11. Status of Higgs Boson Physics

1

11. Status of Higgs Boson Physics
Revised August 2023 by M. Carena (FNAL; Chicago U.; Chicago U., Kavli Inst.), C. Grojean(DESY, Hamburg; Physik, Humboldt U.), M. Kado (MPP, Garching) and V. Sharma (UC San
Diego).

11.1
11.2

Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
The Standard Model and the mechanism of electroweak symmetry breaking . . . .
11.2.1 The SM Higgs boson mass, couplings and quantum numbers . . . . . . . . .
11.2.2 The SM custodial symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.3 Stability of the Higgs potential . . . . . . . . . . . . . . . . . . . . . . . . . .
11.2.4 Higgs boson production and decay mechanisms . . . . . . . . . . . . . . . . .
11.3 The experimental profile of the Higgs boson . . . . . . . . . . . . . . . . . . . . . .
11.3.1 The principal decay channels of the Higgs boson . . . . . . . . . . . . . . . .
11.3.2 The Higgs boson decay to vector bosons . . . . . . . . . . . . . . . . . . . . .
11.3.3 Measurement of the Higgs boson mass . . . . . . . . . . . . . . . . . . . . . .
11.3.4 Higgs decays to third generation fermions (bb and τ + τ − ) . . . . . . . . . . .
11.3.5 Higgs boson production in association with top quarks . . . . . . . . . . . . .
11.3.6 Combining the main channels . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.3.7 Probing the Higgs boson coupling to the second generation . . . . . . . . . .
11.3.8 Searches for rare decays of the Higgs boson . . . . . . . . . . . . . . . . . . .
11.3.9 Higgs boson pair production and self-coupling . . . . . . . . . . . . . . . . . .
11.3.10 Beyond the main Higgs boson production modes . . . . . . . . . . . . . . . .
11.3.11 First results on the main production and decay channels at 13.6 TeV . . . . .
11.4 Main quantum numbers and width of the Higgs boson . . . . . . . . . . . . . . . .
11.4.1 Main quantum numbers J PC . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.4.2 Off-shell couplings of the Higgs boson . . . . . . . . . . . . . . . . . . . . . .
11.4.3 The Higgs boson width . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5 Probing the coupling properties of the Higgs boson . . . . . . . . . . . . . . . . . .
11.5.1 Probing coupling properties . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5.2 Effective Lagrangian framework . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6 New physics models of EWSB in the light of the Higgs boson discovery . . . . . .
11.6.1 Higgs bosons in the minimal supersymmetric standard model (MSSM) . . . .
11.6.2 Supersymmetry with singlet extensions . . . . . . . . . . . . . . . . . . . . .
11.6.3 Supersymmetry with extended gauge sectors . . . . . . . . . . . . . . . . . .
11.6.4 Effects of CP violation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6.5 Non-supersymmetric extensions of the Higgs sector . . . . . . . . . . . . . . .
11.6.6 Composite Higgs models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6.7 Searches for signatures of extended Higgs sectors . . . . . . . . . . . . . . . .
11.7 Summary and outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

11.1 Introduction

1
3
5
5
6
6
15
15
16
18
20
23
26
29
31
36
39
40
40
40
47
48
50
52
60
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71
72
73
78
84
94

Understanding how the masses of the known elementary particles are generated has been one of
the fundamental endeavours in particle physics for several decades. The chiral nature of the weakinteractions forbids an intrinsic mass terms for the quarks and leptons at high energy, and their
S. Navas et al. (Particle Data Group), Phys. Rev. D 110, 030001 (2024)
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11. Status of Higgs Boson Physics

masses can only appear as emergent quantities after the spontaneous symmetry of the electroweak
symmetry. The discovery in 2012 by the ATLAS [1] and the CMS [2] collaborations of a newresonance with a mass of approximately 125 GeV and the subsequent studies of its properties withthe full data set from Run 1, from 2009 to 2012, with a centre-of-mass energy of 7 TeV and 8 TeV,
conclusively provided a first sketch of the Electroweak Symmetry Breaking (EWSB) mechanism.
The much larger dataset collected during the LHC Run 2, from 2015 to 2018, with a higher centreof-mass energy of 13 TeV, demonstrated the compatibility of the measured resonance with the Higgs
boson of the Standard Model (SM) [3] and strongly challenged other contenders. The LHC started
its Run 3 in 2022 and this data taking phase is expected to comprise of four years of operations
until 2026. By then the LHC is expected to deliver proton-proton collision data corresponding toan integrated luminosity of approximately 250 fb−1 per experiment.
In the SM, the electroweak interactions are described by a gauge field theory invariant under
the SU(2)L × U(1)Y symmetry group. The mechanism of EWSB [4] provides a general framework
to keep untouched the structure of these gauge interactions at high energies and still generate theobserved masses of the W and Z gauge bosons as well as those of the quarks and charged leptons.
The EWSB mechanism posits a self-interacting complex EW doublet scalar field, whose CP -even
neutral component acquires a vacuum expectation value (VEV) v ≈ 246 GeV, which sets the scaleof the symmetry breaking. Three massless Goldstone bosons are generated and are absorbed togive masses to the W and Z gauge bosons. The remaining component of the complex doublet
becomes the Higgs boson – a new, and so far unique, fundamental scalar particle. The masses of
all fermions are also a consequence of EWSB since the Higgs doublet is postulated to couple tothe fermions through Yukawa interactions in a way consistent with all the gauge symmetries of theSM.
The initial measurements during the LHC Run 1 were accessible mainly through production
and decay channels related to the couplings of the Higgs boson to the vector gauge bosons. The
outstanding performance of the LHC Run 2, made it possible for the ATLAS and CMS experiments
to independently and unambiguously establish the couplings of the Higgs boson to the charged
fermions of the third generation (the top quark, the bottom quark, and the tau lepton). In all
observed production and decay modes measured so far, the rates and differential measurements arefound to be consistent, within experimental and theoretical uncertainties, with the SM predictions.
In high mass resolution decay channels, such as the ones with four leptons (electrons or muons) or
diphoton final states, the mass of the Higgs boson has been measured at the permill precision level.
And, from the search for Higgs boson decays to muons, there are tentalising experimental evidencesfor Yukawa interactions of the Higgs boson to the second generation of fermions. Nevertheless,several Higgs boson decay channels are very challenging experimentally at the LHC. The couplingsof the Higgs boson to the first generation of fermions, at the level expected in the Standard Model,
remain so far out of reach at the LHC.
Within the current precision, a more complex Higgs sector with additional states, althoughsignificantly constrained, is not ruled out. Nor has it been established whether the Higgs boson isan elementary particle or whether it has an internal structure like any other scalar particle observed
before it. Therefore, Higgs physics remains a vivid and intense field of research on the experimental
and theoretical fronts.
Without the Higgs boson, the calculability of the SM would have been spoiled. In particular,
perturbative unitarity [5] would be lost at high energies since the longitudinal W/Z boson scattering
amplitude would grow with the centre-of-mass energy. In addition, the radiative corrections to thegauge boson self-energies would exhibit dangerous logarithmic divergences that would be difficult toreconcile with EW precision data. With the discovery of the Higgs boson, the SM is a spontaneously
broken gauge theory and, as such, it could a priori be consistently extrapolated well above the
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11. Status of Higgs Boson Physics

masses of the W and Z bosons. Hence, formally there is no need for new physics at the EW scale.
However, as the SM Higgs boson is a scalar particle, it has sensitivity to possible new physics
scales. Quite generally, the Higgs boson mass is affected by the presence of heavy particles andit receives large quantum corrections which destabilise the weak scale barring a large fine-tuningof unrelated parameters. This is known as the Higgs naturalness or hierarchy problem [6], and it
has been the prime argument for expecting new physics right at the TeV scale. To remedy to his
unsatisfactory feature, theoretically motivated paradigms have been explored for several decades,such as a new fermion-boson symmetry called supersymmetry (SUSY) [7] (for recent reviews, see
Refs. [8, 9]), or the existence of strong interactions at a scale of the order of a TeV from which
the Higgs boson would emerge as a composite state [10] (see Refs. [11, 12] for recent reviews).
Alternatively, new agents stabilising the weak scale could also be light but elusive, like in models ofneutral naturalness [13,14]. And it was recently appreciated [15,16] that the cosmological evolutionof the Universe could drive the Higgs boson mass to a value much smaller than the cutoff of thetheory, alleviating the hierarchy problem without the need for TeV scale new physics, even though
there might still be interesting and spectacular signatures [15, 17]. This new approach spurs achange in perspective invoking our Universe as part of a multiverse that should be treated as aquantum statistical system [18].
The Higgs boson is special and, in the eleven years since its discovery, it became a powerfultool to explore the manifestations of the SM and to probe the physics landscape beyond it.
This review is organised as follows. Section 11.2 is a theoretical introduction to the SM Higgs
boson, its properties, production mechanisms and decay rates. The experimental measurements aredescribed in Section 11.3. In Section 11.3.6, the combination of the main Higgs boson production
and decay channels is presented. In Section 11.4, measurements of the main quantum numbers and
CP properties of the Higgs boson are reported and the bounds on its total width are discussed.
In Section 11.5, a general theoretical framework to describe the deviations of the Higgs boson
couplings from the SM predictions is introduced and the experimental measurements of these Higgs
couplings are reviewed. Measurements of differential cross sections are also outlined. Section 11.6
presents, in detail, some interesting models with an extended Higgs sector, addressing the hierarchy
problem or not, and considers their experimental signatures. Section 11.7 provides a short summary
and a brief outlook.

11.2 The Standard Model and the mechanism of electroweak symmetry breaking
In the SM [3], electroweak symmetry breaking [4] is responsible for generating a mass for the W
and Z gauge bosons rendering the weak interactions short ranged. The SM scalar potential reads:
V (Φ) = m2 Φ† Φ + λ(Φ† Φ)2(11.1)

with the Higgs field Φ being a self-interacting SU(2)L complex doublet (four real degrees of freedom)with weak hypercharge Y =1 (the hypercharge is normalised such that Q = T3L + Y /2, Q being theelectric charge and T3L the eigenvalue of the diagonal generator of SU(2)L ):
√ + !
1
2φ
Φ= √
(11.2)
00 ,2 φ + ia
where φ0 and a0 are the CP -even and CP -odd neutral components, and φ+ is the complex charged
component of the Higgs doublet, respectively. V (Φ) is the most general renormalisable scalarpotential invariant under SU(2)L × U(1)Y . If the quadratic term is negative, the neutral componentof the scalar doublet acquires a non-zero (real) vacuum expectation value (VEV)
1 0hΦi = √,
2 v!

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(11.3)

4

11. Status of Higgs Boson Physics

with φ0 = H + hφ0 i and hφ0 i ≡ v, inducing the spontaneous breaking of the SM gauge symmetry
SU(3)C × SU(2)L × U(1)Y into SU(3)C × U(1)em . The global minimum of the theory defines theground state, and spontaneous symmetry breaking implies that there is a (global and/or local)
symmetry of the system that is not respected by the ground state. From the four generators of theSU(2)L ×U(1)Y SM gauge group, three are spontaneously broken, i.e., they do not leave the groundstate invariant. This breaking implies the existence of three massless Goldstone bosons identified
with three of the four Higgs field degrees of freedom. The Higgs field couples to the Wµ and Bµgauge fields associated with the SU(2)L × U(1)Y local symmetry through the covariant derivative
appearing in the kinetic term of the Higgs Lagrangian,LHiggs = (Dµ Φ)† (Dµ Φ) − V (Φ) ,(11.4)

where Dµ Φ = (∂µ + igσ a Wµa /2 + ig 0 Y Bµ /2)Φ, g and g 0 are the SU(2)L and U(1)Y gauge couplings,
respectively, and σ a , a = 1, 2, 3 are the usual Pauli matrices. As a result, the neutral and thetwo charged massless Goldstone degrees of freedom mix with the gauge fields corresponding to
the broken generators of SU(2)L × U(1)Y and become, in the unitarity gauge, the longitudinalcomponents of the Z and W physical gauge bosons, respectively. The Z and W gauge bosons
acquire masses,
g2v2(g 02 + g 2 )v 2
m2W =, m2Z =.
(11.5)
4
4
The fourth generator remains unbroken since it is the one associated to the conserved U(1)emgauge symmetry, and its corresponding gauge field, the photon, remains massless. Similarly, theeight color gauge bosons, the gluons, corresponding to the conserved SU(3)C gauge symmetry with
8 unbroken generators, also remain massless (though confined inside hadrons and mesons as theresult of the asymptotic freedom behaviour of Quantum ChromoDynamics (QCD)). Hence, fromthe initial four degrees of freedom of the Higgs field, two are absorbed by the W ± gauge bosons,one by the Z gauge boson, and there is one remaining degree of freedom, H, that is the physical
Higgs boson — a new scalar particle first imagined by P. Higgs [4]. The Higgs boson is neutral
under the electromagnetic interactions and transforms as a singlet under SU(3)C and hence does
not couple at tree level to the massless photons and gluons.
The fermions of the SM acquire a mass through renormalisable and gauge invariant interactions
between the Higgs field and the fermions: the Yukawa interactions,
LYukawa = −ĥdij q̄Li Φ dRj − ĥuij q̄Li Φ̃uRj − ĥlij ¯lLi Φ eRj + h.c.,(11.6)

which respect the symmetries of the SM but generate fermion masses once EWSB occurs. In the
Lagrangian above, Φ̃ = iσ2 Φ∗ and qL (lL ) and uR , dR (eR ) are the quark (lepton) SU(2)L doubletsand singlets, respectively, while in each term, ĥfij , f = u, d, l is parametrised by a 3 × 3 matrix infamily space. The mass term for neutrinos is omitted, but could be added in an analogous mannerto the up-type quarks when right-handed neutrinos are supplementing the SM particle content(neutrinos can also acquire Majorana masses via non-renormalisable dimension-5 interactions with
the Higgs field [19]). Once the Higgs field acquires a VEV, and after rotation to the fermion mass
eigenstate basis that also diagonalises the Higgs-fermion interactions, ĥfij → hfi δij (the diagonal√
Yukawa coupling hfi is often denoted as yfi ), all fermions acquire a mass given by mfi = hfi v/ 2.
The indices i, j = 1, 2, 3 refer to the three families in the up-quark, down-quark or charged lepton
sectors. Remarkably, if the Yukawa interactions Eq. (11.6) are indeed fully responsible for thefermion masses, the Higgs interactions do not mediate flavour changing neutral currents at treelevel. It should be further noted that the EWSB mechanism provides no additional insight on
possible underlying reasons for the large variety of mass values of the fermions, often referred to as
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11. Status of Higgs Boson Physics

5

the flavour hierarchy. The fermion masses, accounting for a large number of the free parameters of
the SM, are simply translated into Yukawa couplings.
11.2.1 The SM Higgs boson mass, couplings and quantum numbers√
The SM Higgs boson is a CP -even scalar of spin 0. Its mass is given by mH = 2λ√v, where λ isthe self-coupling parameter in V (Φ). The expectation value of the Higgs field, v = ( 2GF )−1/2 ≈246 GeV, is fixed by the Fermi coupling GF , which is determined with a precision of 0.6 ppm frommuon decay measurements [20]. The quartic coupling λ is a free parameter in the SM, and hence,
there is no a priori prediction for the Higgs mass. Moreover the sign of the quadratic coupling,m2 = −λv 2 , in the Higgs field potential V (Φ) has to be negative for the EW symmetry breaking totake place, but there is no a priori understanding of what decides of this sign. The experimentallymeasured Higgs boson mass, mH ' 125 GeV [20], implies that λ ' 0.13 and |m| ' 88.4 GeV.
The Higgs boson couplings to the fundamental particles are set by their masses. This is a new
type of interaction; very weak for light particles, such as up and down quarks, and electrons, but
strong for heavy particles such as the W and Z bosons and the top quark. More precisely, the SM
Higgs couplings to fundamental fermions are linearly proportional to the fermion masses, whereas
the couplings to bosons are proportional to the square of the boson masses. The SM Higgs boson
couplings to gauge bosons and fermions, as well as the Higgs boson self coupling, are summarisedin the following Lagrangian:L = −gHf f¯f¯f H +gHHH 3 gHHHH 4
gHHV V 2
H +H + δV Vµ V µ gHV V H +
H
6
24
2




(11.7)

withgHf f¯ =

mf
2m2V
2m2
3m2H
3m2
, gHV V =, gHHV V = 2V , gHHH =, gHHHH = 2H ,
v
v
v
v
v

(11.8)

where V = W ± or Z and δW = 1, δZ = 1/2. As a result, the dominant mechanisms for Higgs
boson production and decay involve the coupling of H to W , Z and/or the third generation quarks
and leptons. The Higgs boson coupling to gluons [21, 22] is induced at leading order by a one-loop
process in which H couples to a virtual tt̄ pair (with minor contributions from the other lighter
quarks). Likewise, the Higgs boson coupling to photons is also generated via loops, although inthis case the one-loop graph with a virtual W + W − pair provides the dominant contribution [23]and it is interfering destructively with the smaller contribution involving a virtual tt̄ pair (as such,
the Higgs coupling to photons is sensitive to the relative phase of the interactions between bosons
and fermions).
11.2.2 The SM custodial symmetry
The SM Higgs Lagrangian, LHiggs + LYukawa of Eq. (11.4) and Eq. (11.6), is, by construction,
SU(2)L × U(1)Y gauge invariant, but it also has an approximate global symmetry. In the limit
g 0 → 0 and hf → 0, a global SU(2)R symmetry emerges. This symmetry is preserved for nonvanishing Yukawa couplings provided ĥu = ĥd . Once the Higgs field acquires a VEV, both theSU(2)L and SU(2)R symmetry groups are broken but the diagonal subgroup SU(2)L+R remains
unbroken and it is this subgroup that defines the custodial symmetry of the SM [24].
In the limit g 0 → 0, the W ± and Z gauge bosons have equal mass and form a triplet of theSU(2)L+R unbroken global symmetry. Using the expressions for the W and Z gauge boson masses
in term of the gauge couplings, one obtains at tree level
m2W
g2
m2W
2
= 1.
=
≡
cos
θ
i.e.
ρ
≡
W
g 02 + g 2
m2Z
m2Z cos2 θW
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(11.9)

6

11. Status of Higgs Boson Physics

The custodial symmetry protects the above relation from large radiative corrections. All corrections to the ρ parameter are therefore proportional to terms that break the custodial symmetry. For instance, radiative corrections √involving the Higgs boson are proportional to sin2 θW ,2222δρ = −11GF mZ sin θW log(mH /mZ )/(24 2π 2 ), and vanish in the limit g 0 → 0. Since mt 6= mb ,there are also relevant radiative corrections generated by massive fermions. They are proportional
to m2t + m2b − 2(m2t m2b ) log(m2t /m2b )/(m2t − m2b ) and would indeed vanish for mt = mb [25].

