
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2.8. Recent progress: One-loop auto
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2.9. Summary 68cluding the recent c
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3.2. The cut-constructible parts 70
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eplacemen3.2. The cut-constructible
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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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Page 147 and 148: Chapter 5The φqqgg- NMHV amplitude
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Page 169 and 170: 6.5. LHC results 154Eq. (6.11) and
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Page 183: Chapter 7. Conclusions 168one can d
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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
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Page 197 and 198: Bibliography 182[10] R. Feynman, Ma
Page 199 and 200: Bibliography 184[36] M. Bahr et. al
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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
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