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

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1.3. Higgs searches at colliders 17Figure 1.2: A sample Higgsstrahlung diagram in which the Higgs boson is radiatedfrom a massive Z vector boson. Since the Higgs-electron coupling is small this wasthe dominant Higgs production mechanism at LEP.1.3 Higgs searches at collidersIn this section we describe the results of various searches for the Higgs boson atdifferent colliders. We discuss the current lowest bound on the Higgs mass, whichcomes from LEP. We also discuss the exclusion region around 2m W observed by theTevatron, and discuss search strategies and potentials at the LHC.1.3.1 Higgs searches at LEPThe Large Electron-Positron (LEP) collider operated at CERN between 1989 and2000, colliding electrons and positrons with a centre of mass energy between 90 and209 GeV. Its Higgs searches focused primarily on direct production whilst precisionmeasurements of the W and Z mass allowed constraints to be placed on m H throughquantum effects. These indirect searches constrained m H < 193 GeV/c 2 at the 95%confidence level and favoured a mass in the range 81 +51−33 GeV/c 2 [48].Direct production of a Higgs boson at a lepton collider is made more difficult sincethe colliding particles have very small couplings to the Higgs (since the coupling isproportional to the mass of the particle). This means that the dominant productionmechanism of a Higgs boson at a lepton collider is through the Higgsstrahlungprocess, (in which a Higgs is radiated from a Z boson) for which a sample diagramis shown in Fig. 1.2 [49,50]. For the range of Higgs boson masses which were relevantfor the LEP studies the Higgs predominately decayed to bb pairs (with a branching
1.3. Higgs searches at colliders 18ratio of 74%). The branching ratios for the decays to τ + τ − , WW ∗ and gg are around7% with the remaining ≈ 4% decay to cc.The final states which were included in the final combined analyses [51–55] werethe four-jet final state (H → bb)(Z → qq), the missing energy final state (H →bb)(Z → νν), the leptonic final state (H → bb)(Z → l + l − ) l ∈ {e, µ} and the taulepton final states, (H → bb)(Z → τ + τ − ) and (H → τ + τ − )(Z → qq). The resultof the combined direct searches, [51] was a limit on the lightest a SM Higgs bosoncould be. They found a lower bound of 114.4 GeV/c 2 at the 95% confidence level.Fig. 1.3 summarises these results.1.3.2 Higgs searches at the Tevatron and the LHCThe two colliders currently searching for the Higgs boson, Fermilab’s Tevatron andCERN’s LHC are both hadronic colliders (the Tevatron collides protons and antiprotons,the LHC collides protons). As such the main Higgs production mechanismsare completely different from those at LEP and are shown in Figs. 1.4-1.5, the largerenergy associated with these colliders also introduces new Higgs decay modes, whichare shown in Fig. 1.6.The dominant production mechanism at both colliders occurs through the gluonfusion process, which is the main topic of the next section. It is interesting tonote the differences between the subdominant production mechanisms between thecolliders. At the Tevatron the second largest source of Higgs bosons occurs throughW and Z Higgsstrahlung, the quark equivalent of the main process at LEP. However,at the LHC it is Vector-boson fusion (VBF or sometimes referred to as WBF) whichis the sub-dominant process. This is not merely due to the difference in centre ofmass energies between the colliders, but due to the fact that in an anti-proton thereare more valence anti-quarks than in a proton and as result processes in which quarkannihilation occur are favoured at the Tevatron.We note that in Fig. 1.6 there is a clear change in Higgs branching ratio aroundm H ≈ 130 GeV below these values the Higgs decays mostly into bb pairs, whilst
Page 7 and 8: Contentsvii1.4.1 Effective Lagrangi
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Page 47 and 48: 2.1. Unitarity 32of two tree level
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Page 71 and 72: 2.6. The unitarity-bootstrap 56Next
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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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3.4. Cross Checks and Limits 110The
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3.4. Cross Checks and Limits 112−
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3.5. Summary 114The rational terms
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Chapter 4One-loop Higgs plus four-g
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4.2. Cut-Constructible Contribution
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4.3. Rational Terms 124contains two
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4.4. Higgs plus four gluon amplitud
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4.6. Summary 130p µ 2 = (+0.344450
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Chapter 5The φqqgg- NMHV amplitude
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5.1. Introduction 134Figure 5.1: Sa
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5.1. Introduction 136H amplitude φ
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5.2. One-loop results 138A L 4 (φ,
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5.2. One-loop results 140with K 1 =
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5.2. One-loop results 142Relation f
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5.2. One-loop results 144+ 1s 123[
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5.4. Summary 146(φ, 1 −¯q , 2 +
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6.2. Improvements from the semi-num
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6.4. Tevatron results 150The W mass
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6.4. Tevatron results 152m H [GeV]
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6.5. LHC results 154Eq. (6.11) and
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6.5. LHC results 156m H [GeV] 120 1
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6.5. LHC results 158Figure 6.3: The
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6.5. LHC results 160of describing T
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6.5. LHC results 162Figure 6.6: p T
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6.6. Summary 164at LO and the effec
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6.6. Summary 166of Higgs masses, 15
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Chapter 7. Conclusions 168one can d
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Appendix ASpinor Helicity Formalism
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A.1. Spinor Helicity Formalism nota
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A.3. Pure QCD amplitudes 174Further
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Appendix BOne-loop Basis IntegralsI
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B.2. Box Integral Functions 178boxe
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B.2. Box Integral Functions 180L 2
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Bibliography 182[10] R. Feynman, Ma
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Bibliography 184[36] M. Bahr et. al
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Bibliography 186[63] M. Shifman, A.
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Bibliography 188[85] R. V. Harlande
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Bibliography 190[104] R. K. Ellis,
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Bibliography 192[125] G. Ossola, C.
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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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