2.2 Collider phenomenology of the SM Higgs boson
2.2.1 Higgs boson decays
Due to the mass dependence of the Higgs couplings, Eq. (2.25), the SM Higgs boson pre-dominantly decays into the heaviest particle-antiparticle pair that is kinematically accessible,
depending on the available energy mH. From the pole masses9 of the SM gauge bosons and fermions10 [74,75],
MZ = 91.188 GeV, MW = 80.385 GeV, mµ= 0.106 GeV, mτ = 1.777 GeV,
mc= (1.67±0.07) GeV, mb= (4.78±0.06) GeV, mt= (173.34±0.76) GeV, (2.34) all partial widths, Γ(Dj(H)), for the Higgs boson decays to these particles can be calculated.
Here, the various decay modes of the Higgs boson H are denoted by Dj(H). The branching ratio, which is the probability of the Higgs boson decaying into a certain final state, is then given by
BR(Dj(H))≡ Γ(Dj(H)) Γtot
, (2.35)
with the total decay width Γtot = PjΓ(Dj(H)), where the sum runs over all possible decay modes Dj(H). For a reliable prediction of the Higgs boson signal rates at colliders, a precise calculation of Γtot, and hence of all partial widths, is a necessity. Uncertainties in the total width prediction will introduce strongly correlated uncertainties among all the branching ratios.
An overview of the branching ratios of the SM Higgs boson as a function of the Higgs mass is given in Fig. 2.4. The low mass region, mH ∈ [1,100] GeV, depicted in Fig. 2.4(a), was accessible at the e+e− collider LEP, while the high mass region, mH ∈[80,1000] GeV, shown in Fig. 2.4(b), is probed by the hadron collider experiments at the Tevatron and LHC. As expected, the predominant decay modes are those into the heaviest particles allowed by phase space. However, besides the (on-shell) two-body decays in kinematically accessible regions, mH > 2mX, it is important to also take into account the three- and even four-body Higgs decays via off-shell W and Z bosons below the W W/ZZ thresholds.
Due to the proportionality of the Higgs couplings to the masses of the decay products, the total width ranges over many orders of magnitude, namely from 10−4GeV for mH . 10 GeV to 1 TeV for mH ∼1 TeV. The total width for a SM Higgs boson with mH ∼125 GeV is about 4.1 MeV. Experimentally, this is too small to be resolved in invariant mass distributions of the decay products, as the finite energy resolution of the LHC detectors is much larger11. On the theoretical side, the narrow width justifies the approach to factorize the Higgs production process from the subsequent decay in the on-shell region12(known as thenarrow-orzero-width approximation). For very large Higgs masses, however, the Higgs boson would manifest itself as a very broad resonance with a width being of around the size of its mass. This requires a careful theoretical treatment beyond the narrow width approximation, taking also interference
9 The pole mass is defined as the position of the pole in the propagator, which is typically measured by experi-ment. Quark masses, however, cannot be observed directly since they are (except for the top quark) confined in hadrons. The pole mass can be related to therunningmass (in the MS renormalization scheme) [72], which corresponds to the mass parameter in the renormalized Lagrangian. Nevertheless, for the top quark delicate issues (and thus uncertainties) in the interpretation of the measured mass remain, see Ref. [73] for a discussion.
10The masses of the electron and light quarks,u,dands, are too small to be relevant for Higgs phenomenology.
11Even at a future International Linear Collider (ILC) the width is too small to be measured directly from the line-shape [76]. However, by combining signal rate measurements with the ILC measurement of the total e+e− → ZH cross section, cf. Section 2.2.2, the total width can be unambiguously inferred. This will be discussed in Chapter5.
12Recently, it has been pointed out that even for a Higgs mass of 125 GeV interference effects (in the off-shell region) can still play a role and provide sensitivity for probing the total widths at the LHC [77]. See Chapter5 for more details.
µµ s¯s
γγ WW gg c¯c τ τ b¯b
MH[GeV]
BR
100 10
1 1
0.1
0.01
0.001
(a) Low mass region. Taken from Ref. [33].
[GeV]
MH
90 200 300 400 500 1000
Higgs BR + Total Uncert [%]
10-4
10-3
10-2
10-1
1
LHC HIGGS XS WG 2013
b b
τ τ
µ µ c c
t t gg
γ γ Zγ
WW
ZZ
(b) High mass region. Taken from Ref. [30].
