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

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6.4. Tevatron results 153into account and including the finite top mass correction tabulated in Table 6.2 wefind that our NLO Higgs + 1 jet and LO Higgs + 2 jet cross sections in Table 6.1are in agreement with the corresponding numbers (1.280 and 0.336 fb) from Table 2of Ref. [214].6.4.1 Effect of additional search cutsWe also investigate the behaviour of the LO and NLO predictions in the kinematicregion relevant for the latest Tevatron Higgs exclusion limits. Therefore, in additionto the jet cuts above, we also consider cuts on the decay products of the W/W ⋆ thatare produced by the Higgs boson. These cuts correspond very closely to a recentCDF analysis [216], although the treatment of lepton acceptance is simplified.• One of the leptons from the W decays (the “trigger” lepton, l 1 ) is requiredto be relatively hard and central, p l 1t> 20 GeV, |η l 1| < 0.8 whilst the other(l 2 ) may be either softer or produced at slightly higher pseudorapidity, p l 2t >10 GeV, |η l 2| < 1.1.• The invariant mass of the lepton pair is bounded from below (to eliminatevirtual photon contributions), m l1 l 2> 16 GeV.• Each lepton must be isolated. Any jet found by the algorithm that lies withina η − φ distance of 0.4 from a lepton should have a transverse momentum lessthan 10% of that of the lepton itself.• The missing transverse momentum – in our parton level study, the sum ofthe two neutrino momenta – is constrained using the E/ spec t variable definedby [216],[ (E/ spec t = E/ t sin min ∆φ, π )]2. (6.13)∆φ is the distance between the E/ t vector and the nearest lepton or jet. Werequire that E/ spec t > 25 GeV.In Figure 6.1 we see the scale dependence of the LO and NLO cross sections form H = 160 GeV. The upper two curves show the case of the minimal set of cuts in
6.5. LHC results 154Eq. (6.11) and the lower curves show the results when including the Higgs searchcuts above. Applying the additional cuts on the Higgs decay products does notchange the scale dependence, indicating that the isolation and missing transversemomentum cuts (that are sensitive to additional radiation) do not play an importantrole. Applying the additional search cuts does not alter the behaviour of the NLOprediction in the Higgs + ≥ 2 jet bin, so that the results presented in the previoussection (with no cuts on the Higgs decay products) are sufficient to estimate thepercentage theoretical uncertainty.6.5 LHC resultsIn order to study the impact of the NLO corrections at the LHC, we adopt a differentset of cuts to define the jets. The rapidity range of the detectors is expected to bemuch broader, allowing for a larger jet separation too, and we choose a somewhathigher minimum transverse momentum,p t (jet) > 40 GeV, |η jet | < 4.5, R jet,jet > 0.8 . (6.14)In this section we do not consider the decay of the Higgs boson for the sake ofsimplicity.Since results for this scenario have already been discussed at some length [105],we restrict ourselves to a short survey of the essential elements of the phenomenologyat the lower centre-of-mass energy, √ s = 10 TeV. We present the scale dependence ofthe LHC cross section for Higgs + 2 jets (m H = 160 GeV) in Figure 6.2. We have alsochecked the agreement of our calculation with previous results [105] at √ s = 14 TeV,taking into account the different choice of parton distribution functions used in thatreference. As noted in the earlier paper [105], the corrections are quite modest usingour central scale choice, µ 0 = µ H , increasing the cross section by approximately 15%.Once again, although the scale dependence is much reduced it is still substantial.For the sake of illustration we have chosen m H = 160 GeV in the study above.To illustrate the effect of the QCD corrections more broadly, in Table 6.3 we givethe cross sections for Higgs masses in the range 120 GeV < m H < 200 GeV. It is
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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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1.5. 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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2.4. 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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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 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: 6.4. Tevatron results 152m H [GeV]
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
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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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