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

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5.2. One-loop results 137= i A (0)4 (φ, 1 −¯q , 3 − g , 2 + q , 4 − g )+ terms antisymmetric in {3 ↔ 4} . (5.20)We note that all of these amplitudes are finite because of the vanishing of thecorresponding tree-level results (see section 5.1.2).5.2 One-loop resultsIn this section we present analytic expressions for the full one-loop corrections tothe process A (1)4 (φ, 1−¯q , 2 + q , 3− g , 4− g ). All expressions are presented un-renormalised inthe four-dimensional helicity (FDH) scheme (setting δ R = 0) or ’t Hooft-Veltmanscheme (setting δ R = 1).We employ the generalised unitarity method described in chapters 2 and 3 [120,122,123,127,128] to calculate the cut-constructible parts of the left-moving, rightmovingand N f one-loop amplitudes. This relies on the familiar expansion of aone-loop amplitude in terms of scalar basis integrals,A cut−cons.4 (φ, 1 − q , 2+ q , 3− g , 4− g ) = ∑ iC 4;i I 4;i + ∑ iC 3;i I 3;i + ∑ iC 2;i I 2;i . (5.21)In this sum each j-point scalar basis integral (I j;i ) appears with a coefficient C j;i .The sum over i represents the sum over the partitions of the external momentaover the j legs of the basis integral. We use the methods described in previouschapters [120,122,132] to obtain the coefficients. Results were obtained using theQGRAF [207], FORM [210] and S@M [204] packages in order to control the extensivealgebra.5.2.1 Results for A 4;1 (φ, 1¯q , 2 q , 3 − g , 4 − g )The partial amplitude A 4;1 (φ, 1¯q , 2 q , 3 − g , 4− g ) is calculated from three primitive amplitudesaccording to Eq. (5.4). We shall deal with each of these ingredients inturn.
5.2. One-loop results 138A L 4 (φ, 1 −¯q , 2 + q , 3 − g , 4 − g )The full result for this primitive amplitude is given by,− iA L 4 (φ, 1−¯q , 2+ q , 3− g , 4− g ) = −iA(0) 4 (φ, 1 −¯q , 2+ q , 3− g , 4− g ) × V 1Ls 2 []134−F 1m4F2 [1 4][3 4] 〈2 |p φ | 3](s 14, s 34 ; s 134 ) + F 2mh4F (s 12, s 134 ; s 34 , m 2 φ )〈1 |p φ | 2] 2 []+F 1m4F2〈1 |p φ | 4][2 3][3 4](s 34, s 23 ; s 234 ) + F 2mh4F (s 12, s 234 ; s 34 , m 2 φ )+ 1 [ m 4 φ 〈1 4〉2 〈2 4〉−2 〈1 2〉〈2 |p φ | 3] 〈4 |p φ | 3]s 124+ 1 [[2 3] 2 〈4 |p φ | 1] 32 [1 2][1 3] 3 −〈4 |p φ | 3]s 123+ 1 [〈4 |p φ | 2] 3−2 [1 2][2 3] 〈4 |p φ | 3]s 123[× F 2mh4F (s 34 , s 123 ; s 12 , m 2 φ) + F 2mh+ 1 2×〈3 |p φ | 2] 3 ]F 1m4F[1 2][2 4] 〈3 |p φ | 4]s (s 12, s 14 ; s 124 )124m 4 φ 〈1 3〉3 ]F 1m4F〈1 2〉〈1 |p φ | 4] 〈3 |p φ | 4]s (s 12, s 23 ; s 123 )123m 4 φ 〈1 3〉3 ]〈1 2〉〈1 |p φ | 4] 〈3 |p φ | 4]s 123]4F (s 14 , s 123 ; s 23 , m 2 φ)[ m 4 φ 〈1 4〉2 〈2 4〉− 〈3 |p φ| 2] 2 〈3 |p φ | 1]]〈1 2〉〈2 |p φ | 3] 〈4 |p φ | 3]s 124 [1 2][1 4] 〈3 |p φ | 4]s 124[]F 2mh4F (s 34, s 124 ; s 12 , m 2 φ ) + F2mh 4F (s 23, s 124 ; s 14 , m 2 φ )− C 3;φ|12|34 (φ, 1 −¯q , 2+ q , 3− g , 4− g ) F3m 3 (s 12, s 34 , m 2 φ )− C 3;φ|41|23 (φ, 1 −¯q , 2+ q , 3− g , 4− g ) F3m 3 (s 23, s 14 , m 2 φ )+ 2〈1 3〉2 〈3 4〉〈4 |p φ | 3][1 2]ˆL 3 (s 123 , s 12 )3− 〈3 4〉〈3 1〉 (〈4 |p φ| 2][1 3] − 3 〈4 |p φ | 1][2 3])ˆL 2 (s 123 , s 12 )6 [3 1]〈1 3〉(16〈4 |p φ | 2] 2 [1 3] 2 − 3 〈4 |p φ | 2] 〈4 |p φ | 3][2 1][3 1] + 6〈4 |p φ | 1] 2 [2 3] 2)+6s 123 [3 1] 2 [3 2]×ˆL 1 (s 123 , s 12 )− 2s 124〈3 4〉 2 〈1 4〉 [4 2]ˆL 3 (s 124 , s 12 )3+ 〈3 4〉〈1 4〉 2 〈3 |p φ| 2][1 4] − 3 〈3 |p φ | 4][1 2]ˆL 2 (s 124 , s 12 )6 [4 1]+ 〈3 |p φ| 2](9 s 124 〈3 4〉[2 1] + 22 〈3 |p φ | 2] 〈4 2〉[1 2])ˆL 1 (s 124 , s 12 )6 s 124 [4 1][2 1]− 〈1 4〉〈1 3〉〈4 |p φ| 1][1 2]ˆL 2 (s 123 , s 23 )2 [3 1]
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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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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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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 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: 5.1. Introduction 136H amplitude 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.
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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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