Figure 2.4: Branching ratios (BR) of a SM Higgs boson for low (a) and high (b) Higgs boson masses. In (b), the bands indicate the theoretical uncertainty of the BR predictions.
f
H
f¯ (a)
W, Z H
W, Z
(b)
γ
H Q, W
γ, Z (c)
g
H Q
g (d)
Figure 2.5: Leading-order diagrams for the various SM Higgs boson decay channels into a fermion-antifermion (ff¯) pair (a), weak gauge bosons (W,Z) with successive decay to fermions (b), photons and photon-Z boson (c) and gluons (d). Qdenotes any heavy quark.
effects between signal and background processes into account, see e.g. Ref. [30] for a discussion of current developments.
The relevant leading-order Feynman diagrams for the various decay modes of the SM Higgs boson are shown in Fig.2.5. In the following we briefly discuss the main features of the relevant decay channels and give the leading-order expressions for the partial widths.
• H →ff¯
For the Higgs decay into fermion-antifermion (ff¯) pairs, the partial width at leading order (LO) is given by
ΓLO(H →ff¯) = g22Nc
32πMW2 mHm2fβf3, (2.36) with the fermion velocity βf = (1−4m2f/m2H)1/2 and the color factor Nc = 3 (1) for quarks (leptons). According to Eq. (2.34) the relevant decay modes are those to t¯t (for heavy Higgs bosons), b¯b, τ+τ−, cc¯, and, to a lesser extent, µ+µ−. The kinematical factor βf3 in Eq. (2.36) leads to a strong suppression near threshold, mH ' 2mf. The suppression is weaker for a pseudoscalar (or CP-odd) Higgs boson, A, where we have
ΓLO(A → ff¯) ∝ βf. We often encounter pseudoscalar Higgs bosons in non-minimal Higgs sectors of BSM theories, for instance in the MSSM, see Section 2.4.
For quark final states next-to-leading-order (NLO) QCD corrections are sizable and need to be taken into account. A proper treatment of higher-order corrections requires to base the Yukawa coupling on the running quark mass at the scale of the Higgs mass,mq(mH), allowing for the resummation of large logarithms [78]. Furthermore, the threshold regime, mH ' 2mq, deserves particular attention as potential mixing between the Higgs boson and (qq¯) bound states may play a significant role [79].
• H →W W/ZZ →4f
The partial width for a Higgs boson decaying into two on-shell gauge bosons, H → V V (V =W, Z), is given by [80]
ΓLO(H→V V) = g22
128πMW2 m3HδV √
1−4x(1−4x+ 12x2), (2.37) where δW = 2, δZ = 1 due to the symmetry of exchanging the identical Z bosons in the final state, and x=MV2/m2H. Thus, at large Higgs masses, i.e. small x, the decay width toW W is twice the decay width to ZZ.
Below the W W and ZZ thresholds (as is the case for the discovered Higgs boson at mH ∼ 125.7 GeV), these decays have to be treated as three- and four-body decays with off-shell gauge bosons and final state fermions13[81]. Despite the propagator suppression, these decays can still compete with the decayH→b¯bdue to the smallness of the bottom Yukawa coupling, cf. Fig. 2.4. Furthermore, the kinematical details (energy, angular and invariant-mass distributions) of the four-fermion final state allow for the determination of the spin and CP properties of a discovered Higgs boson candidate [82,83].
• H →γγ/γZ
The Higgs decay into two photons or a photon and aZ boson is mediated at leading order by W boson and charged fermion loops, as depicted in Fig. 2.5(c). The dominant and sub-dominant contributions come for theW boson and top quark loop, respectively. The partial width for the decay H →γγ is given by
ΓLO(H →γγ) = g22α2em 1024π3MW2 m3H
X
f
NcQ2fAH1/2(τf) +AH1 (τW)
2
, (2.38)
with the electric charge Qf and color factor Nc of the fermion in the loop. The form factors for spin-1/2 and spin-1 particles are given by
AH1/2(τ) = 2[τ + (τ −1)f(τ)]τ−2, (2.39) AH1 (τ) =−[2τ2+ 3τ + 3(2τ−1)f(τ)]τ−2. (2.40)
13Formulae for the leading order three- and four-body decays can e.g. be found in Ref. [32].
The functionf(τ) is defined by
f(τ) =
arcsin2(√
τ) τ ≤1
−14hlog1+1−√√1−τ1−τ−1−1 −iπi2 τ >1 , (2.41) and theτ parameters are given by τf =m2H/4m2f and τW =m2H/4MW2 . It is important to note that due to the interference terms, the partial width is sensitive to the relative sign of the individual contributions. At a Higgs boson mass of mH ∼ 125 GeV, the top quark and W boson loop contributions have opposite sign and thus the tW interference term yields a negative contribution to the partial width.
