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

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5.3. Numerical results 1455.3 Numerical resultsHere we present evaluations of the new amplitudes at the same kinematic point asused in the previous chapter (eq. 4.49) and in the literature [104, 109]. We haveused a scale µ = m H , set δ R = 1 (corresponding to the ’t Hooft-Veltman scheme)and, in assembling the amplitude A 4;1 , have used N f = 5. The results for the finalHiggs amplitudes presented in Table 5.2 agree with those from the semi-numericalcalculation of ref. [104] to one part in 10 8 . Note that these results depend onan overall phase that can be removed by dividing out by the corresponding Borncalculation. Using the analytic expressions for all the Hgggg, H¯qqgg and H¯qq¯q ′ q ′amplitudes that are now available we can also confirm the numerical values for thematrix elements squared given in ref. [104].5.4 SummaryIn this chapter we have computed the last analytically unknown helicity amplitudecontributing to the NLO corrections to Higgs plus two jet production at hadroncolliders. Once again we used the unitarity method to calculate the cut-constructiblepieces of the amplitude, and Feynman diagrams to calculate the entire rationalpart. We verified our results using the semi-numerical code of [104]. The analyticcalculations needed for this thesis are hence complete and in the next chapter weturn our attention to using the results to perform some phenomenology.
5.4. Summary 146(φ, 1 −¯q , 2 + q , 3− g , 4− g ) (φ† , 1 −¯q , 2 + q , 3− g , 4− g )1/ǫ 2 1/ǫ ǫ 0 ǫ 0A (0)4 0 0 +6.49907535901 0−2.39308144816iA L 4 −19.49722607702 −64.62496304875 −31.60558356648 −17.35549203005+7.17924434447 i −45.76112071571i −137.56039301452 i +6.14361664194 iA R 4 −6.49907535901 −23.12631834140 −48.74190400225 +4.58546771410+2.39308144816 i −14.67020390044i −39.06265552875i −1.38718545292 iA f 4 0 −4.33271690600 −14.98058321393 −0.22812640212+1.59538763210i −9.88874973495i +0.02973170727 iA 4;1 −18.77510659269 −69.27656696526 −51.15745514499 −18.24519911293+6.91334640579 i −41.47211867326i −149.70134751402 i +6.34730120438 iA 4;3 0 +2.61083477136 +17.75737443413 0−0.05119106396i+4.93097014463iTable 5.2: Numerical values of φ¯qqgg and φ †¯qqgg primitive amplitudes (above)and the amplitudes multiplying the two different colour structures (below), at thekinematic point defined in eq. (4.49).
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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 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 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: 5.2. One-loop results 144+ 1s 123[
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
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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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