11.2.3 Stability of the Higgs potential
The discovery of the Higgs boson with mH ≈ 125 GeV has far reaching consequences within the
SM framework. In particular, the precise value of mH determines the value of the quartic coupling
λ at the electroweak scale and makes it possible to study its behavior up to high energy scales. A
larger value of mH would have implied that the self coupling λ would become non-perturbative atsome scale Λ that could be well below the Planck scale [26].
However, for the value of Higgs boson mass experimentally measured, the EW vacuum of
the Higgs potential is most likely metastable [27]. The high-energy evolution of λ shows that it
becomes negative at energies Λ = O(1011 ) GeV (even though λ could remain positive till higher
energy, maybe all the way to the Planck scale, if the top quark mass exceeds its current measured
value by 3σ). When this occurs, the SM Higgs potential develops an instability and the longterm existence of the EW vacuum is challenged. This behaviour may call for new physics at anintermediate scale before the instability develops, i.e., below MP lanck , even though new physics at
MP lanck could influence the stability of the EW vacuum and possibly modify this conclusion [28].
The consequences of the instability of the EW vacuum on high-scale inflation have been discussed inRef. [29]. It was also noticed that Higgs field fluctuations during inflation could seed the formationof primordial black holes, possibly making up the Dark Matter relic abundance [30] or they could
produce a stochastic background of gravitational waves with characteristic structures [31], offeringa probe of the EW vacuum near criticality.
The lifetime of the EW metastable vacuum is determined by the rate of quantum tunnellingfrom this vacuum into the true vacuum of the theory (for the most recent computation of theEW vacuum lifetime within the SM, see Ref. [32]). Within the SM, the running of the Higgs self
coupling slows down at high energies with a cancellation of its β-function at energies just one totwo orders of magnitude below the Planck scale [33]. This slow evolution of the quartic couplingis responsible for saving the EW vacuum from premature collapse. It might also help the Higgs
boson to play the role of an inflaton [34] (see, however, Ref. [35] for potential issues with thisHiggs-boson-as-an-inflaton idea).
11.2.4 Higgs boson production and decay mechanisms
Comprehensive reviews of the SM Higgs boson properties and phenomenology, with an emphasison the impact of loop corrections to the Higgs boson decay rates and cross sections, can be foundin Refs. [36–40]. The main results are summarised here.

11.2.4.1 Production mechanisms at hadron colliders
The main production mechanisms at the Tevatron collider and the LHC are gluon fusion (ggF),
weak-boson fusion (VBF), associated production with a gauge boson (V H), and associated production with a tt pair (tt̄H) or with a single top quark (tHq). Figure 11.1 depicts representative
diagrams for these dominant Higgs boson production processes.
The state-of-the-art of the theoretical calculations in the main different production channels issummarised in Table 11.1.
√
The cross sections for the production of a SM Higgs boson as a function of s, the center of massenergy, for pp collisions, including bands indicating the theoretical uncertainties, are summarised
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225
226
227
228

The main production mechanisms at the Tevatron collider and the LHC are gluon fusion (ggF),
weak-boson fusion (VBF), associated production with a gauge boson (V H), and associated production with a pair of tt quarks (tt̄H) or with a single top quark (tHq). Figure ‘higgs:fig:HiggsProd’ ??
7
11. Status of Higgs Boson Physics
depicts representative diagrams for these dominant Higgs boson production processes.
W, Z

H

t

q

g

33 33

q!

q

g

!!

q!

H

W, Z

q !!!

q

(b)

(a)

W, Z
W, Z

11.11.
StatusStatus
of of
Higgs
Higgs
Boson
Boson
Physics
Physics
g

H

g

H
(c)
tt, b

11.3.611.3.6
Higgs
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1234 1234

Figure 11.1: Main leading order Feynman diagrams contributing to the Higgs boson productionin (a) gluon fusion, (b) Vector-boson
fusion,t, bbt, bt,t, bt, (c)b Higgs-strahlung (or associated production with agauge boson at tree level from a quark-quark interaction), (d) associated production with a gauge(h)(i)
boson (at loop level from a gluon-gluon
interaction), (e) associatedproduction with a pair of top
quarks (there is a similar diagram for the associated production with a pair of bottom quarks),
FigureFigure11.5:
11.5:
FeynmanFeynmandiagrams
diagrams
contributing
contributing
at atleading
leading
order
order
to to
Higgs
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Figure 11.1:
Main
leading
orderdiagrams
contributing
to Higgs
theboson
singleboson pro(f-g) productionin association
withaFeynmansingletop
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throughthrough(a)(a)
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duction in (a) gluon fusion, (b) Vector-boson fusion, (c) Higgs-strahlung (or associated production
with a gauge boson at tree level from a quark-quark interaction), (d) associated production with a
Thegauge
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229
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1252 1252
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1255 1255‘ATLAS:2021fet’‘ATLAS:2021fet’?,‘Sirunyan:2018two’?,‘Sirunyan:2018two’?,‘CMS:2020gxr’?,‘ATLAS:2020jgy’?,‘ATLAS:2020jgy’?,‘CMS:2021ssj’?,‘CMS:2021ssj’?,‘CMS:2020tkr’?,‘CMS:2020tkr’
?, ?,
Table
11.2
summarises
the Higgs boson ?,‘CMS:2020gxr’
production
cross
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uncertainties
for√1256 1256‘ATLAS:2021jki’‘ATLAS:2021jki’?] and?] andthethereferencesreferences
withinwithinthethecombination
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publishedpublishedby bythethecollaboracollaboraa Higgs
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for s = 7,?,8,‘Sirunyan:2018two’
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[‘Aad:2019uzh’[‘Aad:2019uzh’?, ‘ATLAS:2021fet’?, ‘ATLAS:2021fet’?, ‘Sirunyan:2018two’?]. ?].
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arearethethemost
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1259 1259
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sensitive
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1260 1260

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have
have
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sectionis theprocess,gg→ H the+ theX,mediated
bymodetheexchangeofvirtual,heavy
1262 1262
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VBF
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productionmode
is searchedis searchedforaforseparately
separately
pro-pro- top
1263
vidingvidingsensitivity
sensitivity
to fromtheto thecoupling
coupling
involving
involvingtwotwovectorvectorbosonsbosonsandandtwotwoHiggs
Higgs
bosonsbosons
HHVV
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which
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quark1263[45].
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lighterquarkspropagatingin theloop
aresuppressed
proportionally2 . 1264
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and
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2V
2V
studied in detail. Including the full dependence on the (top, bottom, charm) quark and Higgs boson
performed
performed
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CMS
[‘CMS:2020tkr’[‘CMS:2020tkr’?] in?] thein thebb““:
bb““:
masses, the cross section has been calculated at the next-to-leading order (NLO) in αs [46,47]. To avery good approximation,≠1.3
theleading
top-quarkcontribution
be3.1
evaluated≠1.3<
Ÿ<2VŸ2V< 3.5< 3.5(observed),(observed),
≠0.9
≠0.9
< Ÿ<2Vcan
Ÿ2V
< 3.1
<
(expected)(expected)in the limit mt → ∞by matching the SM to an effective theory. The gluon-fusion amplitude is then evaluated from an
th August,
DRAFT
DRAFT
11th11August,20232023
3:24pm3:24pmNot Not
for public
for publicdistribution
distribution

31st May, 2024

11. Status of Higgs Boson Physics

8

Table 11.1: State-of-the-art of the theoretical calculations in the main Higgs boson production
channels in the SM, and, when publicly available, the major MC tools used in the simulations.
Furthermore, all the Higgs-boson production modes have been interfaced with parton-shower event
generators at NLO QCD like Poweg-Box, MG5_aMC@NLO or Sherpa (the entries “—” indicate cases
when the results are implemented in codes that are not yet public). For ggF and V H NNLO
matched simulations now also exist. Differential NNLO QCD results exist for tt̄H [41] (though theexact 2-loop virtual corrections are still missing) and have been implemented in MATRIX [42].

O EW)

L
CD + N

3LO Q

LHC HIGGS XS WG 2016

Differential:
NNLO QCD—NLO QCD + EW
(HAWK)
M(H)= 125 GeV(N
pp → H

VH
Inclusive:
N3LO QCD(n3loxs)
NNLO QCD(VH@NNLO)
Differential:
NNLO QCD—NLO QCD + EW
(HAWK)

Branching Ratioσ(pp → H+X) [pb]

102

VBF
Inclusive:
N3LO QCD
proVBFHH (NNp → qqLO QCDW)+ NLO Ebb

LO EW)QCD + NH (NNLO
EW)
pp → WLO
N+
in 4FS)QCD
LO QCD
H (NNLO
N
Z
,
→
S
5F
pp
D in

WW
gg
ττ

p

1

Differential:
NLO QCD+EW(MG5_aMC@NLO)

1

10-1

10

tt̄H
Inclusive:
NNLO QCD—LHC HIGGS XS WG 2016

ggF
Inclusive:
N3LO QCD + NLO EW(iHixs)N3LO QCD
ggHiggs
Differential:
NNLO+N3LL QCD(Radish+NNLOJET)
N3LO+N3LL0 QCD(TROLL)

-2

10

cc
ZZ

LO QC

H (NN
pp → bb

CD +

−1

10

pp →

ttH

Q
(NLO

pp →

NLO

EW)

ch +

LO
tH (N

, tQCD

γγ
s-ch)

10-3

10−2

Zγ

µµ
-4

6

7

8

9

10 11 12 13 14 15
s [TeV]10
120 121 122 123 124 125 126 127 128 129 130

MH [GeV]Figure 11.2: (Left) The SM Higgs boson production cross sections as a function of the center√of mass energy, s, for pp collisions [43]. The VBF process is indicated here as qqH. (Right)
The branching ratios for the main decays of the SM Higgs boson near mH = 125 GeV [39, 40]. The
theoretical uncertainties are indicated as bands.
effective Lagrangian containing a local HGaµν Ga µν operator [21, 22]. In this approximation, thecross section is known at next-to-next-to-next-to-leading order in αs expansion (N3LO QCD) [48].
The validity of the effective theory with infinite mt is greatly enhanced by rescaling the result by theLO /σ LO
exact LO result: σ = (σmmt =∞ ) × σmt =∞ [40]. The large top-quark mass approximation, aftert
31st May, 2024

11. Status of Higgs Boson Physics

9

Table 11.2: The SM Higgs boson production cross sections for mH =√125 GeV in pp collisions (pp̄ collisions at s = 1.96 TeV for the Tevatron),√
as a function of the center of mass energy, s. The predictions for the LHC
energies are taken from Refs. [37–40, 43], the ones for the Tevatron energy
are the ones used in Ref. [44]. The predictions for the ggF channel at the
LHC include the latest N3LO QCD + NLO EW results. The uncertainties
are estimated assuming no correlation between αS and PDF uncertainties.
The uncertainties on the total cross sections are dominated by the ones on
the gluon fusion process.
√

s
(TeV)

Production cross section (in pb) for mH = 125 GeV
ggF

1.96

WH

ZH

tt̄H

total

+8%
+8%
+8%
+10%
+15%
0.95+17%−17% 0.065−7% 0.13−8% 0.079−8% 0.004−10% 1.23−15%

+5%
+5.6%
+3.1%
+2.2%
+2.2%
16.9+5.5%−7.6% 1.24−2.2% 0.58−2.3% 0.34−3.0% 0.09−10.2% 19.1−7%

7

+2.1%
+2.1%
+3.4%
+5.9%
+5%
21.4+5.4%−7.6% 1.60−2.1% 0.70−2.2% 0.42−2.9% 0.13−10.1% 24.2−7%

8
13
13.6
14

VBF

+5%
+6.8%
+4.1%
+2.0%
+2.1%
48.6+5.6%−7.4% 3.78−2.1% 1.37−2.0% 0.88−3.5% 0.50−9.9% 55.1−7%

+5%
+6.9%
+4.0%
+1.8%
+2.1%
52.2+5.6%−7.4% 4.1−1.5% 1.46−1.9% 0.95−3.6% 0.57−9.9% 59.2−7%

+2.1%
+1.8%
+4.1%
+6.9%
+5%
54.7+5.6%−7.4% 4.28−2.1% 1.51−1.9% 0.99−3.7% 0.61−9.8% 62.1−7%

this rescaling of the cross section, yields a next-to-next-to-leading order (NNLO) QCD result thathas been established to be at the percent level accuracy [49]. Further progress was made to include
full top mass dependence at NNLO QCD [50]. And the bottom and light quark contributions to
the Higgs production have been reassessed in Refs. [51–53].
The LO contribution and NLO QCD corrections [54] amount to about 80% of the total N3LO
QCD cross section. The NNLO QCD corrections [55] further enhance the cross section by approximately 30% of the LO plus NLO result (at µf = µr = mH /2). Electroweak radiative corrections
have been computed at NLO and increase the LO cross section by about 5% for mH ' 125 GeV [56].
Mixed QCD-EW corrections are now being investigated with encouraging results on the computation of the exact 3-loop amplitude [57] complementing the results obtained in either limit ofheavy [58] or massless [59] gauge bosons. The mixed QCD-EW corrections still have to be evaluated at large pT .
At N3LO QCD, the perturbation series is rather stable with a mere enhancement of 3% of thetotal cross section, with a central value quite insensitive to threshold resummation effects with thescale choice mentioned above (µf = µr = mH /2) [40, 48, 60, 61]. At the LHC with a center-of-massenergy of 13 TeV, the most up-to-date value for the production cross section of a 125 GeV Higgs
boson amounts to [40]+2.2 (4.6%)

N3LO
σggF
= 48.6 −3.3 (6.7%) (theory) ± 1.6 (3.2%) (PDF + αs ) pb.

(11.10)This cross-section was first computed in terms of an expansion around the production thresholdof the Higgs boson. This approximation was overcome in Ref. [61]. The PDF uncertainty of order
1-2% quoted above has been questioned as the first global analysis of PDFs at approximate N3LO
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10

11. Status of Higgs Boson Physics

QCD was presented, suggesting an unexpected decrease of the cross-section central value by morethan 5% [62].
Besides considering the inclusive Higgs boson production cross section at the LHC, it is important to study differential distributions in order to probe the properties of the Higgs boson ina detailed way. The Higgs boson rapidity distribution has been computed at the N3LO QCD
order in Ref. [63]. And fully differential N3LO QCD predictions for Higgs production in gluon
fusion have been obtained by combining N3LO QCD predictions for Higgs rapidity distribution
with NNLO QCD predictions for H+jet [64]. A more exclusive account of Higgs boson productionis also required because experimental analyses often impose cuts on the final states in order toimprove the signal-to-background ratio. Using soft-collinear effective theory, large fiducial power
corrections induced by fiducial cuts have been resummed at N3LO+N3LL0 QCD accuracy, i.e. at
next-to-next-to-next-leading-log, incorporating the complete O(αs3 ) singular structure for qT → 0
allowing one to consistently match to N3LO QCD [65]. This is the most accurate result that can bedirectly compared with fiducial measurements. Different fiducial cuts are explored to suppress thesefiducial effects. In addition, progress has been made to improve the calculation of the Higgs boson
production cross section with a jet veto (the “0-jet bin” or in the presence of a veto bounding thetransverse momentum of the hardest accompanying jet) [66], reaching NNLL accuracy matched to
N3LO QCD. These accurate predictions for the jet-veto cross section are required, e.g., to suppress
the tt̄ background in the H → W W channel [67].
ii. Vector boson fusion production mechanism
The SM Higgs boson production mode with the second-largest cross section at the LHC is vectorboson fusion. At the Tevatron collider, VBF also occurred, but for mH = 125 GeV had a smaller
cross section than Higgs boson production in association with a W or Z boson. Higgs boson production via VBF, qq → qqH, proceeds by the scattering of two (anti-)quarks, mediated by t- or
u-channel exchange of a W or Z boson, with the Higgs boson radiated off the weak-boson propagator. The scattered quarks give rise to two hard jets in the forward and backward regions of thedetector with a large rapidity gap [68]. Because of the color-singlet nature of the weak-gauge boson
exchange, gluon radiation from the central-rapidity regions is strongly suppressed. These characteristic features of VBF processes can be exploited to distinguish them from overwhelming QCD
backgrounds, including gluon-fusion induced Higgs boson + 2 jet production, and from s-channel
W H or ZH production with a hadronically decaying weak gauge boson. After the application of
specific selection cuts, the VBF channel provides a clean environment, not only for the Higgs boson
searches originally performed, but also for the subsequent determination of Higgs boson couplingsat the LHC.
The cross-section is known at N3LO QCD at the inclusive level [69] and at NNLO enforcing
the VBF cuts [70] with a residual uncertainty of the order of few permill. However, this result
is obtained in the DIS/factorized approximation [71] where the fusing gauge bosons are emitted
from the two quark legs independently. While, the exact NNLO QCD VBF calculation will remain
out-of-reach in the near future, the leading non-factorisable contributions with two forward jets
have been estimated [72] and the impact of non-factorizable effects have been studied in Ref. [73].
They give some corrections, also of the order of few permill, to inclusive quantities, but they are
an order of magnitude larger for differential observables. Overall, the residual uncertainty is of theorder of a few percent but is quite sensitive to the tagging jet cuts and jet radius modelling [74].
Extensive studies on VBF at fixed order and with parton shower matched computations can befound in Ref. [75]. In addition, EW corrections have been included and the VBF process is known
at NLO QCD+EW order for some time [76, 77].
31st May, 2024

