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

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3.5. Summary 115−ˆ1 − +2 2 + ˆ3− + ˆ3 ˆ1 − + −(a)(b)2 + 2 ++ −+ −ˆ1 − (c)ˆ1 − (d)ˆ1 2 + ˆ1 −2 ++ −+ −−(e)(f)−ˆ3 −4 + 4 +−ˆ3 −4 +4 +− 44 + +Figure 3.12: Allowed diagrams which contribute to the direct recursive rationalpieces associated with the [3, 1〉 spinor shift .
Chapter 4One-loop Higgs plus four-gluonamplitudes: full analytic results4.1 IntroductionIn this chapter we will calculate the φ-NMHV amplitude A (1)4 (φ, 1 + , 2 − , 3 − , 4 − ). Wewill use the unitarity methods introduced in chapters 2 and 3 to calculate thevarious cut-constructible parts of the amplitude. For this amplitude we generatethe rational parts proportional to N f from Feynman diagrams. The other rationalpiece is generated from the recursion relations. We also write down the amplitudeA (1)4 (φ, 1 − , 2 + , 3 − , 4 + ) using the results of chapter 3. We then summarise the Higgsplus four gluon amplitudes by giving explicit formulae for each of the helicity amplitudesA (1)4 (H, 1 λ 1, 2 λ 2, 3 λ 3, 4 λ 4).whereWe choose to expand the one-loop primitive amplitude in the following form,A (1)4 (φ, 1 + , 2 − , 3 − , 4 − ) = c Γ (C 4 (φ, 1 + , 2 − , 3 − , 4 − ) + R 4 (φ, 1 + , 2 − , 3 − , 4 − )), (4.1)c Γ = Γ2 (1 − ǫ)Γ(1 + ǫ)(4π) 2−ǫ Γ(1 − 2ǫ) . (4.2)In (4.1), C 4 (φ, 1 + , 2 − , 3 − , 4 − ) denotes the cut-constructible parts of the amplitude,whilst R 4 (φ, 1 + , 2 − , 3 − , 4 − ) contains the remaining rational pieces. In section 4.2,we focus our attention on C 4 (φ, 1 + , 2 − , 3 − , 4 − ), while an analytic expression for116
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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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2.3. Forde’s Laurent expansion me
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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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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 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: 3.5. Summary 114The rational terms
Page 133 and 134: 4.2. Cut-Constructible Contribution
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
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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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