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

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6.5. LHC results 159Figure 6.4: The √ s dependence of the cross section for m H = 160 GeV at LO(dashed) and NLO (solid). Results are shown for the minimal set of cuts in Eq. (6.14)(two upper red curves) and after application of the additional WBF Higgs searchcuts given in Eq. (6.15) (two lower red curves). The cross section for the weak bosonfusion process is also shown for comparison (four central blue curves).
6.5. LHC results 160of describing Tevatron data. As a result, the dynamic scale H T was suggested as asafer choice. H T , or the hotness, is defined as the sum over the transverse energy ofthe final state particles,H T = ∑ jE j T + EH T . (6.16)The motivation for this being a superior scale choice is shown schematically inFig 6.5. A fixed scale such as m H may do a good job of describing the physics whenthe Higgs boson is radiated with a large p T and the jets are softer in comparisonto the Higgs. However when one produces two hard jets and a relatively soft Higgsm H may not do such a good job of explaining the physics. Dynamic scales, whichadjust on an event by event basis, on the other hand, should be able to cope withboth sorts of kinematics in a reasonable manner. At the LHC high-p T jets will becommon, and hence the choice of scale could become an even more theoreticallyimportant issue than it is today.To investigate the role of dynamic scales we calculated distributions for p T andη for the two hardest jets, H T , at the LHC ( √ s = 7 TeV) using the basic jet cutsof eq. (6.14). The results are shown in Figs. 6.6, 6.7 and 6.8. For the p T andH T distributions the dynamic scale choice µ = H T preserves the shape of the LOcalculation much better than µ = m H . As expected the deviations in shape (for thep T distribution) are largest for the high-p T region. As is also expected, the shape ofthe pseudorapidity distribution is stable under both scale choices.We consider bands of scale uncertainty, which can be obtained by calculatingcross sections at two different scale choices ∆(µ 1 , µ 2 ) = [σ(µ 1 ), σ(µ 2 )] 1 . As is expected,performing a NLO calculation reduces ∆ for both scale choices relative tothe LO case. It is interesting to note that, when using a dynamic scale, one hasto choose lower values µ 1 to obtain ∆ NLO (µ 1 , µ 2 ) ∈ ∆ LO (µ 1 , µ 2 ). It is desirablefor ∆ NLO (µ 1 , µ 2 ) ∈ ∆ LO (µ 1 , µ 2 ) since this indicates that the perturbation series isconverging, and further that the scale variation is indicative of the theoretical uncertainty.Typically when using fixed scales a choice of µ 1 ∼ (0.75 − 0.5)m i will1 Here we define [x 1 , x 2 ] to be the continuous region between x 1 and x 2 including endpoints.
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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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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
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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,
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: 6.5. LHC results 158Figure 6.3: The
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
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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