1111. Status of Higgs Boson Physics

iii. W H and ZH associated production mechanism
The next most relevant Higgs boson production mechanisms are associated production with W and
Z gauge bosons. The cross sections for the associated production processes, pp → V H + X, with
V = W ± , Z receive contributions at NLO QCD given by NLO QCD corrections to the Drell–Yancross section [78,79] and from NLO EW corrections. The latter, unlike the QCD corrections, do notrespect the factorisation into Drell–Yan production since there are irreducible box contributions
already at one loop [76,80]. At NNLO QCD, the Drell–Yan-like corrections to W H production also
give the bulk of the corrections to ZH production [81]. For ZH production there are, however,gluon-gluon induced contributions that do not involve a virtual Z gauge boson but are such that
the Z gauge boson and H boson couple to gluons via top-quark loops [82], see diagram (d) in
Fig. 11.1. NLO QCD virtual corrections to the partonic cross section for gg → ZH, in the highenergy and large top mass limits are available in Refs. [83]. In addition, W H and ZH production
receive non Drell–Yan-like corrections in the q q̄ 0 and q q̄ initiated channels, respectively, at the
NNLO level in QCD, where the Higgs boson is radiated off top-quark loops [84]. The full QCD
corrections up to NNLO order, the NLO EW corrections and the NLO corrections to the gluon-gluon
channel are available in VH@NNLO [85]. NNLO QCD corrections to pp → W H+jet are important for
signal modelling. NLO corrections to cross section inclusive in the number of jets show excellent
convergence while NNLO QCD corrections to exclusive single jet cross section are much moresignificant [86].
As neither the Higgs boson nor the weak gauge bosons are stable particles, their decays also
have to be taken into account. Providing full kinematical information for the decay products
can furthermore help in the suppression of large QCD backgrounds. Differential distributions forthe processes pp → W H → ν̄` `H and pp → ZH → `+ `− H/ν` ν̄` H, including NLO QCD and
EW corrections, have been presented in Ref. [87]. The NNLO QCD corrections to differential
observables for W H production at the LHC, including the leptonic decays of the W boson andthe decay of the Higgs boson into a bb̄ pair, are presented in Ref. [88]. Calculations at the samelevel, including also the ZH process have been performed [89]. The W H production mode has
also been matched to a parton shower at NNLO QCD accuracy [90]. Full NNLO QCD results forboth the production and decay are available [91] and show a large impact of radiation from thefinal-state bottoms. The W H and ZH production modes, especially in the boosted regime, provide
a relatively clean environment for studying the decay of the Higgs boson into bottom quarks [92].
Bottom mass effects have been computed at NNLO [93, 94] and tend to increase the rates by 6-7%.
The inclusive cross section for associated Higgs boson production with a massive gauge bosonis recently known up to N3LO QCD too [95].
iv. Higgs boson production in association with tt
Higgs boson radiation off top quarks, pp → tt̄H, provides a direct probe of the top-Higgs Yukawa
coupling. The LO cross section for this production process was computed in Ref. [96]. Later, the
NLO QCD [97] and NLO EW corrections [98] were evaluated yielding a moderate increase in the
total cross section of at most 20%, but significantly reducing the scale dependence of the inclusive
cross section. The EW corrections can be enhanced by large electroweak Sudakov logarithms inparticular in the boosted regime often used in the phenomenological analyses [99]. The resummationof soft gluon contributions close to the partonic kinematical threshold are considered in Refs. [100]to reach a result at NLO+NNLL QCD order. Full off-shell calculations with decaying top quarks
are computed at NLO QCD [101] and NLO QCD + EW [102] order, respectively. The fixed-order
NLO QCD calculation has been interfaced with the standard parton shower Monte-Carlo generators
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11. Status of Higgs Boson Physics

12

in Refs. [103], allowing an accurate description of the tt̄H signal, from the energy scale of the hard
scattering to the hadronisation energy scale. These programs provide the most flexible tools to date
for the computation of differential distributions, including experimental selection cuts and vetoeson the final-state particles and their decay products. The exploitation of this tt̄H channel requires,
however, a proper description of the background, in particular tt̄bb̄, which exhibits a huge k-factor1
enhancement from shower effects, see Ref. [40] for a detailed discussion. While the H → bb̄ decay
mode was first considered, the focus has been broadened and other modes have been studied too,in particular the multilepton channel and other backgrounds such as tt̄W and tt̄Z have become
relevant and intensively analyzed.
The total theoretical uncertainties, estimated by combining the ones from factorisation andrenormalisation scales, strong gauge coupling, and parton distributions, amount to 10–15% of
the corresponding inclusive cross section. To match the experimental precision envisioned at theend of HL-LHC, NNLO QCD predictions are required. Using the qT subtraction formalism for
tt̄H production, Ref. [104] presented the first quantitative results at NNLO. The calculation isaccurate at NLO in QCD and agrees with the results obtained using the conventional subtraction
methods. The NNLO corrections are computed for the flavour off-diagonal partonic channels but
their contribution turn out to be at the permill level. The results for the diagonal channels havebeen obtained in Ref. [41]. The two-loop amplitudes are not yet known, but they have been reliably
evaluated by using a soft Higgs boson approximation. At the 13 TeV centre-of-mass energy, the
NNLO corrections increase the NLO result for the total cross section by about 4% and lead to asignificant reduction of perturbative uncertainties. Also recently, the fragmentation and splitting
functions for the production of a Higgs boson have been computed at order yt2 αs and they canbe used to compute differential cross sections with arbitrary top-quark and Higgs-boson masses
directly from the results in the massless limit [105].
v. Other single Higgs boson production mechanisms at the LHC
The Higgs boson production in association with a single top quark, though subdominant, can bringvaluable information, in particular regarding the sign of the top Yukawa coupling. This is due toan almost totally destructive interference between two large contributions, one where the Higgs
boson couples to a space-like W boson and the other where it couples to the top quark. This
process has been computed at NLO QCD in a five-flavour scheme [106] and amounts to about 90 fb√
at s = 14 TeV (with the opposite sign of the top Yukawa coupling, the cross section increases
by one order of magnitude while the cross section for associated production with a pair of top
quarks is unaffected). Recently, the tHj (and tZj) process has been computed at NLO QCD+EW
accuracy [107]. The NLO EW correction is found to be within the NLO QCD theory uncertainties
if the 4 vs 5 flavour scheme uncertainty is taken into account. The EW corrections reduce the total
cross section by 3-4%.
The Higgs boson production in association with a pair of bottom quarks (bb̄H) has been computed at the N3LO QCD order in the 5-flavour scheme [108], while the production with one/twob-jets, defined by specific kinematic cuts, is known respectively at NLO QCD in the 4-flavour
scheme and at NNLO QCD in the 5-flavour scheme [109–111]. The coupling of the Higgs boson toa b-quark is suppressed in the SM by the bottom-quark mass over the Higgs VEV, mb /v, implyingthat associated production of a SM Higgs boson with b-quarks is small at the LHC. Yet, at highenergy, large logarithms are present and need to be resummed, leading to an enhancement of the√
inclusive cross section. At s = 14 TeV, the bbH cross section can be as large as 550 fb, still two orders of magnitude below the ggF production cross section. Furthermore, the overwhelming ZH and1

the k-factor is defined as the ratio of a physical quantity with and without radiative corrections included.
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11. Status of Higgs Boson Physics

VBF backgrounds (at the inclusive but also differential levels) make it challenging to extract genuine bottom Yukawa signal in a traditional cut-based analysis [112] but innovative machine-learningtechniques are a promising avenue to obtain information complementary to the ones extracted fromgg → h → bb̄, in particular for what concerns the phase of the bottom Yukawa coupling [113]. In a
two Higgs doublet model or a SUSY model, which will be discussed in Section 11.6, this couplingis proportional to the ratio of neutral Higgs boson vacuum expectation values, tan β, and can besignificantly enhanced for large values of this ratio. Consequently, the bbH mode can even become
the dominant production process for the Higgs boson, unlike in the SM.
The Higgs boson production in association with charm quarks is also known at NNLO QCD√
and its cross section is approximately 85 fb at s = 13 TeV [40].
vi. Double Higgs boson production at the LHC
The main interest in the double Higgs boson production is that it can provide invaluable informationon the Higgs potential. In particular, it gives access to the Higgs trilinear self coupling. The
dominant production is via gluon fusion gg → HH (slightly more than 31 fb at 13 TeV) andit accounts for more than 90% of the total inclusive cross-section, the sub-leading production
mechanisms are VBF HHjj (around 1.7 fb at 13 TeV), HHW (0.50 fb), HHZ (0.36 fb) and tt̄HH(0.8 fb). The fixed order QCD corrections, computed in the infinite top mass limit, are large,
typically doubling the cross section from LO to NLO QCD [114], further enhancing it by 20%
and reducing the scale uncertainty by a factor 2-3 from NLO to NNLO QCD [115], with a milder
increase of order 3% at N3LO [116] to finally reach at 13 TeV+0.66%σ(gg → HH)N3LO
ggF,mt →∞ = 31.31 −2.8% fb.

(11.11)

Recently, the complete NLO corrections with all top quark mass effects also became available
numerically [117], intriguingly revealing a k-factor much less flat than predicted in the large top
mass approximations. The non-trivial dependence of the results on the renormalisation schemeand scale for the top quark mass questions the assessment of the scale uncertainty and would
warrant a proper NNLO computation that will however remain out of reach for quite some time.
At the differential level, the destructive interference between the box and the triangle contributions
complicates the predictions made in the infinite top mass limit for both the HH invariant massand the leading Higgs boson pT distributions. With an inclusive cross section of about 35 fb at√
s = 13 TeV and a difficult signal vs background discrimination, the double Higgs boson production
remains a challenging channel to probe and will greatly benefit from the high-luminosity run of the
LHC and the combination of various decay modes [118]. The double Higgs channel is definitively
a prime target on the Higgs physics agenda and the forthcoming analyses will greatly benefit fromthe solidification of the fixed order predictions and the detailed uncertainty budget estimate thatis underway [119].
11.2.4.2 Production mechanisms at e+ e− colliders
The dominant Higgs boson production cross sections at an e+ e− collider are from the Higgsstrahlung process [21, 120], e+ e− → ZH, and the W W fusion process [121], e+ e− → ν̄e νe W ∗ W ∗ →ν̄e νe H. The cross-section for the Higgs-strahlung process scales as the inverse of the collisioncentre-of-mass squared energy, s, and is predominant at low energies, while the cross-section for
the W W fusion process scales as ln(s/m2H ) and dominates at high energies [122]. The ZZ fusion
mechanism, e+ e− → e+ e− Z ∗ Z ∗ → e+ e− H, also contributes to the Higgs boson production, with across-section suppressed by an order of magnitude with respect to that of W W fusion. The process√e+ e− → tt̄H [123] becomes important for s ≥ 500 GeV. For a more detailed discussion of Higgs
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11. Status of Higgs Boson Physics

boson production properties at lepton colliders, see for example Refs. [124]. Interesting progresshas been made recently [125] to accurately account for beamstrahlung and initial state radiation
using the factorisation approach primarily developed for hadron colliders and this method is being
implemented in Monte Carlo event generators. Further information about Higgs physics at an e+ e−
collider can be found in Ref. [126].
11.2.4.3 SM Higgs boson branching ratios and total width
For the understanding and interpretation of the experimental results, the computation of all
relevant Higgs boson decay widths is essential, including an estimate of their uncertainties and, whenappropriate, the effects of Higgs boson decays into off-shell particles with successive decays into
lighter SM ones. A Higgs boson mass of about 125 GeV allows to explore the Higgs boson couplings
to many SM particles. In particular the dominant decay modes are H → bb̄ and H → W W ∗ ,followed by H → gg, H → τ + τ − , H → cc̄ and H → ZZ ∗ . With much smaller rates follow
the Higgs boson decays into H → γγ, H → γZ and H → µ+ µ− . Since the decays into gluons,
diphotons and Zγ are loop induced, they provide indirect information on the Higgs boson couplings
to W W , ZZ and tt̄ in different combinations. The uncertainties in the branching ratios include themissing higher-order corrections in the theoretical calculations as well as the errors in the SM input
parameters, in particular fermion masses and the QCD gauge coupling, involved in the decay. In thefollowing the state-of-the-art of the theoretical calculations compiled by the LHC Higgs Working
Group [43] will be discussed and the reader is referred to Refs. [37–40, 127] for detail.
The evaluation of the radiative corrections to the fermionic decays of the SM Higgs boson are
implemented in HDECAY [128] at different levels of accuracy. The computations of the H → bb̄ andH → cc̄ decays include the complete massless QCD corrections up to N4LO, with a corresponding
scale dependence of about 0.1% [129]. Both the electroweak corrections to H → bb̄, cc̄ as well as
H → τ + τ − are known at NLO [130] providing predictions with an overall accuracy of about 1–2%
for mH ' 125 GeV.
The loop induced decays of the SM Higgs boson are known fully at NLO and partially beyond
that approximation. For H → gg, the QCD corrections are known up to N3LO in the limit ofheavy top quarks [47, 131] and the uncertainty from the scale dependence is about 3%. For the
H → γγ, the full NLO QCD corrections are available [47, 132] and the three-loop QCD corrections
have also been evaluated [133]. The NLO electroweak corrections to H → gg and H → γγ
have been computed in Ref. [134]. All these corrections are implemented in HDECAY [128]. For
mH ' 125 GeV, the overall impact of known QCD and EW radiative effects turns out to be well
below 1%. In addition, the contribution of the H → γe+ e− decay via virtual photon conversion
has been computed in Ref. [135]. The partial decay width H → Zγ is only implemented at LO in
HDECAY, including the virtual W , top-, bottom-, and τ -loop contributions. The QCD corrections
have been calculated and are at the percent level [136]. The theoretical uncertainty due to unknown
electroweak corrections is estimated to be less than 5%, an accuracy that will be hard to achievein the measurement of this process at the LHC.
The decays H → W W/ZZ → 4f can be simulated with the Prophecy4f Monte-Carlo generator [137] that includes complete NLO QCD and EW corrections for Higgs decays into any possible
four-fermion final state. All calculations are consistently performed with off-shell gauge bosons,
without any on-shell approximation. For the SM Higgs boson, the missing higher-order corrections
are estimated to be roughly 0.5%. Such uncertainties will have to be combined with the parametric
uncertainties, in particular those associated to the bottom-quark mass and the strong gauge coupling, to arrive at the full theory uncertainty. A detailed treatment of the differential distributions
for a Higgs boson decay into four charged leptons in the final state is discussed in Refs. [39, 138].
The total width of a 125 GeV SM Higgs boson is ΓH = 4.07 × 10−3 GeV, with a relative uncer31st May, 2024

11. Status of Higgs Boson Physics

15

Table 11.3: The branching ratios and the relative uncertainty for a SM
Higgs boson with mH = 125 GeV [39, 40].
Decay channel
H → γγH → ZZ

H → W +W −H → τ +τ −H → bb̄
H → cc̄
H → Zγ

H → µ+ µ−

Branching ratio

Rel. uncertainty

2.27 × 10−3

2.62 × 10−2
2.14 × 10−1
6.27 ×10−2

5.82 × 10−1

2.89 × 10−2

1.53 × 10−3
2.18 × 10−4

2.1%
±1.5%
±1.5%
±1.6%
+1.2%
−1.3%

+5.5%
−2.0%

±5.8%
±1.7%

tainty of +4.0%−3.9% . The branching ratios for the most relevant decay modes of the SM Higgs boson as
a function of mH , including the most recent theoretical uncertainties, are shown in Fig. 11.2 (right)
and listed for mH = 125 GeV in Table 11.3. Further details of these calculations can be found in
the reviews [37–40] and references therein.

11.3 The experimental profile of the Higgs boson
The observation [1, 2] at the LHC of a narrow resonance with a mass of about 125 GeV wasan important landmark in the decades-long direct search [44, 139] for the SM Higgs boson. Thisobservation is being followed by a detailed exploration of properties of the Higgs boson at the√different runs of the LHC at s = 7, 8,13 and 13.6 TeV.
√
The dataset at s =13 TeV collected during the Run-2 phase of the LHC operation is the largest
analysed dataset so far and corresponds to an integrated luminosity of about 160 fb−1 delivered to
the ATLAS and CMS experiments, see Table 11.4 [140]. The datasets effectively useful for analysis
need to take into account the data-taking efficiency with fully operational detectors and the data
quality efficiency. The typical total inefficiency for both ATLAS and CMS is approximately 10%,where approximately half is due to the data aquisition inefficiency and the other half from data
quality requirements.
In this section, most of the references for the Run-1 measurements that have been updatedwith the data delivered in Run 2 are given in the previous version of this review [141] and are notrepeated herein.
11.3.1 The principal decay channels of the Higgs boson
For a given mH , the sensitivity of a channel depends on the production cross section of the Higgs
boson, its decay branching fraction, the reconstructed mass resolution, the selection efficiency andthe level of background in the final state. It is defined typically as the expected significance forthe observation of a given process or in terms of expected upper limit at 95% Confidence Level(CL). At the LHC, for a Higgs boson with a mass close to 125 GeV, five decay channels play animportant role. In the H → γγ and H → ZZ ∗ → 4` channels, all final state particles can bevery precisely measured and the reconstructed mH resolution is excellent (typically 1-2%). The
H → W ± W ∓(∗) → `+ ν` `0− ν̄`0 channel has a relatively large branching fraction. However, the31st May, 2024

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11. Status of Higgs Boson Physics
Table 11.4: The LHC pp collision centre-of-mass energies and approximate collision samples delivered to ATLAS & CMS experiments.
Year
2010
2011
2012
2015
2016
2017
2018
2022
2023

