2.4. Higgs Boson Production at Hadron Colliders
The Higgs mechanism, as described in Sec. 2.1.1, yields the most popular and minimal solution to solve the problem of mass generation. It predicts the existence of at least one single Higgs boson. The Higgs boson is a scalar massive particle, carrying no electric and colour charge. Within the SM, the Higgs boson mass is an unknown parameter.
Only upper and lower limits can be set by theoretical arguments. However, previous experiments, such as LEP and the Tevatron, were able to set exclusion limits and shrink the possible Higgs mass range. At the LHC, the search for the Higgs boson and the measurement of its properties is a fundamental part of the physics program.
On July 4th, 2012, the discovery of a new boson of mass near 125 GeV was claimed [1, 2], which is consistent with the SM Higgs boson. The properties of the SM Higgs boson and the different production mechanisms, as well as recent results are described in the remainder of this section. Non-minimal models with more Higgs bosons are not discussed in this thesis.
2.4.1. Higgs Boson Mass Constraints
Within the minimal SM no mass for the Higgs boson is predicted, but theoretical argu-ments suggest some constraints [83–89]. With increasing Higgs mass, the W W scattering cross section via Higgs boson exchange also increases. In order to not violate the unitarity in W W scattering, the Higgs bosons mass must be smaller than mH ∼1 TeV, unitarity bound. An additional upper limit on the Higgs boson mass has been derived from the φ4 dependence of the Higgs potential of mH < 700 GeV, triviality bound. In addition, the Higgs potential is bounded from below, since the vacuum has to remain stable, vacuum stability bound. With decreasing value of λ, the potential becomes flatter, which could cause an instability of the vacuum and therefore results in a lower bound on λ. As the Higgs mass is proportional to √
λ, the Higgs mass is limited, as well, by mH > 7 GeV.
Both the upper and the lower limits on the Higgs boson mass are dependent on the cut-off scale Λ up to which the SM is expected to be valid.
Figure 2.14:“Chimney plot”: Upper and lower limits on the Higgs boson mass as a function of the cut-off scale Λ up to which the SM is expected to be valid [90].
Figure 2.14 shows the Higgs boson mass as a function of Λ taking the theoretical
2. Z Boson and Higgs Boson Production in the Context of the Standard Model
arguments from above into account. The upper limit is given by the trivality bound, while the lower limit has been determined from the vacuum stability bound.
Further constraints on the Higgs boson mass were set by indirect and direct mea-surements from the experiments. The former is determined from a global fit to data considering precision measurements of weak neutral currents and the W and Z masses.
An essential part is the sensitivity of the W mass on electroweak radiative corrections, since it is proportional to ln (mH) but also proportional to m2t, which makes the de-termination quite complicated. The combination of electroweak precision measurements from LEP and the Tevatron results in an upper limit on the Higgs boson mass of about 152 GeV at 95% confidence level (CL) [91]. Direct measurements from LEP have set a lower limit of mH = 114.4 GeV at 95% CL [92]. In addition, the combined results of the Tevatron experiments CDF and DØ could exclude the Higgs boson in the mass region 147 GeV< mH <180 GeV at 95% CL [93].
2.4.2. Higgs Boson Decay
The Higgs boson couples directly to massive particles, coupling to massless particles are realised via massive gauge boson or heavy quark loops. Within the SM, the possible Higgs boson decays are predicted for a given Higgs boson mass. The probability of the different decay channels is expressed by the individual branching ratios. Figure 2.15 shows the set of branching ratios for a Higgs boson mass in the range 90 GeV< mH <1000 GeV with the corresponding theoretical uncertainties.
[GeV]
MH
100 200 300 400 500 1000
Higgs BR + Total Uncert
10-3
10-2
10-1
1
LHC HIGGS XS WG 2011
b b
τ τ
c c
t t gg
γ γ Zγ
WW ZZ
Figure 2.15: Branching ratios of the SM Higgs boson, together with their corresponding theo-retical uncertainties [94].
For a light Higgs boson, below theW W threshold, the dominant decay channel is the decay into a bottom-antibottom quark pair with a branching ratio of ∼90% followed by the decay intoτ τ with∼10%. This difference comes from the fact that the partial decay width for fermion decays is proportional to the fermion mass squared and the b-quark mass is a factor of three higher than the τ mass. Above the W W threshold, the decays into W W and ZZ are dominant. For a heavy Higgs boson, mH > 350 GeV, the Higgs boson can also decay into a top-antitop quark pair.
At hadron colliders, final states containing jets must compete with a large amount of multi-jet background, which make searches in these channels, e.g. H→b¯b, quite difficult.
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2.4. Higgs Boson Production at Hadron Colliders
Therefore, searches with purely leptonic final states or photons are favoured. For a light Higgs boson the decays into an oppositely charged τ pair and into a pair of photons are the preferred ones.
