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

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1.5. Higgs plus two jets: Its phenomenological role and an overview ofthis thesis 29However, in addition to the weak process, a significant number of such eventsmay also be produced via the strong interaction. In order to accurately predictthe signal and, in particular, to simulate faithfully the expected significance in agiven Higgs model, a fully differential NLO calculation of QCD production of aHiggs and two hard jets is also required. The interference between the weak bosonfusion process and gluon fusion have been calculated and shown to be experimentallynegligible [102].In the Standard Model the Higgs couples to two gluons via a top-quark loop.Calculations which involve the full dependence on m t are difficult and a drasticsimplification can be achieved if one works in an effective theory in which the mass ofthe top quark is large [65,72,73]. For inclusive Higgs production this approximationis valid over a wide range of Higgs masses and, for processes with additional jets,the approximation is justified provided that the transverse momentum of each jetis smaller than m t [67]. Tree-level calculations have been performed in both thelarge-m t limit [64,103] and with the exact-m t [67] dependence.Results for the one-loop corrections to all of the Higgs + 4 parton processes havebeen published in 2005 [104]. Although analytic results were provided for the Higgs¯qq¯qq processes, the bulk of this calculation was performed using a semi-numericalmethod. In this approach the loop integrals were calculated analytically whereasthe coefficients with which they appear in the loop amplitudes were computed numericallyusing a recursive method. Although some phenomenology was performedusing this calculation [105], the implementation of fully analytic formulae will leadto a faster code and permit more extensive phenomenological investigations, whichis the main goal of this thesis.Since then there has been a drive to produce analytic results for the process,with the aim of improving the speed of the calculation. This thesis contains calculationsfor the most complicated helicity configurations; the φ-NMHV helicityconfigurations (both the pure gluon and qqgg cases), and the non-adjacent MHVhelicity gluon configuration. The remaining calculations have been performed elsewhere;the rational amplitudes (φ + + + +), (φ, − + ++) and (φ, qq + +) have
1.5. Higgs plus two jets: Its phenomenological role and an overview ofthis thesis 30been performed in [106] the all minus and adjacent minus MHV case can be foundin [107,108], whilst the φqq-MHV amplitudes (as well as φqqQQ helicity amplitudes)can be found in [109].This thesis proceeds as follows, in chapter 2 we present an overview of the on-shelltechniques which we will use throughout the thesis. Chapter 3 contains the calculationof the φ MHV amplitude with general helicites, we present the cut-constructiblepieces for all multiplicities, whilst for the rational pieces we focus on the four-gluonamplitude we are ultimately interested in. Chapter 4 describes the calculation ofthe φ-NMHV and summarises the results for the four gluon amplitudes. The lastchapter dealing with analytic calculations is chapter 5, which presents the remaininghelicity amplitude, the φqq-NMHV amplitude. Chapter 6 then moves from analyticcalculations into describing some phenomenology which can be performed with thenew results. In chapter 7 we draw our conclusions. Appendix A contains a reviewof both the spinor helicity formalism and colour ordering of tree and one-loop amplitudesas well as a list of useful tree amplitudes. Appendix B contains explicitformulae for the basis integrals we use in this work.
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 39 and 40: 1.4. Effective coupling between glu
Page 41 and 42: 1.4. Effective coupling between glu
Page 43: 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 80
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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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