√

s (TeV)
7.0
7.0
8.0
13.0
13.0
13.0
13.0
13.6
13.6

R

L.dt (fb−1 )
0.04
6
23
4
39
51
61
39
32

Period
Run 1
Run 1
Run 1
Run 2
Run 2
Run 2
Run 2
Run 3
Run 3

presence of neutrinos, which are not reconstructed in the final state, means that the mH resolution,
obtained through observables sensitive to the Higgs boson mass such as the transverse mass, ispoor (approximately 20%). The H → bb̄ and the H → τ + τ − (with the tau subsequently decaying
to electrons or muons and two neutrinos τ → `ν ν̄ or to hadrons and one neutrino τ → hadrons ν)channels suffer from large backgrounds and lead to an intermediate mass resolution of about 10%
and 15% respectively.
With the increase in the size of datasets, measurements in the most sensitive channels are now
carried out differentially or in exclusive modes depending on specific production characteristics.
These measurements are discussed in Section 11.5.1.5.
The candidate events in each Higgs boson decay channel are split into several mutually exclusive
categories (or event tags) based on the specific topological, kinematic or other features present in
the event. The categorization of events increases the sensitivity of the overall analysis and allows aseparation of different Higgs boson production processes. Most categories are dominated by signal
from one Higgs boson decay mode but contain an admixture of various Higgs boson production
processes. For example, a typical VBF selection requires Higgs boson candidates to be accompaniedby two energetic jets (≥ 30 GeV) with a large dijet mass (≥ 400 GeV) and separated by a large
pseudo-rapidity (∆ηjj ≥ 3.5) [142]. While such a category is enriched in Higgs bosons produced via
VBF, the contamination from the ggF or VH production mechanisms can be significant. Hence, ameasurement of the signal rate in the VBF category is not equivalent to a measurement of VBF
production cross section since one cannot resolve the contamination from ggF. Simulations are used
to determine the relative contributions of the various Higgs boson production modes in each of thespecific categories.
11.3.2 The Higgs boson decay to vector bosons
11.3.2.1 H → γγ
In the diphoton channel, the measurement of a narrow peak over a smoothly falling backgroundin the invariant mass distribution of two high pT photons is performed. The background in thischannel is conspicuous and stems from prompt γγ processes for the irreducible backgrounds, andthe γ+jet and dijet processes for the reducible backgrounds where one jet fragments typicallyinto a leading π 0 . In order to optimise search sensitivity and also to separate the various Higgs
boson production modes, ATLAS and CMS split events into several mutually exclusive categories.
Diphoton events containing high pT muons or electrons, or missing energy (ETmiss ) consistent withthe decay of a W or Z boson, are tagged in the V H production category. Diphoton events containing
energetic dijets with a large mass and pseudo-rapidity difference are assigned to the VBF production
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11. Status of Higgs Boson Physics

category, and events with two jets compatible with the hadronic decay of a W or a Z are consideredin the V H category. . While the leptonic V H category is relatively pure, the VBF category has
significant contamination from the gluon fusion process. Finally more complex topologies aiming
at selecting events from the ttH productiuon mode in the semi-leptonic and fully hadronic top
decays are also considered and discussed in more detail in Section 11.3.5.1 Events are also further
categorised according to their expected mγγ resolution and signal-to-background ratio. Categories
with good mH resolution and larger signal-to-background ratio contribute most to the sensitivityof the search.
Both ATLAS and CMS have studied in detail the calibration of the energy response of photons,
in particular using Z → e+ e− , Z → µ+ µ− γ and the response of muons in the calorimeter (forATLAS) from Z → µ+ µ− events. This information is used to correct the simulated signal massline-shapes. In each category, parametric signal models are adjusted to these line-shapes to provide
a functional form for the signal. Simple functional forms of the backgrounds are determined by a
fit to the mγγ distribution in each category (typically exponential, Bernstein polynomials, Laurent
series or power laws). All categories are fitted simultaneously to determine the signal yield at agiven Higgs boson mass hypothesis.
The results are expressed in terms of signal strength, which can be defined as µ = (σ · BR)obs /(σ · BR)SM , the observed product of the Higgs boson production cross section (σ) and its branchingratio (BR) normalised to the corresponding SM values. A more detailed definition is given in
Section 11.3.6 and Eq. 11.14. The signal strength overall for this channel and for specific production
processes are summarised in Fig. 11.3. All results are in agreement with the SM expectation within
the overall measurement precisions of approximately 9% for both experiments.
11.3.2.2 H → ZZ ∗ → `+ `− `0+ `0−
In the H → ZZ ∗ → `+ `− `0+ `0− channel, a search is performed for a narrow mass peak over asmall continuous background dominated by non-resonant ZZ ∗ production from qq annihilation andgg fusion processes. The contribution and the shape of this irreducible background is taken fromsimulation. The subdominant and reducible backgrounds stem from Z + bb̄, tt̄ and Z + jets events.
Their contribution is suppressed by requirements on lepton isolation and lepton impact parameterand their yield is estimated from control samples in data.
To distinguish the Higgs boson signal from the dominant non-resonant ZZ ∗ background, both
ATLAS and CMS use multivariate techniques as well as a matrix element likelihood approach toconstruct a kinematic discriminant built for each 4` event based on the ratio of complete leadingorder matrix elements |Msig 2 /Mbkg 2 | for the signal (gg → H → 4`,qq → V H(→ 4`) and qq →qqH(→ 4`)) and background (qq → ZZ → 4`) hypotheses.
To improve the sensitivity to more exclusive production processes such as VBF, V H, and ttH,
the experiments divide 4` events into mutually exclusive categories. Events are categorised interms of the number of reconstructed jets, the number of additional leptons (from the decay of avector boson in the associated production mode), number of jet tagged as containing a b-hadron,the transverse momentum of the Higgs boson (or e.g. its associated vector boson) and missing
transverse momentum. Dijets with a large mass and pseudo-rapidity difference populate the VBF
category. ATLAS requires the presence of an additional lepton in the V H category. In events withless than two jets, CMS uses the p4`
T to distinguish between production via the gluon fusion andthe V H/VBF processes.
Since the m4` resolutions and the reducible background levels are different in the 4µ, 4e and2e2µ sub-channels, they are analysed separately and statistically combined to produce the final
results.
The results for this channel, overall and in specific production processes are summarised in
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11. Status of Higgs Boson Physics

Fig. 11.3. All results are in agreement with the SM expectation within the overall measurement
precisions of approximately 9% and 12% for the ATLAS and CMS experiments respectively.
11.3.2.3 H → W + W − → `+ ν`− ν
In this challenging channel, experiments search for an excess of events with two leptons (electrons or muons) of opposite charge accompanied by missing energy and/or jets. A typical event
selection is described below in order to give an idea of the main intricacies. Specific selections
vary between experiments and between Run-1 and Run-2 analyses. Events are divided into several
categories depending on the lepton flavour combination (e+ e− , µ+ µ− and e± µ∓ ) and the number ofaccompanying jets (Njet = 0, 1, ≥ 2). The Njet ≥ 2 category is optimised for the VBF production
process by selecting two leading jets with a large pseudo-rapidity difference and with a large mass
(typically mjj > 500 GeV).
Backgrounds contributing to this channel are numerous and depend on the category of selected
events. Reducing them and accurately estimating the remainder is a major challenge in this analysis. For events with opposite-flavour leptons and no accompanying high pT jets, the dominantbackground stems from non-resonant W W production. Events with same-flavour leptons sufferfrom large Drell–Yan contamination (note that also the opposite-flavour leptons analysis has Drell–
Yan τ τ̄ background in 0-jet category). The tt̄ , tW and W + jets (with the jet misidentified as a
lepton) events contaminate all categories. Non-resonant W Z, ZZ and W γ processes also contributeto the background at a sub-leading level.
A requirement of large missing transverse energy (ETmiss ) is used to reduce the Drell–Yan andmulti-jet backgrounds. In the e+ e− and µ+ µ− categories, events with m`` consistent with the Zmass are vetoed. The tt̄ background is suppressed by a veto against identified b-jets and tightisolation requirements diminish the W +jets background. The scalar nature of the Higgs boson andthe V − A nature of the W boson decay implies that the two charged leptons in the final state are
preferentially emitted at small angles with respect to each other. Therefore the dilepton invariant
mass (m`` ) and the azimuthal angle difference between the leptons (∆φ`` ) are used to discriminate between the signal and non-resonant W W events [143]. The transverse mass, constructed``
miss and the azimuthal angle between E miss and p`` , is defined asfrom theTT
q dilepton pT (pT ), ET
miss (1 − cos ∆φ miss ) and serves as an effective discriminant against backgrounds.
mT = 2p``
E
ET ``
T T
The transverse mass variable also tracks the Higgs boson mass but with a poor mass resolution.
Background rates except for the small contributions typically from non-resonant W Z, ZZ and W γ
are evaluated from data control samples with floating normalization.
ATLAS and CMS have also searched for the associated Higgs boson production in this channel.
The signal consists of up to three (W H) or four (ZH) high pT isolated leptons with missing
transverse energy and low hadronic activity. The major backgrounds stem from triboson anddiboson production where each boson decays leptonically.
Measurements by ATLAS and CMS, in terms of signal strengths, for the five largest Higgs
boson production modes are displayed in Fig. 11.3. All measurements are in agreement with the
SM expectation within the overall measurement precisions of approximately 12% and 9% for ATLAS
and CMS respectively.
11.3.3 Measurement of the Higgs boson mass
To measure the mass of the Higgs boson, ATLAS and CMS collaborations rely on the twohigh mass-resolution channels, γγ and ZZ ∗ /4`. The ATLAS and CMS approaches are very similarin these two analyses with small differences on the usage of categories, additional discriminating
variables and per-event errors. In these two channels, the mass resolutions range from 1.4 GeV to
2 GeV for ATLAS and from 1.0 GeV to 2.8 GeV for CMS (see Ref. [144] and the reconstruction31st May, 2024

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11. Status of Higgs Boson Physics

performance references therein). An excellent mass resolution is obtained for both experiments inthe diphoton channel for central diphoton pairs (typically for events where both photons are notconverted). However, the best precision in this measurement at Run 2 is obtained using the four
lepton channel and in particular in the sub-channel of four muons (followed, in precision, by thetwo-electrons and two muons channel where the mass resolution is driven by the reconstruction of
the lower mass di-lepton pair with typically lower transverse momentum leptons).
Both ATLAS and CMS have produced several Higgs boson mass measurements, including
the individual and combined Run-1 measurements [144] and several Run-2 measurements by ATLAS [145, 146] and CMS [147, 148] for both the 4` and the diphoton channels. The measurements
performed by ATLAS include the full Run-2 dataset whereas in the case of CMS, the mass measurements were done with a fraction of the Run-2 data corresponding to the data collected in 2016.
An overall combination of all available measurements has not yet been performed. The Run-1
combination including both ATLAS and CMS measurements yielded [144]:
mH = 125.09 ± 0.21 (stat.) ± 0.11(syst.) GeV.
The current most precise di-photon channel result is obtained by ATLAS using the full Run-2
dataset and a combination with the Run-1 measurements in the H → γγ yielding a measurementof [149]:mH = 125.22 ± 0.11 (stat.) ± 0.09(syst.) GeV.
The systematic uncertainty of 90 MeV is worth noting, as it results from a very challenging calibration and estimates of the amount of material upstream of the calorimeter to extrapolate thecalorimeter energy response calibration from electrons in Z boson decays to photons. This result is
promising for prospects in precision measurements in this channel. In Ref. [149], ATLAS has also
estimated the expected effect of the interference between the signal and the gluon fusion continuum
di-photon background to be of 24 MeV. This ATLAS measurement is significantly more precise than
the full Run-2 measurement in the 4` channel, however the latter is dominated by the statisticaluncertainty of 170 MeV with a systematic uncertainty of 30 MeV [150]. The ATLAS diphoton channel measurement reached the same senstivity as the early Run-2 and Run-1 combined measurementof CMS, which uses both channels but with a much smaller amount of Run-2 data, corresponding
only to the 2016 LHC run, which yielded [148]:mH = 125.38 ± 0.11 (stat.) ± 0.08(syst.) GeV.
ATLAS has also combined its results in the diphoton and the four-lepton channels yielding thecurrent most precise measurement with a precision of 0.09% [151]:
mH = 125.11 ± 0.09 (stat.) ± 0.06(syst.) GeV.
The most precise single channel result has very recently been obtained by CMS in the 4` channel
with the full Run 2 dataset [152]:mH = 125.08 ± 0.12 GeV.
The analysis of the entire Run-2 dataset and the LHC combination of the two experiments will
be of great interest and important for the combination of all Higgs boson measurements acrossexperiments.
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11.3.4 Higgs decays to third generation fermions (bb and τ + τ − )In the SM, fermions acquire a mass through gauge invariant interactions with the Higgs field
which is also responsible for the electroweak symmetry breaking and thus for generating the massesof gauge bosons (see Section 11.2 for more details). While this minimal solution is very elegant,there is no fundamental reason for it to be the case, and probing the couplings of the Higgs boson
to fermions is therefore of fundamental importance, in particular since BSM physics can largely
change the SM predictions.
The discovery of the Higgs boson was made essentially through the bosonic final states. These
decays probed mostly the couplings of the Higgs boson to vector bosons (the decay of the Higgs
boson to photons occurring only through loops is also dominated in the SM by the coupling of the
Higgs boson to W bosons). However, the predominant Higgs boson production mode is the gluon
fusion, occurring only through loops dominated by the coupling of the Higgs boson to fermions.
The observation of the Higgs boson in the two photons or two gluons decay modes is also anindirect evidence for the coupling of the Higgs boson to fermions (and in particular to the top
quark). Nevertheless, the observation of either decays to fermions or production modes whichunambiguously proceed through fermion couplings provide direct probes of the coupling of the
Higgs boson to fermions and is thus of fundamental importance.
At hadron colliders, the most promising channel for probing the coupling of the Higgs field
to the quarks and leptons are H → bb̄ and H → τ + τ − , respectively. For a Higgs boson withmH ≈ 125 GeV, the branching fraction to bb̄ is about 58% and to τ + τ − is about 6%. Nevertheless,the presence of very large backgrounds makes the measurement of a Higgs boson signal in thesechannels challenging.
One of the most prominent goals of the LHC Run-2 physics program was the direct observationof the Yukawa coupling of the Higgs boson to fermions of the third generation (bottom quarks, tau
leptons and top quarks). This goal has been reached independently by both ATLAS and CMS andwith only partial Run-2 datasets.
11.3.4.1 H → τ + τ −In the H → τ + τ − search, τ leptons decaying to electrons (τe ), muons (τµ ) and hadrons (τhad )are considered. The τ + τ − invariant mass (mτ τ ) is reconstructed from a kinematic fit of the visible
products from the two τ leptons and the missing energy observed in the event. Due to the presenceof missing neutrinos, the mτ τ resolution is poor (≈ 10% − 15%). As a result, a broad excess overthe expected background in the mτ τ distribution is searched for. The major sources of backgroundstem from Drell–Yan Z → τ + τ − and Z → e+ e− , W +jets, tt̄ and multijet production. Events in all
sub-channels are divided into categories based on the number and kinematic properties of additionalenergetic jets in the event and the transverse momentum of the reconstructed Higgs boson and the
distance ∆R distance between the two τ ’s. The sensitivity of the search is generally higher for
categories with one or more additional jets. The VBF category, consisting of a τ pair with twoenergetic jets separated by a large pseudo-rapidity, has the best signal-to-background ratio andsearch sensitivity, followed by the τ + τ − +1 jet category. The signal to background discrimination
relies in part on the mτ τ resolution, which improves with the boost of the Higgs boson. The
non-VBF categories are further subdivided according to the observed boost of the τ + τ − system.
ATLAS and CMS combine various kinematic properties of each event categories with multivariatetechniques to build the final discriminant.
Searches for H → τ + τ − decays in the V H production mode are also performed in final states
where the W or Z boson decays into leptons or jets. The irreducible background in this search arises
from non-resonant W Z and ZZ diboson production. The reducible backgrounds originate from W ,Z, and tt̄ events that contain at least one fake lepton in the final state due to a misidentified jet.
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The shape and yield of the major backgrounds in each category are estimated from control samples
in data. Contributions from non-resonant W Z and ZZ diboson production are estimated fromsimulations but corrected for reconstruction efficiency using control samples formed from observed
data.
The first clear evidence of direct decays of the higgs boson to taus was achieved by ATLAS and
CMS in combination [153], with the observation of an excess with a significance of 5.5σ and the+0.24
combined signal strength is µ = 1.11−0.22, consistent with the SM expectation. The early Run-2
data fully corroborated these results to establish an unambiguous observation in each experiment
independently. ATLAS [154] and CMS [155, 156] analysed an early Run-2 dataset to provide
independent observations, with significances of 4.4σ and 4.9σ respectively.
Both ATLAS [157] and CMS [158, 159] have then completed the analyses of the full Run-2
dataset in various production channels. These results are summarised in Fig. 11.3. These results
perform simultaneously measurements of the VBF production, the gluon fusion mode where the
Higgs boson has a sizeable boost, and the associated production with a vector boson as well as
the associated production with a pair of top quarks. It is interesting to note that the with thecurrent measurements the gluon fusion channels have a sensitivity which is very close to the VBF
production.
11.3.4.2 H → bb
To measure the decays of the Higgs boson to a pair of b-quarks, the most sensitive production
modes are the associated W H and ZH processes allowing use of the leptonic W and Z decays
which are helpful for triggering the events and to reject QCD backgrounds. The W bosons arereconstructed via their leptonic decay W → `ν̄` where ` = e, µ or τ . The Z bosons are reconstructed
via their decay into e+ e− , µ+ µ− or ν ν̄. The Higgs boson candidate mass is reconstructed from twob-tagged jets in the event. Backgrounds arise from production of W and Z bosons in association
with gluon, light and heavy-flavoured jets (V +jets), tt̄, diboson (ZZ and W Z with Z → bb̄) andQCD multi-jet processes. Due to the limited mbb̄ mass resolution, a SM Higgs boson signal is
expected to appear as a relatively broad enhancement in the reconstructed dijet mass distribution.
The crucial elements in this search are b-jet tagging with high efficiency and low fake rate, accurate
estimate of b-jet momentum and estimate of backgrounds from various signal depleted control
samples constructed from data.
At the Tevatron, the H → bb̄ channel contributed the majority of the Higgs boson searchsensitivity below mH = 130 GeV. To separate signal from background, CDF and D0 used multivariate analysis (MVA) techniques that combined several discriminating variables into a single
final discriminant. Each channel was divided into exclusive sub-channels according to various lepton, jet multiplicity, and b-tagging characteristics in order to group events with similar signal-tobackground ratio and thus optimise the overall search sensitivity. The combined CDF and D0 data
showed [44, 160] an excess of events with respect to the predicted background in the 115–140 GeV
mass range in the most sensitive bins of the discriminant distributions suggesting the potential+0.69
presence of a signal. At mH = 125 GeV, the observed signal strength was µ = 1.59−0.72.
At the LHC, in order to reduce the dominant V +jets background, following Ref. [92], experiments select a region in the V H production phase space where the vector boson is significantly
boosted and recoils from the H → bb̄ candidate with a large azimuthal angle ∆φV H . For eachchannel, events are categorised into different pT (V ) regions with varying signal/background ratios.
Events with higher pT (V ) have smaller backgrounds and better mbb̄ resolution. Experiments use
MVA classifiers based on kinematic, topological and quality of b-jet tagging and trained on different values of mH to separate Higgs boson signal in each category from backgrounds. The main
discriminating variables in this analysis are the transverse momentum of the vector boson and the
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11. Status of Higgs Boson Physics

di-b-jet invariant mass.
The direct observation of the Higgs boson decaying to a pair of b-quarks, a major result ofRun 2, was obtained by both ATLAS and CMS independently after the update of their search withsimilar analyses as those performed at Run 1 but with a larger dataset of approximately 80 fb−1 ofdata collected in 2015, 2016 and 2017. The increase in signal cross sections of nearly a factor of 3 at
the centre-of-mass energy of 13 TeV with respect to 7 TeV, has also been instrumental in bringing
the two experiments to the required sensitivity to claim an evidence for this decay mode in the V H
production mode (in the high transverse momentum of the vector boson fiducial region of interestfor this channel). The expected significance for a SM Higgs boson was 4.3σ for ATLAS [161]and 4.9σ for CMS [162]. Both ATLAS and CMS observed significant excesses corresponding to
4.9σ and 4.8σ respectively with Run-2 data only. When combined with results obtained in Run 1,
the observed (expected) significance of the excesses were 5.4σ (5.5σ) and 5.6σ (5.5σ) respectively.
These results provided direct and unambiguous observation for the H → bb decay through the V H
production mode.
Since these important observations, both experiments have completed the analysis of the full
Run-2 dataset using two reconstruction techniques. The first is based on the reconstruction of the
Higgs boson with two jets is referred to as resolved. The second is based on the reconstruction of
the Higgs boson as a large radius jet and is referred to as boosted. These measurements expand therange of measurements of the Higgs boson decays to b-quarks in association with a vector boson at
higher transverse momentum, above 400 GeV. These results are summarised in Fig. 11.3. It should
be noted that the sensitivity of these analyses are already limited by systematic uncertainties.
Also, the LHCb collaboration has performed a search for the V H production with subsequent
decay of the Higgs boson to a pair of b-quarks [163] with 1.98 fb−1 of data taken at a centre-of-massenergy of 8 TeV. The final state is required to have two reconstructed b quarks and one lepton in
the LHCb acceptance of 2 < η < 5. The sensitivity of this search is an expected 95% CL exclusionof 84 times the SM production rate. This analysis is also used to set a limit on the V H production
with the subsequent decay of the Higgs boson in a pair of c quarks with a 95% CL limit at 6.4×103
times the SM production rate, while the expected sensitivity corresponds to an exclusion of 7.9×103
times the SM production rate.
ATLAS and CMS have also searched for H → bb̄ in the VBF production mode. The event
topology consists of two VBF-tagging energetic light-quark jets in the forward and backward direction relative to the beam direction and two b-tagged jets in the central region of the detector. Dueto the electroweak nature of the process, for the signal events, no additional energetic jet activity(excluding that from the Higgs boson) is expected in the rapidity gap between the two VBF-tagging
jets. The dominant background in this search stems from QCD production of multi-jet events andthe hadronic decays of vector bosons accompanied by additional jets. A contribution of Higgs
boson events produced in the ggF process but with two or more associated jets is expected in thesignal sample. The signal is expected as a relatively broad enhancement in the mbb̄ distribution
over the smoothly falling contribution from the SM background processes. Both ATLAS [164] andCMS [165] have produced results in this channel with Run-1 data, but with limited sensitivity.
Both experiments performed a similar analysis with Run-2 data [166, 167].
Two of the main difficulties for the VBF production mode are the large QCD background andthe difficulty in triggering fully hadronic events. Both difficulties are addressed, by the proposal
made in Ref. [168], where the requirement of an additional photon in the final state reduces the
background through an interference effect and enhances the possibilities for triggering. This analysis
has been carried out by ATLAS at Run 2 [169] and its result combined with the standard VBF
channel. The sensitivity in this channel is smaller than in the fully hadronic mode. Through the
combination of these channels ATLAS has reached a first evidence at 3 standard deviations of the
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11. Status of Higgs Boson Physics

Higgs boson decaying to a pair of b quarks in the VBF production mode. The results are reported
below
+0.18
ATLAS µVbbBF (γ) = 0.99 +0.30−0.30 (stat) −0.16 (syst),+0.40
CMS µbb
V BF = 1.01 ± 0.36 (stat) −0.27 (syst).