2.4.3. Higgs Boson Production
The SM predicts various production mechanisms for the Higgs boson, but only a limited number of them is accessible at the LHC, due to their in general low production cross sections compared to other SM processes. Figure 2.16 shows the cross sections of the indi-vidual production mechanisms accessible at the LHC with their corresponding theoretical uncertainties at a centre-of-mass energy of 7 TeV in pp-collisions.
[GeV]
MH
100 200 300 400 500 1000
H+X) [pb] →(pp σ
10-2
10-1
1 10
= 7 TeV s
LHC HIGGS XS WG 2010
H (NNLO+NNLL QCD + NLO EW) pp →
qqH (NNLO QCD + NLO EW) pp →
WH (NNLO QCD + NLO EW) pp →
ZH (NNLO QCD +NLO EW) pp →
ttH (NLO QCD) pp →
Figure 2.16: Production cross section for the SM Higgs boson as a function of its mass with its corresponding theoretical uncer-tainties at a centre-of-mass en-ergy of 7 TeV in pp-collisions [94].
At the LHC, the dominant production mechanism over the whole Higgs boson mass range is the gluon fusion via a virtual heavy quark loop. The second most important contribution to the overall production cross section is the weak boson fusion (WBF), which has a ten times smaller cross section than the gluon fusion. The WBF production is characterised by two high energetic, well separated forward jets and reduced central jet activity in the final state, which can be used for background suppression. Other possible production mechanisms are the associated Higgs boson production with weak bosons or top quarks. Figure 2.17 shows the LO Feynman diagrams of the dominant production mechanisms at the LHC.
2. Z Boson and Higgs Boson Production in the Context of the Standard Model
(a) Gluon fusion (b) Weak boson fusion
(c) Higgs-Strahlung (d) Top fusion
Figure 2.17.: LO Feynman diagrams for the dominant Higgs boson production mechanisms at the LHC: (a) the gluon fusion, (b) the weak boson fusion, (c) the associated Higgs boson production with vector bosons and (d) top quarks.
By moving to higher centre-of-mass energies the cross sections will be significantly increased, as shown in Fig. 2.18.
[GeV]
MH
100 200 300 400 500 600 700 800 900 1000
H+X) [pb] →(pp σ
10-1
1 10 102
LHC HIGGS XS WG 2012
=14 TeV s H+X at pp →
=8 TeV s H+X at pp →
=7 TeV s H+X at pp →
Figure 2.18: Total production cross section of the SM Higgs bo-son as a function of its mass for different centre-of-mass energies inpp-collisions [94].
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2.4. Higgs Boson Production at Hadron Colliders
2.4.4. Experimental Measurements of Higgs Boson Production
Searches at previous colliders, such as LEP and the Tevatron, were able to shrink the possible Higgs boson mass range, as discussed in Sec. 2.4.1. In addition, recent results from the Tevatron have shown an excess with a global significance of∼2.5σ in the mass range 115 GeV< mH <140 GeV [93].
The LHC has successfully started the quest for the Higgs boson. On July 4, 2012, both the ATLAS collaboration and the CMS collaboration claimed the discovery of a new boson with a mass of 126.0±0.4 (stat)±0.4 (syst) GeV (ATLAS) [1] and 125.3±0.4 (stat)±0.5 (syst) GeV (CMS) [2] with a local significance above 5 σ. Re-cent results from ATLAS and CMS from the end of 2012 using a combined dataset of up to 4.8 fb−1 at √
s = 7 TeV and 13 fb−1 at √
s = 8 TeV (ATLAS) and up to 5.1 fb−1 at
√s = 7 TeV and 12.2 fb−1 at √
s = 8 TeV (CMS) have shown an increased local signif-icance of the new boson of 7.0 σ (ATLAS) [95] and 6.9 σ (CMS) [96] for a Higgs boson mass hypothesis near mH = 125 GeV. Figure 2.19 shows the observed local probability p0 for both experiments for the individual channels and the combination.
[GeV]
mH
115 120 125 130 135
0p Combined observedγ observed
γ
Combined expected 01σσ
2σ
110 115 120 125 130 135 140 145
Local p-value
Figure 2.19.: Observed local probability p0 for the individual channels and the combination for (a) the ATLAS experiment [95] and (b) the CMS experiment [96]. The dashed black line shows the expected local probability p0 as a function of the Higgs boson mass.
The properties of this boson are consistent with the expectations of a SM Higgs boson, but the uncertainties on the properties are still very large. So far, the LHC shows evidence only in the vector boson decay modes H →γγ, H →ZZ and H →W W.
From now on, the highest priority is to establish the nature of this new boson, which also implies the observation of the boson decaying to fermions, such as H → τ τ. One of the most promising channels would be the WBF production, since it provides a very clean signature in the detector.