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

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6.4. Tevatron results 151|η jet | < 2.5 |η jet | < 2Process σ LO [fb] σ NLO [fb] σ LO [fb] σ NLO [fb]Higgs + 0 jets 1.25 1.98 1.25 2.05Higgs + 1 jets 0.84 1.16 0.74 1.07Higgs + ≥ 2 jets 0.35 0.48 0.28 0.39Table 6.1: Cross section for Higgs + jet production and decay into W − (→µ −¯ν)W + (→ νe + ) at √ s = 1.96 TeV for M H = µ = 160 GeV. In the second andthird columns, only the cuts of Eq. (6.11) are applied. For the results in the final twocolumns the more stringent cut, |η jet | < 2 is applied, in order to allow a comparisonwith Ref. [214].as 4.9%. Our number is deficient in that it does not include NNLO corrections tothe Higgs + 0 jet rate. Our calculation treats all jet bins consistently at NLO. Theinclusion of the NNLO correction to the Higgs + 0 jet bin will reduce our number.On the other hand, the calculation of Ref. [214] is deficient because it does nottreat all bins consistently at NNLO, i.e. it does not include NNLO corrections forthe Higgs +1 jet rate or NLO+NNLO effects for the Higgs + ≥ 2 jet rate. Weroughly estimate that including the NNLO effects in the Higgs +0 jet bin wouldmove our central value from 11% to 10%. Overall, because the corrections are quitesubstantial, the theoretical estimate of the fraction of events in the Higgs + ≥ 2 jetbin is quite uncertain.Despite the fact that the fraction of events in the Higgs + ≥ 2 jet bin is small,it is important because the associated uncertainty is large. We investigate this issuein Table 6.2, where we give the cross section for the process of Eq. (6.7) usinga selection of values for the Higgs mass of current interest for the Tevatron. Inthe table we give the results for the leading order and next-to-leading order crosssections, calculated using LO and NLO MSTW2008 PDFs respectively. For therange of Higgs masses considered, the QCD corrections increase the cross sectionby approximately 40% (for the central value, µ = m H ). The theoretical error isestimated by varying the common renormalization and factorization scale in the
6.4. Tevatron results 152m H [GeV] 150 160 165 170 180Γ H [GeV] 0.0174 0.0826 0.243 0.376 0.629σ LO [fb] 0.329 +92%−45%0.345 +92%−44%0.331 +92%−44%0.305 +92%−44%0.245 +91%−44%σ NLO [fb] 0.447 +37%−30%0.476 +35%−31%0.458 +36%−31%0.422 +41%−30%0.345 +37%−31%R 1.098 ± 0.003 1.113 ± 0.003 1.122 ± 0.004 1.130 ± 0.005 1.149 ± 0.005Table 6.2: Cross section for Higgs + 2 jet production and decay into W − (→µ −¯ν)W + (→ νe + ) at √ s = 1.96 TeV. Only the cuts of Eq. (6.11) are applied. Thecorrection factor for each Higgs mass, given by Eq. (6.4), is also shown.range, m H /2 < µ < 2m H . As can be seen from the table, even though includingthe next-to-leading order corrections leads to a considerable improvement in thetheoretical error, the remaining error is still quite sizeable. We do not include afactor to correct for the finite top mass, but in order to facilitate comparison withother calculations we also tabulate this factor R (computed using Eq. (6.4)) usinga value for the top quark mass of m t = 172.5 ± 2.5 GeV.In the spirit of Ref. [214], we can now estimate the theoretical uncertainty on thenumber of Higgs signal events originating from gluon fusion. By using the fractionsof the Higgs cross section in the different multiplicity bins taken from Ref. [215], wecan update Eq. (4.3) of Ref. [214] (for a Higgs boson of mass 160 GeV) with,∆N signal (scale)N signal= 60% · (+5%−9%)+ 29% ·( +24%−23%)+ 11% ·( +35%−31%) (=+13.8%)−15.5%(6.12)This equation represents the scale variation associated with the Higgs plus 0-, 1-and ≥ 2-jet cross sections using NNLO (0-jet) and NLO (1- and 2-jet) PDFs. Eachterm is weighted by the % of events with the relevant jet multiplicities reported bythe CDF collaboration. Only the uncertainty on the Higgs + ≥ 2 jet bin has beenmodified, using the results from Table 6.2. The corresponding determination usingthe LO uncertainty in the Higgs + ≥ 2 jet bin is (+20, 0%, −16.9%) [214], so thisrepresents a modest improvement in the overall theoretical error.The correspondence of our results with those of Anastasiou et al. is somewhatobscured by the fact that the total Higgs width used in Ref. [214] is about 7%smaller at m H = 160 GeV than the value given in our Table 6.2. Taking this fact
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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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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 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: 6.4. Tevatron results 150The W mass
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
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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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