(11.12)The sensitivity in the inclusive search for the Higgs boson in the ggF production mode with H → bb̄
is limited by the overwhelming background from the inclusive production of pp → bb̄ + X via thestrong interaction. With the increase in centre-of-mass energy to 13 TeV, and taking advantage ofthe harder transverse momentum spectrum of the gg → H production mode with respect to the
QCD background, a search for high pT Higgs boson decaying to a pair of b quarks in association withan energetic Initial State Radiation (ISR) jet. Considerable efforts have been made using state-ofthe-art deep learning techniques to improve the performance of the identification of a Higgs boson
decaying to b quarks and reconstructed as a large radius jet at high transverse momentum. In orderto gain sensitivity in this channel and reconstruct the Higgs boson within one jet of radius 0.8 or 1.0
a lower cut at 450 GeV of transverse momentum is required. This analysis was performed by both
ATLAS [170] and CMS [171] with the entire Run-2 data dataset. As in the case of V H productionmode, this analysis is sensitive also to the inclusive Z → bb production, which is an important
step in the validation of the analysis chain. The Z → bb decay is observed with a significance inexcess of five standard deviations, in agreement with the expected rate from the Standard Model. .
This estimate has a non negligible uncertainty from the precise estimate of the fiducial signal crosssection in the specific acceptance of this analysis. CMS observes an excesses at mH = 125 GeV of
1.2σ [171] with a sensitivity of 0.9σ. It should be noted that the estimates of the signal expectationin this remote region of phase space at high transverse momentum for the production are highly
non-trivial and subject to fairly large theoretical and statistical uncertainties:
ATLAS µbb
inclusive = −0.1 ± 3.5 (1.0 ± 3.4 expected),+1.9
CMS µbb
inclusive = 2.1 −1.7 .

(11.13)

In addition to the inclusive production, in [171] CMS has also performed a search sensitive to the
VBF production in the boosted Higgs regime, yielding a sensitivity of 0.9σ. In this channel a broadexcess has been observed which results in an observed excess with a significance of 3.0σ. These
results are particularly interesting as these measurements will bring a strong complement to themain channels in the high transverse momentum regime.
Another important production mode sensitive to the decay of the Higgs boson to bottom quarks,
is the associated production with a pair of top quarks. The results of the searches for this process
have been combined with the channels described above, to provide an additional constraint on
the Yukawa coupling of the Higgs boson to bottom quarks. The channels corresponding to thisproduction mode are described in Section 11.3.5.
11.3.5 Higgs boson production in association with top quarks
11.3.5.1 The associated production with top quark pairs
As discussed in Section 11.2, the coupling of the Higgs boson to top quarks plays a special rolein the electroweak symmetry breaking mechanism in the SM, as well as in its possible extensions.
Substantial indirect evidence of this coupling is provided by the compatibility of observed ratesof the Higgs boson in the principal discovery channels, given that the main production process –gluon fusion – is dominated by a top quark loop. Direct evidence of this coupling at the LHC andthe future e+ e− colliders will be mainly available through the ttH final state and will permit a clean
measurement of the top quark-Higgs boson Yukawa coupling. The ttH production cross section at
the LHC is small in comparison with the ggF or even V H production modes. The production cross
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11. Status of Higgs Boson Physics√
section for a 125 GeV Higgs boson in pp collisions at s = 8 TeV of about 130 fb made it challenging
to measure the ttH process with the LHC Run-1 dataset. However, at Run 2, the increase in cross√section at s = 13 TeV is substantial, reaching approximately 500 fb.
The analysis channels for such complex final states can be separated in four classes according
to the decays of the Higgs boson. In each of these classes, most of the decay final states of the top
quarks are considered (fully hadronic, semi-leptonic and dilepton decay final states).
The first analysis is the search for ttH production in the H → γγ channel. This analysis relieson the search for a narrow mass peak in the mγγ distribution. The background is estimated fromthe mγγ sidebands. The sensitivity in this channel is mostly limited by the available statistics.
The second analysis is the search for the Higgs boson decaying to ZZ ∗ and subsequently to four
leptons (electrons and/or muons). This channel is currently limited by the low statistics due to thesmall branching fraction of the Z decays to leptons.
In the third analysis the W + W − , τ + τ − and ZZ ∗ final states are searched for inclusively inmultilepton event topologies (but not including the resonant H → 4` channel that is covered in thespecific analysis described in Section 11.3.2). The corresponding ttH modes can be decomposedin terms of the decays of the Higgs boson and those of the top quarks as having two b-quarks andfour W bosons (or two W and two taus, or two W and two Z) in the final state.
The fourth channel is the search in the H → bb channel. This search is intricate due to thelarge backgrounds, both physical and combinatorial in resolving the bb system from the Higgs
boson decay, in events with six jets and four b-tagged jets. Already with the Run-1 dataset, thesensitivity of this analysis was strongly impacted by the systematic uncertainties on the background
predictions.
Prior to its start, it was unclear if this process would at all be observable at the LHC. A
first milestone was reached with the completion of the Run-1 analyses by ATLAS and CMS witha complete set of results in these channels and their combination [172, 173]. These results arereported in Table 11.5. However the sensitivity remained very limited. The breakthrough in the
search for this process of fundamental importance came with the Run-2 data at a higher centre-ofmass energy of 13 TeV and the increase of a factor of nearly four of the production cross section of
the tt̄H associated production process.
Using only a partial Run-2 dataset, ATLAS and CMS were able to independently make anunambiguous observation of this process. For these results ATLAS and CMS had different strategies. ATLAS relied mostly in the tt(H → γγ) channel where a narrow peak over a continuous
background is searched for. It is interesting to note that the rapid evolution of the sensitivity inthe diphoton channel owes not only to the large increase in cross section, but also to the fact thathigh mass diphoton events in an environment with additonal leptons, jets and b-tagged jets thesearch for a pair of photon at high mass has a low background. In contrast with the inclusive searchfor H → γγ, the analyses in this channel reached a signal-to-background ratio in excess of unity.
This channel, which is characterised by a narrow peak over a continuous background, also has theadvantage of being less prone to systematic uncertainties than channels where the assessment ofbackgrounds cannot be made through the use of sidebands. ATLAS used up to 79.8 fb−1 of Run-2
data to reach an expected sensitivity of 4.9σ and an observed significance of 5.8σ with the Run-2
partial dataset alone, and 6.3σ (with 5.1σ expected) in combination with the Run-1 results [174].
CMS instead relied on a smaller dataset of 35.9 fb−1 and relied on all channels. The most sensitivein this case was the ttH(bb) whose sensitivity was limited by systematic uncertainties. CMS reacheda sensitivity of 4.2σ and observed an excess with respect to the background-only hypothesis of 5.2σ,
combining the Run-1 and Run-2 results [175].
This direct observation of the Yukawa coupling of the Higgs boson to top quarks was particularly
important in comparison to the indirect evidence through the gluon fusion production process
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11. Status of Higgs Boson Physics

dominated by the top quark loop
Since the observation of this important process, with few exceptions, all channels have been
updated with the full Run-2 dataset, by both experiments.
For the principal decays of the Higgs boson in the diphoton and four lepton channels, themeasurements are done in the framework of ’Simplified Template Cross Section’ discussed in Section 11.5.1.5). The diphoton channels were updated by both the ATLAS and CMS experiments
in Refs. [176, 177]. The four lepton decays of the Higgs boson in the associated production witha pair of top quarks is a search for a narrow peak in the busy ttH environment. It was also performed by ATLAS [176] and CMS [177] with the full Run-2 datasets. These results are reported
in Table 11.5. This channel has currently very low statistic but also very high purity, reaching
signal-to-background ratios in excess of 10.
To address the W W , ZZ and τ τ decay modes, an approach based on multiple channels withelectrons, muons and taus decaying hadronically, the so-called “multi-lepton”, is adopted by bothexperiments. This analysis excludes the H → 4` channel. CMS has analysed the Full Run-2
dataset [178] and ATLAS only part of it [179]. In a preliminary release of this analysis usinga larger, but not full Run-2 dataset corresponding to an integrated luminosity of approximately
80 fb−1 , the ATLAS experiment found that the normalisation of the ttW background was larger
than expected from SM calculations by factors ranging from 1.3 to 1.7 and modelling issues wereobserved in analysis regions where the ttW process is dominant [179]. The search for Higgs boson
decays to tau leptons in association with a pair of top quarks was carried out by ATLAS with the full
Run-2 dataset and discussed in 11.3.4.1 [180]. Using the full dataset in this channel CMS obtained
an observation of the Higgs boson production in association with top quarks with an observed
significance of 4.7 standard deviations (5.2σ expected). The results are reported in Table 11.5. The
rate of the ttW background in this analysis is also high by a factor of approximately 1.4.
Both ATLAS and CMS have performed the analysis of Higgs bosons decaying to b-quarks inthe ttH production mode with the full Run-2 dataset. In ATLAS, this analysis was performed in
the semi-leptonic and di-leptonic channels [181], including a resolved mode where the Higgs bosonis reconstructed as two standard jets and a boosted mode where the Higgs boson is reconstructed
as a single large radius jet. CMS also performed this analysis with the full Run-2 dataset, including
in addition the fully hadronic mode where both W bosons from top decays subsequently decay
hadronically [182]. The results reported in Table 11.5. It should be noted that in this channel adeficit in observed Higgs boson decays is observed. This deficit is rather significant and in tension
with the observation of the other tt̄H modes as well as the observation of the Higgs boson in thebb channels.
The discrepancies observed in both the multilepton and the H → bb channels will require further
studies.
A combination of all available channels has been performed by ATLAS [183] and CMS [184]and is reported in Fig. 11.3. It should be noted that the latest ttH(→ bb) channel from CMS withthe full Run 2 data has not yet been included in the combination. A fit of individual decay modesin the ttH production is also given therein.
11.3.5.2 The associated production with a single top quark
An additional production mode of the Higgs boson in association with a top quark is the single
top associated production mode. There is an interesting similarity between this production modeand the H → γγ decay mode. Both processes proceed through either the top Yukawa coupling or
the interaction of the Higgs boson with the W boson, with a negative interference between the two.
Representative Feynman diagrams for this production process are shown in Fig. 11.1. Contrary to
the diphoton decay channel, in this production mode the interference occurs at the tree level and31st May, 2024

11. Status of Higgs Boson Physics

26

Table 11.5: Summary of the results of searches for a Higgs boson in association with a top quark
pair by ATLAS and CMS. The results are given in terms of a measured signal strength.
ttH
H → γγH → 4`ATLAS Run 1

CMS Run 1

ATLAS Run 2

CMS Run 2+2.5
1.3 +2.6−1.7 −1.7+2.6
1.2 +2.5−1.7 −1.8+0.26
1.38 +0.33−0.31 −0.18

2.27+0.86−0.74

3.3 ± 1.4

+0.30
1.56 +0.30−0.29 −0.27—

H → W W/τ τ /ZZ 1.4 ± 0.6 ± 1.0
H → bb

Combination

1.4 ± 1.0 ± 0.6

1.7 ± 0.5 ± 0.8—

1.6 +1.6−1.5
2.6 +1.0−0.9+1.4
1.2 −0.8

0.00 +0.91−0.00
0.92 +0.26−0.23

0.35 ± 0.20 ± 0.30 0.33 ± 0.16 ± 0.21
0.97 ± 0.14 +0.14−0.13

0.94 ± 0.20 +0.09−0.14

is dominant. This process can therefore be used to further discriminate a negative relative sign
between the couplings of the Higgs boson to fermions and its couplings to gauge bosons [185].
ATLAS and CMS have produced specific searches for the tH production mode with the Run1 and Run-2 data exploiting a variety of Higgs boson decay modes resulting in final states withphotons, bottom quarks, and multiple charged leptons, including tau leptons. In particular, with
the Run-2 data, CMS has searched for multi-leptonic decay signatures from the H → W W ∗ ,H → τ + τ − and H → ZZ ∗ modes [186]. This analysis restricts values of κt , the top-Higgs couplingnormalised to its SM value, to [−1.25, 1.60] at 95% CL. CMS has also performed an analysis of the2015 dataset to search for the H → bb mode [187], yielding much less stringent constraints.
The diphoton channel has also been used to search specifically for this production mode by
ATLAS using Run-1 data, yielding the restricted range of allowed values of κt at the 95% CL to[−1.3, 8].
The strongest constraint on the negative (relative) sign of κt was obtained by CMS using therecent analysis of the full dataset [178] in the multilepton (H → W W , H → ZZ, H → τ τ ) discussed
in 11.3.5.1, negative values of κt are disfavoured and the only non excluded negative values of κt
at 95% CL. range between -0.9 and -0.7.
11.3.6 Combining the main channels
The analysis strategy used by the LHC experiments to perform the searches for the Higgs bosonhas been based on the Higgs boson decay modes. It is a natural choice given that it focusses on
the decay products of the object searched for. However, for each channel, exclusive sub-channels
have been defined to target different production modes and kinematic regimes, and these subchannels have been combined. The natural extension of this approach in order to probe further
the production and decay modes of the Higgs boson is to combine the analysis channels together.
Such a combination is also used in Section 11.5 to further measure the coupling properties of the
Higgs boson.
At the LHC, the total cross section cannot be measured independently of the decay branching
fractions. As a consequence, the total width of the Higgs boson cannot be directly measured.
However, a combined measurement of the large number of categories described above with different
sensitivities to various production and decay modes, permits a wide variety of measurements of the
production, decay and coupling properties. These measurements, however, rely on assumptions.
Combining Higgs observation channels requires that measurements in all channels are done
under the same Higgs boson mass hypothesis. This is always the case within experiments but is
not necessarily the case across experiments. At Run 1, prior to combining the measurements of rates
in ATLAS and CMS, a common and thus combined Higgs boson mass measurement was made. Only
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11. Status of Higgs Boson Physics

27

thereafter were the ATLAS and CMS measurements combined [153]. The Run 1 full combination
results were derived by the two collaborations, taking rigorously into account all correlations in thesystematic uncertainties and in the large number of channels and their categories. For a review of
the Run-1 combined results see former PDG reviews in [188] and references therein.
It is important to note that, between the Run-1 and the Run-2 results, the signal theoreticalsystematic uncertainties have improved significantly.
At Run 2, ATLAS [183] and CMS [184] have already produced combined measurements of thecoupling properties and production cross section ratios of the Higgs boson.
In this section, only the results on the main Higgs boson production and decay modes will be
discussed. Only a brief presentation of the combination framework is given here (a more detailed
description is given in Ref. [189]). This framework will also be used in Section 11.5 to discuss themeasurements of the coupling properties of the Higgs boson.
11.3.6.1 Principles of the combination
The combination of the Higgs boson analysis channels in each experiment and for the two
experiments together was done using a fit of a signal and background model to the data. As
described above, the data was made of a large number of categories, aiming at reconstructing
exclusive production and decay modes. In the combination of ATLAS and CMS [153], there wereapproximately 600 categories. The combination was a simultaneous fit to the data across all thesecategories, using a reduced number of parameters of interest and the Higgs boson mass fixed toits measured value at Run 1 [144]. The much larger number of categories present in the ATLAS
and CMS combination [153] is due to additional separation in terms of finer exclusive production
regions, decay channels of the Z and the W bosons, and taus, control regions where little-to-no
signal is present, and different center-of-mass energies.
In their Run-2 individual combinations, ATLAS and CMS have not considered the Zγ channel.
Both ATLAS and CMS experiment have included the µµ channel based on a partial Run-2 dataset
corresponding to an integrated luminosity of 36 fb−1 only.
The key to understanding how the combination of channels works relies on the combination
master formula, which expresses for each category, indexed by c, of a given channel (typically acategory covers mostly one decay mode, but possibly various production modes), the measured
number of signal events ncs as a function of a limited number of parameters as follows:X
 × Lc .
ncs =  µi σiSM × Acif × εcif × µf BRSM
f

(11.14)i,f

The production index is defined as i ∈ {ggF, VBF, ZH, W H, tt̄H, tH, . . .} (including specific modes
and regions of phase space) and the decay index is defined as f ∈ {γγ, W W, ZZ, bb, τ τ, µµ, Zγ},
while σiSM and BRSM
f are the corresponding production cross sections and decay branching fractions,estimated as described in Section 11.2, assuming that the Higgs boson is that of the SM. Acif andεcif are the signal acceptance and the reconstruction efficiency for the given production and decay
modes in the category c. Lc is the integrated luminosity used for that specific category. For the
purpose of this review, these parameters can be considered as fixed2 .
The parameters of interest in the master formula are the signal strength parameters µi andµf . It is important to note that the formula relies on the factorisation of the production crosssection and decay branching fraction, which assumes the narrow width approximation. The widthof the Higgs boson will be discussed in Section 11.4, however, for the precision needed here, thefact that the Higgs boson has been observed in decay channels with high mass resolution as a2

In the combination performed by ATLAS and CMS, the systematic uncertainties on these parameters are taken
into account by allowing these parameters to vary within their constraints in the fit.
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11. Status of Higgs Boson Physics

28

resonance is sufficient to validate this hypothesis. It is also manifest in the above equation thatthe ten parameters for the production modes (µi ) and decay modes (µf ) cannot be determined
simultaneously. This illustrates that total cross sections or branching fractions cannot be measured
without further assumptions in this fit.
ATLAS (Tot. unc.)

