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

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6.5. LHC results 161p Hp 1 p 2p 1j 2p 2p Hj 1j 2j 1Figure 6.5: Possible momentum configurations in a Higgs plus two jet events. On theleft hand diagram two jets are produced with large p T and the Higgs is a relativelysoft in comparison. On the right hand side the Higgs has a high p T . Whilst µ = m Hmight adequately describe the physics of the second diagram one might not expectit to be a good choice on the left hand side.ensure that ∆ NLO (µ 1 , µ 2 ) ∈ ∆ LO (µ 1 , µ 2 ), whereas to ensure this condition for H Tone finds, µ 1 ∼ (0.3 − 0.4)H T . The results are summarised in Fig. 6.9 and we notethat the total variation over the range µ 0 /4 ≤ µ ≤ 4µ 0 is roughly equal for bothscale choices. What should be noted is that when attempting to estimate the totalscale uncertainty for dynamic scales one should use a lower limit of around H T /4rather than H T /2 (which is often the choice used for fixed scales).6.5.3 Considerations from the effective theoryWe observed in the previous section that the dynamic scale H T preserved the shapesof the LO distributions for p T and H T , whereas the fixed scale m H failed to do so.We note, however, that typical values of H T are ∼ 350 GeV ≈ 2m t . This is preciselythe scale at which our effective theory breaks down, therefore one could argue thatthis scale choice is inappropriate for our calculation. In addition we note that topquark mass effects become important when p T > m t .To clarify the situation we investigated the effects of the top mass on the p Tdistribution for Higgs plus jet events at the LHC, (for which the full theory result
6.5. LHC results 162Figure 6.6: p T distributions for the hardest (left) and second hardest (right) jets.The distribution with a dynamic scale choice µ = H T is shown in red, whilst theblue curves represent the fixed scale choice µ = m H . In both cases the NLO resultsare represented by a solid line. The dashed line represents the LO distribution,normalised to the NLO cross section.Figure 6.7: Pseudorapidity plots for the two hardest jets using different scale choices.The distribution with a dynamic scale choice µ = H T is shown in red, whilst theblue curves represent the fixed scale choice µ = m H . In both cases the NLO resultsare represented by a solid line. The dashed line represents the LO distribution,normalised to the NLO cross section.
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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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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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Page 129 and 130: 3.5. Summary 114The rational terms
Page 131 and 132: Chapter 4One-loop Higgs plus four-g
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Page 139 and 140: 4.3. Rational Terms 124contains two
Page 141 and 142: 4.4. Higgs plus four gluon amplitud
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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,
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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: 6.5. LHC results 160of describing 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
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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