Due to the suppression by the additional electromagnetic coupling constant, the loop decays H→γγ and H →Zγ are only important for light Higgs bosons,mH .130 GeV, where the total width is rather small. Despite its rather small branching ratio, theH →γγ channel provides an experimentally clean collider signature and thus played a major role in the discovery of the Higgs boson, see Chapter 3. Moreover, these loop-induced decay modes feature a great sensitivity to new heavy charged particles of BSM theories: Due to the proportionality of the Higgs couplings to the particle masses the loop mass suppression is compensated, hence virtual particles do not decouple in the heavy mass limit. A precise measurement of the H → γγ and H → Zγ partial widths thus probes potential effects induced by heavy charged particles, which might be too heavy to be produced directly at current collider experiments14.
• H →gg
The Higgs boson decay to two gluons is mediated by heavy quark loops, as depicted in Fig.2.5(d), with the dominant contribution coming from top quarks and a small contri-bution from bottom quarks. The partial width at leading order is given by
ΓLO(H →gg) = g22α2s 288π3MW2 m3H
3 4
X
Q
AH1/2(τQ)
2
, (2.42)
with the strong coupling constant αs, the loop function AH1/2 given by Eq. (2.39) and τQ = m2H/4m2Q. For this process, the NLO QCD corrections (entering at the two-loop level) are very important, leading to an increase of the partial width by up to∼70% for mH . 2MW and at the t¯t threshold [102]. Even beyond NLO [85] the partial width is further increased by about 20% in the light Higgs regime.
The numerical values of the SM Higgs branching ratios and total width for Higgs masses in the proximity of the discovered Higgs boson are listed in Tab. (2.2), taken from Ref. [30]. These values are evaluated with the state-of-the-art tools HDecay[86, 87] and Prophecy4f [88]. We furthermore list the maximal uncertainty estimates15 (relative to the quoted branching ratio),
14 As a nice example, it was shown in Ref. [84] that theH →γγsignal strength measured at the LHC excludes the existence of a fourth generation of fermions (assuming fourth generation fermion masses ofmf0≤800 GeV).
15 Note, that the uncertainty for the total width is derived by adding the partial width uncertainties linearly.
Furthermore, PUs and THUs are added linearly [30]. We find this to be an (overly) conservative approach and discuss an alternative approach in Section4.2.2, which also allows to account for correlations among the branching ratio uncertainties in global Higgs couplings fits.
Higgs mass Branching ratios to fermionic final states Total width
[GeV] b¯b τ+τ− cc¯ µ+µ− t¯t [GeV]
125.0 57.7%+3.2−3.3 6.32%+5.7−5.7 2.91%+12.2−12.2 0.0219%+6.0−5.9 − 4.07·10−3 +4.0−3.9
125.5 56.9%+3.3−3.3 6.24%+5.7−5.6 2.87%+12.2−12.2 0.0216%+5.9−5.8 − 4.14·10−3 +3.9−3.9
126.0 56.1%+3.3−3.4 6.16%+5.7−5.6 2.83%+12.2−12.2 0.0214%+5.9−5.8 − 4.21·10−3 +3.9−3.8
Higgs mass Branching ratios to bosonic final states Total width
[GeV] gg W W∗ ZZ∗ γγ γZ [GeV]
125.0 8.57%+10.2−10.0 21.5%+4.3−4.2 2.64%+4.3−4.2 0.228%+5.0−4.9 0.154%−8.8+9.0 4.07·10−3 +4.0−3.9
125.5 8.52%+10.2−9.9 22.3%+4.2−4.1 2.76%+4.2−4.1 0.228%+4.9−4.9 0.158%−8.8+8.9 4.14·10−3 +3.9−3.9
126.0 8.48%+10.1−9.9 23.1%+4.1−4.1 2.89%+4.1−4.1 0.228%+4.9−4.8 0.162%−8.8+8.8 4.21·10−3 +3.9−3.8
Table 2.2: Branching ratios and total width of the SM Higgs boson in the mass region of the discovered Higgs boson. The quoted upper and lower uncertainties are relative to the predicted value and given in percentage. Numbers are taken from Ref. [30].
comprised of parametric uncertainties (PUs) derived from variations of the input parameters (αs, mc, mb, mt) as well as theoretical uncertainties (THUs) for the missing higher-order corrections [89]. As can be seen from Tab. 2.2 and Fig. 2.4(b), with the mass value of the discovered Higgs boson, mH ∼ 125.7 GeV, Nature kindly provides us with the opportunity to measure various Higgs decay modes, since all channels except H → t¯t are accessible with current or future collider experiments. This further allows to probe the various Higgs couplings and thus provides an important test of the SM predictions.