ATLAS Syst. [Nature 607, 52 (2022)]

0.10
ATLAS 1.04 -+0.10

γγ
ATLAS µ γ γ = 1.09 ± 0.09
CMS
µ γ γ = 1.13 ± 0.09

CMS

ZZ

0.30
ATLAS 1.36 -+0.26

0.12
1.08 +- 0.11

CMS

CMS

0.14
0.93 +- 0.13

CMS

CMS Syst. [Nature 607, 60 (2022)]

0.56
ATLAS 1.53 -+0.51

0.35
1.00 +- 0.32

CMS

0.52
ATLAS 1.33 +- 0.43

0.11
ATLAS 0.95 +- 0.10

ATLAS µ = 1.04 ± 0.09
ZZ
CMS
µ = 0.97 ± 0.12

CMS (Tot. Unc.)

0.61
ATLAS -0.22 +- 0.54

0.54
1.43 +- 0.47

CMS

0.33
ATLAS 0.90 +- 0.31

0.71
1.19 +- 0.62

CMS

1.17
ATLAS 1.50 +- 0.94

0.34
1.38 +- 0.29

1.68
ATLAS 1.68 +- 1.11

0.48
0.32 +- 0.00

CMS

0.73
0.00 +- 0.00

ZZ

0.13
ATLAS 1.14 +- 0.13

WW
ATLAS µ= 1.20 ± 0.12
WWCMSµ
= 0.97 ± 0.09

CMS

1.21
ATLAS 2.26 +- 1.02

0.19
ATLAS 1.13 +- 0.18

0.11
0.90 +- 0.10

CMS

CMS

0.28
0.73 +- 0.24

1.84
ATLAS 2.86 +- 1.33

0.72
2.41 +- 0.70

CMS

0.65
ATLAS 1.64 +- 0.61

0.75
1.76 +- 0.67

CMS

0.32
1.44 +- 0.32

WW

0.29
ATLAS 0.90 +- 0.26

ττ
ATLAS µ τ τ = 0.96 ± 0.12CMSµ τ τ = 0.85 ± 0.10

CMS

0.21
0.66 +- 0.21

0.21
ATLAS 1.00 +- 0.18

0.62
ATLAS 1.00 +- 0.59

0.62
ATLAS 1.00 +- 0.59

0.17
0.86 +- 0.16

0.65
1.89 +- 0.56

0.61
1.33 +- 0.57

CMS

CMS

0.35
ATLAS 0.99 +- 0.34

bb
ATLAS µ = 0.91 ± 0.14bb
CMS
µ = 1.05 ± 0.22

CMS

0.54
1.01 +- 0.45

CMS

0.28
ATLAS 1.06 +- 0.26

0.25
ATLAS 1.00 +- 0.23

0.42
1.26 +- 0.41

0.36
0.90 +- 0.34

CMS

CMS

0.86
ATLAS 1.37 +- 0.75

CMS

0.44
0.35 +- 0.37

0.34
ATLAS 0.35 +- 0.33

CMS

0.46
0.90 +- 0.44

bb

0

0.5

1

1.5

ggF+bbH

0

0.5

1

1.5

VBF

ATLAS µ = 1.03 ± 0.07
ggF
CMS
µ = 0.97 ± 0.08
ggF

ATLAS µ= 1.11 ± 0.13
VBF
CMS
µ
= 0.80 ± 0.12
VBF

0 0.5 1 1.5

0 0.5 1 1.5

0 0.5 1 1.5

WH

ZH

ttH+tHATLAS µ = 1.15 ± 0.23
WH
CMS
µ = 1.49 ± 0.26
WH

ATLAS µ = 0.96 ± 0.22
ZH
CMS
µ = 1.29 ± 0.24
ZH

ATLAS µ = 0.74 ± 0.24
ttH
CMS
µ
= 1.13 ± 0.18
ttH+thFigure 11.3: Combined measurements by ATLAS [183] and CMS [184] of the products σ · BR,
normalised to the SM predictions, for the five main production and five main decay modes.
The master formula also illustrates an important caveat to the measurement of signal strengthparameters. In case these are interpreted as scale factors of the production cross sections or branching fractions, then all the other quantities such as the acceptances and efficiencies, Acif and εcif , need
to be assumed as independent and fixed to their estimated values for the SM Higgs boson. An additional important caveat to note concerning these combined results is that only the normalisation isvaried, while the discriminating variables for the signal are not modified and are still used in the fit.
These caveats are of particular importance in the use of the combination to measure the coupling
properties of the Higgs boson, as discussed in Section 11.5. For relatively small perturbations of
the couplings of the Higgs boson from the SM values, this hypothesis is valid.
However, the products µi × µf can be considered as free parameters and in principle measurable(if there is sufficient sensitivity from specific categories). Measuring the products of signal strengths
can be viewed as measuring the cross sections times the branching fraction, σ · BR. Measurements
by ATLAS and CMS of σ · BR, normalised to the SM predictions, for the five largest Higgs boson
production modes and five major Higgs decay modes are displayed in Fig. 11.3.
Other fits involving ratios of cross sections, which are less sensitive to theory uncertainties, areperformed and reported in Ref. [189].
The most constrained fit in the combination allows for only one single parameter to vary,i.e., ∀(i, f ), µi = µf = µ. This global-signal-strength model provides the simplest probe of thecompatibility of the signal with the SM Higgs boson. Indeed, it is sensitive to any deviation fromthe SM Higgs boson couplings provided that these deviations do not cancel overall. The full Run-1
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11. Status of Higgs Boson Physics

combination determines the global signal strength to beµ = 1.09 ± 0.11 = 1.09 ± 0.07 (stat.) ± 0.04 (expt.) ± 0.03 (th. bkg.) ± 0.07 (th. sig.),(11.15)where the statistical, experimental uncertainties as well as the theoretical uncertainties on the
background and on the signal are reported separately. The ATLAS Run-2 combination of the
global signal strength yields [183]:µ = 1.05 ± 0.06 = 1.05 ± 0.03 (stat.) ± 0.03 (exp.) ± 0.02 (th. bkg.) ± 0.04 (th. sig.),(11.16)

while the CMS Run-2 combination yields [184] µ = 1.002 ± 0.057.
These overall signal strengths are fully compatible with the SM expectation, µ = 1, with a
precision of 6%. It is interesting to note that the main uncertainty in these measurements arises
from the limited precision in the theoretical predictions for the signal production processes. The
precision reached with the individual experiments combinations using partial Run-2 data sets havealready exceeded the full Run-1 ATLAS and CMS combination precision.
11.3.6.2 Main decay modes
Despite the large number of decay channels, since the cross sections cannot be independently
measured, from the measurements described in this section it is impossible to measure the decaybranching fractions without a loss of generality. The simplest assumption that can be made isthat the production cross sections are those of the SM, which is equivalent to assume that, for alli indices, µi = 1. All branching fractions µf can then be measured in a simple 7 parameter fit.
Results of these measurements are reported in Fig. 11.3.
11.3.6.3 Main production modes
Most analysis channels are divided into exclusive categories allowing for an increased overallsensitivity and permitting to access the various Higgs boson production modes. The cross sectionsof the main production modes can be measured assuming that the branching fractions are those of
the SM, i.e., for all f indices µf = 1. These assumptions lead to a 6 parameter combination.
The gluon fusion production process is the dominant production mode. Although no numericalestimate of combined significance of observation for this process has been given by the experiments,
it is considered as established due to the overwhelming evidence from the three main discovery
channels. At the LHC, all production modes have been unambiguously observed. The intricate
V H production mode has been unambiguously observed by ATLAS and CMS independently (asdiscussed in Section 11.3.4) through the V (H → bb) channel. The results of these measurements
are reported in Fig. 11.3.
With the Run-2 data, all the main production processes have been established, and in particular
the pp → ttH process, which provides direct evidence of the coupling of the Higgs boson to top
quarks. This is another milestone in the LHC physics program.
11.3.7 Probing the Higgs boson coupling to the second generation
11.3.7.1 First evidence for H → µ+ µ−
The branching fraction in the H → µ+ µ− channel for a 125 GeV SM Higgs boson is 2.2 × 10−4 ,about ten times smaller than that for H → γγ. The major challenge in this channel is the extremely
small, permil level, signal-to-background ratio. The dominant and irreducible background arises
from the Z/γ ∗ → µ+ µ− process which has a rate several orders of magnitude larger than thatfrom the SM Higgs boson signal. Due to the precise muon momentum measurement achieved by
ATLAS and CMS, the mµ+ µ− mass resolution is very good (≈ 2–4% for ATLAS and ≈ 1–3% for
CMS depending on the selected categories; a better resolution is expected for CMS due its higher
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11. Status of Higgs Boson Physics

magnetic field strength in the inner detector). A search is performed for a narrow peak over a large
but smoothly falling background. For optimal search sensitivity, events are divided into several
categories. Either taking advantage of the superior muon momentum measurement in the central
region, events can be subdivided by the pseudo-rapidity of the muons, or designing selections aimingat specific production processes such in particular as the vector boson fusion.
ATLAS and CMS analyses target the main production modes such as gluon fusion, associatedproduction with a vector boson (including in the vector boson leptonic decay modes), vector boson fusion and associated production with a top-quark pair. The analyses use multivariate anddeep machine learning methods to discriminate signal from background in these Higgs production
categories. The signal in both experiments is extracted from a fit to the di-muon invariant mass
spectrum and the background is modeled using a suite of analytical functions, except in the caseof the most sensitive channel (VBF) in the CMS analysis where the distribution of a discriminant
Deep Neural Network output is used.
With the Run-2 dataset, ATLAS measured [190] a signal strengths of µ = 1.2 ± 0.6 with anobserved (expected) significance of 2.0(1.7)σ. The 95% CL limit on pp → H → µ+ µ− was set at
2.2 times the SM prediction while the expected limit on a H → µ+ µ− signal assuming the absence(presence) of a SM signal was 1.1 (2.0). CMS reported [191] the first evidence for H → µ+ µ− at
3σ level with a signal strength of µ = 1.19 ± 0.40 (stat.) ± 0.15 (syst.) and an expected analysis
sensitivity of 2.5σ. These measurements provide the first direct evidence for the decay H → µ+ µ−
and thus of the Yukawa coupling of the Higgs boson to second generation fermions.
11.3.7.2 Constraints on Higgs boson coupling to charm quarks
The possibility of probing the Yukawa coupling to the charm has been discussed early in
Ref. [192] where indirect bounds are estimated from a combined fit to the Higgs data and theimportance of using charm tagging is emphasised. A SM decay rate in standard production waslong thought to be out of reach at the LHC. However recent results, in particular from CMS haveshown that a different perspective might be emerging [193].
The channels which are currently foreseen to be most sensitive are similar to those aiming at theb-quark Yukawa coupling, and pertain to the V H production mode. As was discussed in [188], thetypical sensitivity of these analysis using the LHC Run-2 data on the production times branching
fraction was approximately a factor of 30 times the expected rate in the Standard Model.
The key aspect to bring sensitivity to the charm coupling is the ability of flavour tagging
algorithms to discriminate charm quark initiated jets from both b quark and light quark jets.
Significant progress was recently made in development of parton flavour taggers using state-ofthe-art machine learning techniques [194] and additional information to these algorithms. Novelalgorithms have also been used to identify pairs of charm quarks resulting from the decay of a
Higgs boson, in particular in a regime where the Higgs boson is reconstructed as a large radius jetswith a distinctive substructure. These new techniques have resulted in impressive improvements
which have led to the first observation of Z boson decays to charm quarks at a hadron collider
with a significance of 5.7 standard deviations [193] and an expected sensitivity to the exclusion ofa Higgs boson signal decaying to a pair of charm quarks of 7.6 times the Standard Model rate.
The observed limit for CMS is at 14 times the SM rate. This led CMS to set limits on the absolutevalue of κc , the Yukawa coupling of the Higgs boson to charm quarks with respect to its value in
the Standard Model. The expected 95% CL interval is |κc | < 3.4. The observed 95% CL intervalis the following:
1.1 < |κc | < 5.5(11.17)This is the most stringent constraint today. The ATLAS analysis [195], in contrast, is still relying
on traditional techniques and sets an observed (expected) limit at 26 (31) times the SM rate, using
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the VH production mode where the vector boson decays to leptons.
CMS complemented this search in the VH production mode with an inclusive search for the
Higgs boson produced at high transverse momentum (in excess of 450 GeV) and decaying to a pairof charm quarks [196]. The observed (expected) limit at 95% CL is 47 (39) times the SM rate,
which is also an impressive result as it is almost comparable to the previous results obtained in the
more sensitive VH channel.
With this striking improvement in sensitivity, CMS reappraised their prospect for the searchof Higgs boson decays to charm quarks at the HL-LHC and showed that a CMS could reach a
relative precision on the the production rate of approximately 80%. In combination with ATLAS
and potential improvements in the analysis, this is bringing the Yukawa coupling of the Higgs bosoncloser to being at reach at the HL-LHC.
11.3.8 Searches for rare decays of the Higgs boson
11.3.8.1 Combined evidence for H → Zγ and the first evidence for the Dalitz H → `+ `− γ decay
The search for H → Zγ is performed in the final states where the Z boson decays into opposite
sign and same flavour leptons (`+ `− ), ` here refers to e or µ. While the branching fraction for
H → Zγ is comparable to H → γγ (about 10−3 ) at mH = 125 GeV, the observable signal yield isbrought down by the small branching ratio of Z → (e+ e− + µ+ µ− ) = 6.7 × 10−2 . In these channels,
the m``γ mass resolution is excellent (1–3%), therefore the analyses search for a narrow mass peakover a continuous background. The major backgrounds arise from the Z + γ final state radiation in
Drell–Yan decays and from the Z +jets processes where a jet is misidentified as a photon. The ratioof signal over background in this channel is typically of the order of 0.5%. In a narrow window of afew GeV around 125 GeV, several hundreds of events are expected in a Run-2 dataset corresponding
to approximately 36 fb−1 . Events are divided into mutually exclusive categories on the basis eitherof the expected mZγ resolution or exclusive production mode categories.
With the full Run-2 dataset, ATLAS observes an excess with a significance of 2.2σ while anexcess with a significance of 1.2σ is expected. CMS observes an excess with a significance of 2.6σ
while 1.2σ is expected. ATLAS and CMS have jointly published a combination of these results,
yielding a first evidence for the Higgs boson decay to a Z boson and a photon at the LHC withan observed significance of 3.4σ and an expected sensitivity of 1.6σ [197]. This combined result iscompatible with the SM hypothesis at 1.9σ.
Both ATLAS and CMS experiments have extended the search for the so-called Dalitz Higgs
boson decays H → γ ∗ γ → `+ `− γ in the low mass γ ∗ range of approximately 20-30 GeV. This
decay mode has a substantially larger branching fraction compared to the Zγ decay, as Γ (H →γ ∗ γ → e+ e− γ) ∼ 3.5% × Γ (H → γγ) and Γ (H → γ ∗ γ → µ+ µ− γ) ∼ 1.7% × Γ (H → γγ), whileΓ (H → Zγ) = 2.3% × Γ (H → γγ) (which does not account for the subsequent decay of the Zboson to electrons or muons). With the Run-1 dataset, CMS observes an upper limit of 6.7 times
the SM branching ratio [198]. With a partial Run-2 dataset, in the γ ∗ γ CMS obtained a much
more stringent limits on the cross section times the corresponding branching fractions of 1.4 (6.1)
times the SM cross section [199]. CMS also performed a combination of this mode with H → Zγ,
obtaining a combined observed (expected) limit of 3.9 (2.0) times the SM branching fractions.
Using the full Run-2 dataset corresponding to 139 fb−1 , ATLAS obtained the first evidence for
Higgs boson decays to a low-mass dilepton pair and a photon with a significance of 3.2 (2.1) standard
deviations (expected) [200]. The invariant mass requirement on the di-lepton is m`` < 30 GeV. The
corresponding signal strength is µ = 1.5 ± 0.5, compatible with the SM expectation.
11.3.8.2 Higgs coupling to first generation, search for H → e+ e−
Probing the Yukawa couplings to the first generation fermions is extremely challenging at the
LHC given the overwhelming backgrounds and very small signal rates.
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A search similar to the H → µ+ µ− is performed in the non-VBF categories by CMS in the
di-electron channel [201]. In this search, the contribution from the peaking background from
Higgs boson decays to diphotons mis-identified as di-electrons (when converted photons are faking
electrons) needs to be carefully assessed. The sensitivity to the SM Higgs decays is negligible
given the extremely small branching fraction to e+ e− , approximately 40,000 times smaller than the
branching fraction to dimuons. It is nevertheless interesting to probe this decay channel to searchfor potential large anomalous couplings. Assuming a SM Higgs boson production cross section,
the observed limit on the H → e+ e− branching fraction at the 95% CL is 3.0 × 10−4 , more than
five orders of magnitude larger than the expected SM prediction. ATLAS has also performed asearch for the H → e+ e− decay mode with the Run-2 dataset, placing a limit of 3.6 × 10−4 on the
branching fraction [202].
It is important to note that processes not depending on the electron Yukawa coupling such as
the H → e+ e− γ (where the photon is soft), are sizeably larger than the direct Yukawa coupling
process, but also much smaller than the current constraints, making any interpretation in terms of
constraint on the electron Yukawa couplings far from straightforward.
11.3.8.3 Invisible decays of the Higgs boson
The discovery of the Higgs boson immediately raised the question of its couplings to DM andhow it could be used to reveal at colliders the existence of a dark sector coupled to the SM via
the Higgs boson portal, see Ref. [203] and references therein. If kinematically accessible and witha sufficiently large coupling to the Higgs boson, DM particles, such as, e.g., neutralinos in SUSY
models, graviscalars in models with extra dimensions or heavy neutrinos in the context of fourgeneration fermion models, would manifest themselves as invisible decays of the Higgs boson, thus
strongly motivating searches for the invisible decays of the Higgs boson.
It should be noted that in the Standard Model the branching fraction of a Higgs boson into
invisible decays through the H → ZZ ∗ → νννν process has a branching fraction of 0.12%.
To identify an invisibly decaying Higgs boson at the LHC, it must be produced in association
with other particles. Searches for invisible decays of the Higgs boson at the LHC have been carriedout in the three associated production modes of the Higgs boson with the highest SM cross sections
and target events with large missing energy.
The ggF production mode has the largest SM cross section but it usually results in the Higgs
boson being created alone and hence leaving no characteristic signature in the detector of its invisible
decay. One way to search for invisible decays in ggF production mode is to look for events withthe monojet topology arising from initial state gluon radiation and containing missing energy. The
major irreducible background in such searches stems from Z + jets events where the Z boson decays
into a pair of neutrinos [204]. The analysis with the best sensitivity targets the VBF production
topology but it suffers from large backgrounds arising from events with two jets and large missing
energy. The V H mode has much smaller cross section but the presence of a W or Z boson allows
a variety of final states that can be tagged with relatively low background.
ATLAS and CMS have searched for such final states at Run 1 and have observed no significant
excess over the predicted backgrounds (for references, see the previous edition of this review [141]).
Table 11.6 summarises the 95% CL limits on the invisible decays of the Higgs boson assuming a
SM Higgs boson production cross section and the corresponding detector acceptances.
ATLAS and CMS have performed the search for invisible decays of the Higgs boson at Run 2
with the full dataset in all the aforementionned channels [205–207]. The results are summarised inTable 11.6.
These constraints can then be further used to probe Higgs portal models to DM [203], where an
additional weakly interacting particle χ with mass lower than mH /2 is introduced as DM candidate
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Table 11.6: Summary of the channels searched for and the corresponding 95% CL limits fromATLAS and CMS on the branching fraction for the Higgs boson decay to invisible particles assuming
a SM Higgs boson production cross section. The results in parentheses are the expected exclusions.
ATLAS (Run 1)
ggF (monojet); H → inv.
VBF; H → inv.
ZH; Z → `+ `− ; H → inv.
VH; Z, W → jj; H → inv.
ZH; Z → bb; H → inv.
tt̄H; H → inv.
Run 1 & 2 Combination

ATLAS (Run 2)–
33 (38) %28 (31) %14.5 (10.3) %75 (62)%18.5 (18.5) %78 (86)%83 (58) %–––38 (30)%10.7 (7.7)%

CMS (Run 1)

CMS (Run 2)

67 (71) %49 (32)%57 (40) %18 (10) %75 (91) %–21 (18)%182 (189)%–
26 (30)%15 (8)%

and where the Higgs boson is considered as the only mediator between the SM particles and DM.
In this model, it is interesting to express the limit on the invisible branching fraction in terms ofstrength of interaction of DM with standard matter, i.e., in terms of it interaction cross section
with nucleons σχ−N . In this model, the couplings of the Higgs boson to SM particles are assumed
to be those of the SM and the interaction of the Higgs boson with the nucleon is parametrised ina Higgs-Nucleon form factor estimated using lattice QCD calculations [203]. The results for the
ATLAS llimits are shown in Fig. 11.4.

Figure 11.4: 90% CL upper limits on the spin-independent WIMP-nucleon scattering cross section as a function of the DM particle mass for direct detection experiments experiments and theinterpretation of the H → invisible combination result in models where the Higgs boson is a portal
between the SM matter and the Dark Sector. For the vector UV-model, m2 are two representative values of the predicted Dark Higgs particle with mixing angle α. The regions above the limit
contours are excluded in the range shown in the plot. From Ref. [205].

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11.3.8.4 Exclusive Higgs boson decays
A possibility to access the charm Yukawa coupling has been discussed in Ref. [208]. It relieson the decays of the Higgs boson to a final state with quarkonia. Searches have been performed inseveral channels including H → Υ γ, J/Ψ γ, φγ, ργ these processes can provide indirect constraints
on the Higgs boson Yukawa coupling to b, charm, strange and light quarks. The limits obtained so
far in these channels [209,210] are reported in the Higgs particle listings [188]. Limits on branching
fractions range between 10−3 –10−4 .
CMS has also performed a search of the decays of the Higgs boson in the J/Ψ J/Ψ and Υ Υ final
states to cover the cases where the photon in the J/Ψ γ decay is virtual and transforms into a J/Ψ
meson, These decays provide an additional channel potentially sensitive to BSM phenomena [211].
More recently a search for Higgs boson decays to mesons and a photon in the channels H → ωγand H → K ∗ γ have been carried out by the ATLAS experiment [212]. The limits on these processes
are of 1.5 × 10−4 and 8.5 × 10−5 on the ωγ and the K ∗ γ respectively.
Another class of searches for exclusive decays of the Higgs boson is H → ZQ where Q is aquarkomium state. This decay results from the interference of two contributions, one where the
Higgs boson couples to a quark-anti-quark pair which forms a quarkonium and radiates a Z boson atleading order, and another one from the off-shell decay H → ZZ ∗ or H → Zγ ∗ and the conversionof the off-shell Z or photon into a quarkonium. A search was carried out by ATLAS in the ZJ/Ψand Z/ηc channel in the Z → `+ `− and a light hadronically decaying resonance signature [213] andby CMS in the ZJ/Ψ and ZJ/Υ channels in fully leptonic final states [214].
11.3.8.5 Lepton flavour violating (LFV) Higgs boson decays
Given the Yukawa suppression of the couplings of the Higgs boson to quarks and leptons of thefirst two generations and the small total width of the Higgs boson, new physics decay modes could
easily have sizeable branching fractions. One very interesting possibility is the Lepton Flavour
Violating (LFV) decays of the Higgs boson, in particular in the τ µ and τ e modes. These decays
are suppressed in the SM but they could easily be enhanced in theories such as two-Higgs-doublet
models (discussed in Section 11.6). Indirect constraints on the LFV Yukawa couplings |Yτ µ | canbe obtained from channels such as the τ → 3µ or τ → µγ, or a re-interpretation of the search for
Higgs boson decays to τ + τ − . A direct search at the LHC, however, complements these indirect
limits.
The search for LFV decays in the τ µ, τ e and µe channels were carried out with the Run-1 andearly Run-2 datasets in several channels according to the subsequent decay of the τ [215–220]. The
limits on LFV decays of the Higgs boson are reviewed in this volume of the particle listings [188]and reached 0.15% in the τ µ channel and 0.22% in the τ e channel.
ATLAS [221] has performed the analysis with the full Run-2 dataset, yielding limits of 0.20%
and 0.18% on the eτ and µτ channels respectively. CMS [222] has performed analyses with thefull Run-2 dataset of the eµ channel reaching a limit of 4.4 × 10−5 at 95% CL.
The CMS search in the eµ channel was done not only at the specific Higgs boson mass, but in a
wider mass domain between 110 GeV and 160 GeV. A mild excess with a global significance of 2.8
standard deviations is observed for a mass hypothesis of approximately 146 GeV.
11.3.8.6 Flavour changing neutral current decays of the top quark
The discovery of the Higgs boson at a mass smaller than the top quark mass opened a new decay
channel for the top quark. The decays of the top quark to a Higgs boson and a charm or an up quark
proceed through a Flavour Changing Neutral Current (FCNC) which are forbidden in the Standard
Model at tree level and suppressed at higher orders through the Glashow–Iliopoulos–Maiani (GIM)
mechanism [3]. The SM prediction for these branching fractions is BR(t → Hc) = 10−15 and twoorders of magnitude less for the Hu final state. These decay channels of the top quark are, therefore,
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11. Status of Higgs Boson Physics

very interesting to probe possible FCNC interactions in the Yukawa couplings to the quark sector,
see Section 11.6.
ATLAS has searched for FCNC top decays specifically in channels involving a Higgs boson that
subsequently decays into a pair of b quarks, two photons, a tau pair or two W bosons [223]. It
has also reinterpreted a search for the tt̄H production in the multilepton final state (discussed
in Section 11.3.5.1) [173]. The latter channel covers Higgs boson decays to a pair of W bosons
and a pair of taus. No significant excess was observed in any of the specific channels (as discussed
in Section 11.3.5.1, a slight excess is observed in the tt̄H multilepton channel) and 95% CL upper
limits are set on BR(t → Hc) < 0.46% with an expected sensitivity of 0.25% and BR(t → Hu) <0.45% with an expected sensitivity of 0.29%. CMS has performed a search for these FCNC top
decays in the diphoton and multi-lepton channels [224], placing a 95% CL upper limit on BR(t →Hc) < 0.40% with an expected sensitivity of 0.43%.
From these limits on branching fractions, constraints on non-flavour-diagonal Yukawa couplingsof a FCNC Lagrangian of the form:
LFCNC = λtcH tHc + λtuH tHu + h.c.

(11.18)can be derived. The 95% CL observed (expected) upper limits from ATLAS on the |λtcH | and|λtuH | couplings are 0.13 (0.10) and 0.13 (0.10), respectively.
The results above are derived from the combination of several channels for searches performed
with Run-1 data. Both ATLAS and CMS have produced updates of individual channels with Run-2
data. ATLAS has searched for FCNC top decays with subsequent decays of the Higgs boson to apair of photons [225], yielding a 95% CL upper limit on BR(t → Hc) < 0.22% with an expected
sensitivity of 0.16%. CMS has searched for FCNC top decays with subsequent decays of the Higgs
boson to a pair of b-quarks [226], yiedling a 95% CL upper limit on BR(t → Hu) < 0.079% withan expected sensitivity of 0.011% and on BR(t → Hc) < 0.094% with an expected sensitivity of
0.086%.
11.3.8.7 Exotic Higgs boson decays
The 125 GeV Higgs boson serves not only as a probe for potential DM candidates, but also tosearch for other exotic particles arising from fields associated with a low-mass hidden sector (fora review, see for instance Ref. [227]). Such hidden sectors are composed of fields that are singlet
under the SM gauge group SU(3) × SU(2) × U (1). These models are referred to as hidden valley
models [228]. Since a light Higgs boson is a particle with a narrow width, even modest couplings
to new states can give rise to a significant modification of the Higgs boson phenomenology throughexotic decays. Simple hidden valley models exist in which the Higgs boson decays to an invisible
fundamental particle, which has a long lifetime to decay back to SM particles through a small mixing
with the SM Higgs boson, see Ref. [228] for a concrete example. The Higgs boson may also decay
to a pair of hidden valley “v-quarks,” which subsequently hadronise in the hidden sector, forming“v-mesons.” These mesons often prefer to decay to the heaviest state kinematically available, sothat a possible signature is H → 4b. Some of the v-mesons may be stable, implying a mixed
missing energy plus heavy flavour final state. In other cases, the v-mesons may decay to leptons,
implying the presence of low mass lepton resonances in high-HT events [229]. Other scenarios
have been studied [230] in which the Higgs boson decays predominantly into light hidden sector
particles, either directly, or through light SUSY states, and with subsequent cascades that increase
the multiplicity of hidden sector particles. In such scenarios, the high-multiplicity hidden-sector
particles, after decaying back into the SM, appear in the detector as clusters of collimated leptons
known as “lepton jets”.
A variety of models have been investigated searching for final states involving dark photons
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11. Status of Higgs Boson Physics

and hidden valley scalars. The resulting topologies typically have leptons or light hadrons which
in some cases can be prompt (i.e., originating from the hard process interaction point) or not andare in some cases collimated and reconstructed as jets [231, 232], and long-lived weakly interacting
particles. The latter occur not only in hidden valley scenarios, but also in gauge-mediated extensionsof the minimal SUSY standard model (MSSM), the MSSM with R-parity violation, and inelastic
DM scenarios [233]. Finally, CMS has performed a search for pair production of light bosons [234].
Such a scenario can occur in SUSY models with additional hidden (or dark) valleys.
11.3.9 Higgs boson pair production and self-coupling
Higgs boson pair production in the SM is a rare but very important mode to measure and searchfor. The measurement of Higgs boson pair production is essential to directly constrain the trilinear
Higgs boson self coupling and the search for Higgs boson pair resonances is key in a variety of BSM
models. The latter searches are discussed in Section 11.6.7.
In the SM, the main non-resonant production mode of two Higgs bosons proceeds through aloop, mainly of top quarks, see Fig. 11.1 (h). Another production mode is via the trilinear couplingof the Higgs boson, see Fig. 11.1 (i), whose amplitude is not negligible compared to the former.
These diagrams interfere negatively, making the overall production rate smaller than what would
be expected in the absence of a trilinear coupling.
11.3.9.1 Searches for Higgs boson pair production
The searches for Higgs boson pair production both resonant and non-resonant are important
probes for a variety of BSM theories, and they can be done in a large number of Higgs boson
decay channels. At Run 1, ATLAS and CMS have searched for both resonant and non resonant
Higgs boson pair production in the following channels: (i) HH → bbγγ; (ii) HH → bbτ +τ − ; (iii)
HH → bbbb; (iv) HH → bb4`; (v) HH → W W ∗ γγ; (vi) in final states containing multiple leptons (electrons or muons) covering the W W ∗ W W ∗ , W W ∗ ZZ ∗ , ZZ ∗ ZZ ∗ , ZZ ∗ τ + τ − , W W ∗ τ + τ − ,ZZ ∗ bb, τ + τ − τ + τ − channels; and (vi) γγτ + τ − channels.
At Run 2, similarly to the ttH production process, the di-Higgs production profits from asignificant increase in production cross section of a factor in excess of 3 from 8 TeV to 13 TeV, andmost of these channels have been updated both by ATLAS [235] and CMS [184, 236]. The detailed
description of the various analyses used can be found in the references therein. All the results andtheir combinations are summarised in Table 11.7 and in Fig. 11.5 (left). The channels (i)-(iii) are
the most sensitive to the HH production. These three channels have been updated with the full
Run-2 dataset except the HH → bbτ +τ − channel by CMS and the HH → bbbb channel by ATLAS
which have both been analysed using a partial Run-2 dataset.
In several of these analysis channels the VBF production mode is searched for separately providing sensitivity to the coupling involving two vector bosons and two Higgs bosons HHVV which
is an expected coupling in the Standard Model.
——————————————————————
The current single channel most stringent limits obtained on the HHVV coupling modifier
denoted κ2V are obtained from the analysis performed by CMS [237] in the bbbb:−0.1 < κ2V < 2.2 (observed),−0.4 < κ2V < 2.5 (expected)

and for the overall most stringent constraints are obtained through the combination of channels in
ATLAS, yielding [235]:−0.1 < κ2V < 2.0 (observed),

0.0 < κ2V < 2.1 (expected)

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11. Status of Higgs Boson Physics
Table 11.7: Summary of the final states investigated in the search for
Higgs boson pair production by ATLAS and CMS, the results reported inbold are based on the full Run-2 dataset. For ATLAS, the result indicatedby (*) uses mostly the bbW + W − channel. Results are 95% CL upper limits
on the observed (expected) signal strengths.
Channel

ATLAS

CMS

bbγγ

4.2 (5.7)

8.4 (5.5)bbbb

5.4 (8.1)

7.2 (4.2)bbτ + τ −4.7 (3.9)

3.3 (5.2)-

32 (40)W +W −W +W −160 (120)–

W + W − γγ

230 (170)

97 (52)bbV V

305 (305)*

14 (18)Multi-lepton–

19 (21)

Combination

2.4 (2.9)

3.4 (2.5)

bb4`

11.3.9.2 The Higgs boson self coupling
The Higgs boson self coupling is an extremely important direct probe of the Higgs potential
with implications on our understanding of the electroweak phase transition. Constraints on thetrilinear self coupling from HH processes is an outstanding long term goal of the LHC and thereach in sensitivity has been reappraised in the light of the recent HH analyses from ATLAS and
CMS, shedding a different light on the achievable sensitivity [118]. Constraints from the HHH
final state on the quartic Higgs boson self coupling are out of reach at the LHC due mostly to thevery small production rates and intricate final states.
In the SM, the Higgs boson pair production through the trilinear Higgs boson self coupling
has an on-shell component and a large off-shell component. The on-shell H → H ∗ H ∗ is strongly
disfavoured, requiring two off-shell Higgs bosons in the final state. The sensitivity region to thetrilinear coupling production as in Fig. 11.1 (i), is mainly in the kinematic region where the two
Higgs boson in the final state are on-shell and the Higgs boson acts as a propagator (off-shell). As
discussed in the introduction to this section, this process interferes negatively with the background
Higgs boson pair production (Fig. 11.1 (h)). The extraction of the trilinear component of the diHiggs production measurements is very similar to the extraction of the off-shell component of the
Higgs coupling to vector bosons discussed in Section 11.4.2.
The measurement of the trilinear coupling requires separating the contributions of the diagramof Fig. 11.1 (i) from the box diagram of Fig. 11.1 (h), and therefore a precise knowledge of the topYukawa coupling is needed. Each diagram alone would produce a rather distinct mHH distribution.
And, for values of the trilinear coupling close to the SM value, an additional discriminating featureof the signal with respect to one obtained with the box contribution alone is a deficit in the numberof events. With large variations of the trilinear coupling, an excess of events over the SM prediction
would be observed (for a value of the trilinear coupling about 6 times larger than its SM value, thenumber of events is equal to the SM expectation). Additional sensitivity to the trilinear couplingis also obtained from the kinematical distributions of the signal taking in particular into accountthe effect of the HH mass distribution which discriminates the main contributions of Fig. 11.1.
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11. Status of Higgs Boson Physics

This further discrimination is instrumental in resolving the degeneracy in the total cross section
mentioned above. Bounds on the trilinear coupling are obtained from limits on the HH production
as a function of the trilinear coupling factor κλ as illustrated in Fig. 11.5. As the sensitivity in thischannel grows it will be interesting to more closely look at the combined and individual likelihoods
as a function of the trilinear coupling to quantify the exclusion of the secondary minimum inducedby the degeneracy between the value of κλ yielding the same overall HH rate as the Standard
Model (i.e. κλ = 1). The results obtained by ATLAS [235] and CMS [184] are the following:(ATLAS) − 0.6 < κλ < 6.6 (observed), −2.1 < κλ < 7.8 (expected),(CMS) − 1.2 < κλ < 6.5 (observed),(11.19)where κλ is the ratio between the trilinear coupling value left free in the fit and its expected value
in the SM (κλ = 1 corresponds to the SM). For the CMS result the expected excluded range is not
specified in [184], however its illustration in the exclusion figure therin shows that it is compatible
with the observation. The so-called κ formalism is discussed in more detail in Section 11.5.1.1.
These results are also illustrated in Fig. 11.5.

Figure 11.5: (Left) Upper limits obtained by CMS on the total pp → HH production crosssection. (Top right) Upper limits obtained by ATLAS on the total pp → HH production crosssection as a function of the trilinear coupling modifier κλ . The variation of the limit corresponds tovariations in the signal acceptance. The expected total production cross section is also illustrated(red). (Bottom right) Likelihood contours for the ATLAS di-Higgs and single-Higgs combined
results as a function of κλ and κt .
Single Higgs production can indirectly also be used to further constrain the trilinear coupling of
the Higgs boson, both using inclusive total or differential cross sections. A combination of di-Higgs
and single-Higgs boson production results has been performed by the ATLAS collaboration yielding
the following limits [235]:−0.4 < κλ < 6.3 (observed),
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11. Status of Higgs Boson Physics

It is interesting to note that currently the direct (−0.6 < κλ < 6.6) and indirect constraints(−4.0 < κλ < 10.3) on the Higgs boson trilinear self-coupling are of comparable strength. However,the double Higgs boson measurements are dominated by statistical uncertainties and are expected
to improve more rapidly than the precision on single Higgs boson measurements. It should also
be stressed that the constraints on the trilinear self-coupling obtained via the NLO fit of single
Higgs boson data are model-dependent since the NLO effects induced by a shift of the trilinear selfcoupling compete with possible LO effects sourced by the deviations of the Higgs boson couplings
to the other SM particles. The different effects can be disentangled by the measurements of various
kinematical differential distributions in addition to the study of the inclusive rates [238], but the
expected sensitivity obtained in such global fits are not as strong as when only the Higgs boson
self-coupling is allowed to deviate from its SM value [119]. It should also be noted that in this fit
the parameters κt , κb , κτ and κV are fit simultaneously.
The analyses performed at Run 2 bring substantial improvements from those of Run 1, andthey were first used to reappraise the sensitivity of the LHC in the High Luminosity regime in theframework of the update of the European Strategy for Particle Physics [118]. The result in termsof bounds on the trilinear coupling indicated that the significance of the observation of the HH
process reaches 4σ. It is also apparent that the degeneracy of secondary minimum at intermediate
values of κλ is resolved by the use of the kinematic discriminants. This secondary minimum was
expected to be excluded at 99.4% CL and at HL-LHC, the foreseen precision on κλ was estimatedto reach approximately 50%. These studies were based on early LHC Run-2 analyses. Then in
the framework of the Snowmass2021 studies [239] and more recently using the latest HH searches
results, these projections have been updated. Both experiments have reappraised their studies at
HL-LHC [240], to reach individually a sensitivity of approximately 3.5σ, a significant improvementcompared to the sensitivities estimated between 2.5σ and 3σ in [118]. These studies indicate thata sensitivity of 5σ in combination of the two experiments should be reached at HL-LHC.
Higher precisions can be reached at pp colliders (and e+ e− colliders) at higher centre-of-massenergies. The foreseen precision for a High-Energy (HE) LHC at a centre-of-mass energy of 27 TeV
is expected to be within 10% to 20% [118]. At a very large hadron collider at a centre-of-massenergy of 100 TeV, a 5% sensitivity is expected to be reached, provided that the theoretical andparametric uncertainties are kept at the 1% level [241].
One of the main open questions in particle physics is related to the precise history of the
EWSB mechanism. This in turn can be of relevance to provide a mechanism for generating thematter -antimatter asymmetry of the universe at the electroweak scale, the so called electroweak
baryogenesis (EWBG) (see Refs. [242, 243] for some reviews). In the SM EWBG is ruled out, but
new physics models, in particular those additional scalar particles coupled/mixed with the Higgs
boson, can provide a successful alternative. Given that di-Higgs production will become an excellent
probe of trilinear Higgs coupling modifications, it will provide a unique window into the history of
EWSB and will become a powerful test of EWBG models.
11.3.10 Beyond the main Higgs boson production modes
Most of the production modes illustrated in Fig.11.1 have been investigated at the LHC so far.
These processes are often referred to as the ’main production modes’. Beyond these production
modes, two additional SM processes involving the Higgs boson have been investigated and are worth
noting.
The first is the four top production mode which is closely related to the ttH mode. This process
has recently been unambiguously observed at the LHC by both ATLAS [244] and CMS [245]. This
production mode has a non trivial contribution from the exchange of a Higgs boson. A first limiton the Yukawa coupling of the Higgs boson has thus been derived using this four top process,31st May, 2024

40

11. Status of Higgs Boson Physics|κt | < 1.8(1.6), under the assumption that the Yukawa coupling of the Higgs boson to top quarks
in CP even [244].
Another process beyond the main production modes is the associated W H production through
Vector Boson Fusion (VBF) yielding a topology of events with two jets in the forward region witha large rapidity gap, a W boson and a Higgs boson. This process is particularly interesting as it issensitive to the relative sign of the coupling of the Higgs boson to the W and Z boson through theinterference of the processes where the Higgs boson couples either to the W or the Z bosons in thevector boson fusion process. ATLAS has carried out analyses targeting at the decay of the Higgs
boson to bb and W + W − for this process, resulting in the exclusion of the opposite sign hypothesisby 8 standard deviations and an upper limit corresponding to 11.2 times the cross section expectedin the Standard Model [246].
11.3.11 First results on the main production and decay channels at 13.6 TeV
After a long shutdown between 2019 and 2022, devoted to the upgrades of the experiments andthe machine to prepare for the High Luminosity phase , in the Spring 2022 the LHC delivered pp collisions data at an enhanced centre-of-mass energy of 13.6 TeV. During this high-energy run, ATLAS
and CMS have collected datasets corresponding to integrated luminosities of approximately 60 fb−1
each. The first preliminary measurements of Higgs boson production at this increased centre-ofmass energy using the two high-resolution channels H → γγ and H → ZZ ∗ → `+ `− `0+ `0− havebeen carried out by ATLAS [247], see Fig. 11.6. The measurements are in good agreement within
the precision with the theoretical prediction which display the expected increase of approximately
7% in inclusive cross section from the increase in centre-of-mass energy.

Figure 11.6: Higgs boson production cross sections as a function of the pp centre-of-mass energy.
The SM predictions are shown by the shaded band.

11.4 Main quantum numbers and width of the Higgs boson
11.4.1 Main quantum numbers J PC
Probing the Higgs boson quantum numbers is essential to further unveiling its coupling properties. The measurements of the signal event yields in all the channels discussed in Section 11.3
and their compatibility with the SM Higgs boson predictions, give a qualitative but, nonetheless,compelling indication of its nature. For the observed particle not to be of spin 0 and +1 parity
would require an improbable conspiracy of effects. It is nevertheless important to test this hypoth31st May, 2024

11. Status of Higgs Boson Physics

41

esis independently, in particular since the measurements of coupling properties of the Higgs boson
assume that it is a CP -even state.
This qualitative picture is further complemented by the implications of the observation of theparticle in the diphoton channel. According to the Landau–Yang theorem [248], the observation
made in the diphoton channel excludes the spin-1 hypothesis and restricts possibilities for the spin
to 0 or 2.
The Landau–Yang theorem does not apply if the observed state is not decaying to a pair ofphotons but to a pair of scalars subsequently decaying to two very collimated pairs of photons (asfor example in the case of H → a1 a1 → 4γ). This possibility has not been rigorously excluded
but is not experimentally favoured since tight selection criteria are applied on the electromagnetic
shower shapes of the reconstructed photons. A more systematic analysis of shower shapes andthe fraction of conversions could be performed to further discriminate between the single prompt
photon and the two overlapping photons hypotheses. There are also potential theoretical loopholes
concerning the applicability of the Landau–Yang theorem, such as off-shell vector boson decays.
The spin 1 hypothesis has therefore been investigated quantitatively with the LHC Run-1
dataset and has been excluded at more than 95% CL through the analysis of the Higgs boson
decays to W W ∗ and ZZ ∗ channels. These results are reported in previous versions of this review
and will not be covered herein. [188].
11.4.1.1 Charge conjugation
The charge conjugation quantum number is multiplicative, therefore given that the Higgs-likeparticle is observed in the H → γγ channel, and given that photons are C-odd eigenstates, assuming
C conservation, the observed neutral particle should be C-even.
11.4.1.2 Spin and parity
To probe the spin and parity quantum numbers of the discovered particle, a systematic analysis
of its production and decay processes is performed in several analyses. These analyses are designed
to be independent of the measured event yields and they rely instead on the production and the
decay angles, and on the threshold distributions as long as a significant signal is observed, i.e.,
in situations when an excess over the expected background can be used to further discriminate
between signal hypotheses. These analyses are based on probing various alternative models of spin
and parity [249]. These models can be expressed in terms of an effective Lagrangian [250] or interms of helicity amplitudes [251]. The two approaches are equivalent.
i. Spin-0 models
The interaction Lagrangian relevant for the analysis of spin-0 particle interaction with a pair of W
or Z bosons with either fixed or mixed SM and BSM CP -even couplings or CP -odd couplings, isthe following [252]:
LW,Z
⊃
0



cos(α)κSM

1
gHZZ Zµ Z µ + gHW W Wµ+ W −µ
2



i
1 h
cos(α)κHZZ Zµν Z µν + sin(α)κAZZ Zµν Z̃ µν
4Λ
i
1 h
+
+
−
cos(α)κHW W Wµν
W −µν + sin(α)κAW W Wµν
W̃ −µν H,2Λ

−(11.20)where V µ = Z µ , W + µ are the vector boson fields, V ±µν are the reduced field tensors, Ṽ ±µν =1/2 εµνρσ Vρσ are the dual tensor fields, and Λ defines an effective theory energy scale. The factors
κSM , κHZZ , κHW W , κAZZ , κAW W denote the coupling constants corresponding to the coupling of
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11. Status of Higgs Boson Physics

42

the SM and BSM CP -even and CP -odd components of the Higgs boson to the W and Z fields.
The mixing angle α allows for the production of a CP -mixed state and the CP -symmetry is broken
when α 6= 0, π.
This formalism can be used to probe both CP -mixing for a spin-0 state, as discussed in Section 11.4.1.5 or specific alternative hypotheses, as discussed below, such as a pure CP -odd state(J P = 0− ) corresponding to α = π/2, κSM = κHV V = 0 and κAV V = 1. A BSM CP -even state
J P = 0+ corresponds to α = 0, κAV V = 0, κHV V = 1 and κSM arbitrary. These hypotheses arecompared to the SM Higgs boson hypothesis corresponding to α = 0 and κHV V = κAV V = 0 andκSM = 1. This formalism has been adopted by the ATLAS experiment.

Figure 11.7: Definition of the production and decay angles defined for the H → ZZ (∗) → 4` final
state.
A different parametrisation of anomalous couplings of a spin-zero boson with two gauge bosons
V V can also expressed in the general form of the scattering amplitude A:"A∼κV V q 2 + κV V q 2 κV V (q1 + q2 )2
aV1 V − 1 1 V V 22 2 − 3(Λ1 )(ΛVQV )2#∗(1) ∗(2)µν∗(1) ˜∗(2)µν
m2V1 ε∗V1 ε∗V2 + aV2 V fµνf+ aV3 V fµνf(11.21)

where εi is the polarization vector of the boson Vi , fµν = εµi q ν − ενi q µ is a scalar tensor constructed∗(i)from the vector boson Vi polarization and four momentum, f˜µν = 12 εµνρσ f ∗(i)ρσ is the corresponding pseudo-scalar tensor. Λ1 and ΛQ are new physics scales, a1,2,3 are coupling strength modifiersVand |κV(1,2,3)| = 0 or 1. This parametrisation can be used both for gluons, photons and electroweak
vector bosons, as well as the Zγ coupling. In the case of the W and Z bosons, the custodial symmetry would require that aW W = aZZ and, at tree-level, the only non-zero contributions would comefrom the a1 term. It is fully equivalent to the interaction Lagrangian approach described above.
This formalism has been adopted by the CMS experiment.
Finally, CP -odd interactions can also be expressed in the framework of the Standard Model
Effective Field Theory (SMEFT) in various possible bases (as discussed in Section 11.5.2). This
formalism is more in line with analyses of a broader ensemble of observable probing the Standard
Model. In this case the effective Lagrangian is defined as a function of the Φ† Φ gauge invariant and
I and B
the gauge field tensors before the electroweak symmetry breaking Wµνµν with three operators,
†
I
Iµν
†
I
µν
†
µν
Φ ΦW̃µν W , Φ ΦW̃µν B , and Φ ΦB̃µν B , and their corresponding Wilson coefficients cH W̃ ,cH W̃ B , and cH B̃ respectively.
∗(i)

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11. Status of Higgs Boson Physics

It is important to note that, as is apparant in Eq. (11.20), CP -odd couplings of the Higgs boson
to vector boson are not allowed at tree level and are therefore suppressed at higher order by thescale Λ. Instead, CP -odd couplings of the Higgs boson to fermions are allowed at tree level, thesecan be parametrised in a somewhat simpler fashion with the following Lagrangian which accounts
only for an additional pseudo-scalar term:λf ψ
L0 f ⊃ √ κf Hψ f ψf + iκ̃f Hψ f γ5 ψf .
2

(11.22)This formulation is equivalent to a definition a CP -mixing angle ϕf = tan κff .
It is interesting to note that CP -odd Higgs couplings to fermions could have a significant impact
on the very clean and precisely measured low energy observables as the electron EDM [253]. Owing
to its large Yukawa couplings, the CP -odd top Yukawa is strongly constrained by the stringent
electron EDM limits to better than κ̃t < 0.001 [253]. This makes it very challenging at the LHC to
surpass. However, one should keep in mind that EDM experiments provide an indirect constraint
on the SM Yukawa couplings, in particular in this case they constrain the product κe × κ̃t , and oneneeds to make assumptions on the value of κe , a quantity that remains out of reach experimentally.
The limits on the tau Yukawa coupling from the electron EDM constraints are much less stringent
and at the level of κ̃τ < 0.3 [253]. This makes the possibility of measuring CP mixing of the fermion
Higgs Yukawa couplings particularly interesting in the tau channels since these can be accessed fromthe Higgs decays directly using tau polarisation sensitive variable and will be discussed herein. For
more details on the searches for CP -odd couplings of the Higgs boson to vector bosons please see
previous versions of this review [188].
κ̃

ii. Spin-2 model
The graviton-inspired interaction Lagrangian for a spin-2 boson X µν that does not carry any color,weak and electromagnetic charge and that uniquely interacts with the energy momentum tensor
T V,f of vector bosons V or fermions f , can be written as follows [252]:


X
X
1
L2 ⊃  ξV T V X µν +
ξf T f X µν  ,

Λ

µν

V

µν

(11.23)fwhere the strength of the interaction is determined by the couplings ξV and ξf . The simplest
scenarios, referred to as universal couplings (UC), correspond to ξV = ξf . They predict a large
branching ratio to photons (of approximately 5%) and negligible couplings to massive gauge bosons(W and Z). They are therefore disfavoured, and other models are investigated where the couplingsof the W , Z and γ are assumed to be independent. Universality of the couplings refers to ξg = ξq .
Two other scenarios are considered: ξq = 0 and ξq = 2ξg . In these scenarios, a large enhancement of
the tail of the transverse momentum of the spin-2 state is expected and requires a further selection
requirement in order to probe the models within the range of validity of the effective field theory.
X
Two requirements are considered, pX
T < 300 GeV and pT < 125 GeV [250].
11.4.1.3 The V H production at D0
The mass of the V H system is a powerful discriminant to distinguish a J P = 0+ , with athreshold behaviour in dσ/dM 2 ∼ β, β 3 , β 5 from a 0+ , 0− and 2+ state, respectively [254]. The
V H mass observable not only discriminates signal hypotheses, but also has an increased separation
between the 0− and 2+ hypotheses with respect to the backgrounds, thus allowing, with a small
and not yet significant signal yield, to exclude that the observed state is 0− at 98% CL [255] and31st May, 2024

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11. Status of Higgs Boson Physics

2+ at the 99.9% CL [256], assuming a signal produced with their best fit signal strength (which wasµ = 1.23).
11.4.1.4 Probing the spin in the γγ channel at the LHC∗
In the H → γγ channel, the analysis is performed inclusively using the production angle cos θCS
and the transverse momentum of the diphoton pair [250]. The polar angle in the rest frame is definedwith respect to the bisector axis of the momenta of the incoming protons and is referred to as thepolar angle in the Collins–Soper frame [257]. The SM Higgs boson signal distribution is expected to
be uniform with a cutoff due to the selection requirements on the photons transverse momentum.
The H → γγ channel is mostly sensitive to the gluon-initiated spin-2 production scenarios, which∗ distribution peaking at values close to 1. The ATLAS limits are derived from a fit
yield a cos θCS∗of the signal in bins of cos θCSand diphoton transverse momentum. The data is compatible with+
the SM 0 hypothesis and contributes strongly to the exclusion of several spin-2 scenarios. The
conclusions are the same from CMS results [251].
11.4.1.5 Probing CP -mixing and anomalous HV V couplings
The careful study of the kinematic properties of angular distributions in events observed in the
H → ZZ (∗) → 4` and H → W W (∗) → `ν`ν channel, as well as the analysis of production observables sensitive to anomalous HVV interactions in the VBF or VH production have been used to set
limits wither on CP -mixing parameters, amplitude terms ot Wilson coefficients in the frameworkof SMEFT. These analysis assume that the observed particle is a spin-0 state, several results wereobtained by the ATLAS [258] and CMS [251] collaborations, all show a good agreement with theStandard Model CP -even hypothesis. Recent specific examples are given here.
In the H → W W (∗) → `ν`ν channel, the production and decay angles cannot be easily reconstructed due to the presence of neutrinos in the final state, however, sensitivity arises from the V −A
structure of the decay of the W bosons. A scalar state thus yields a clear spin correlation patternthat implies that the charged leptons e or µ from the decays of the W bosons are produced close to
one another in the transverse plane. This feature impacts observables such as the azimuthal angle
between the two leptons ∆Φ`` or their invariant mass m`` in addition to the threshold behaviourof the decay. It can be used to discriminate between various spin and parity hypotheses.
The H → ZZ (∗) → 4` coupling analysis, as described in Section 11.3, also uses a discriminant
based on the 0+ nature of the Higgs boson to further separate signal and background. In thisanalysis, this feature is used to discriminate between signal hypotheses. The observables sensitive
to the spin and parity have first been identified in Ref. [249,259,260] the masses of the two Z bosons(due to the threshold dependence of the mass of the off-shell Z boson [249, 261]), two production
angles θ∗ and Φ1 , and three decay angles, Φ, θ1 and θ2 . The production and decay angles aredefined as:– θ1 and θ2 , the angles between the negative final state lepton and the direction of flight of Z 1and Z 2 in the rest frame.
– Φ, the angle between the decay planes of the four final state leptons expressed in the four
lepton rest frame.
– Φ1 , the angle defined between the decay plane of the leading lepton pair and a plane definedby the vector of the Z 1 in the four lepton rest frame and the positive direction of the proton axis.
– θ∗ , the production angle of the Z 1 defined in the four lepton rest frame with respect to theproton axis.
These angles are illustrated in Fig. 11.7 [260].
These analyses are sensitive to various J P hypotheses and in particular discriminate the 0+
hypothesis from the 0− . In all scenarios investigated, and for both ATLAS and CMS, the data iscompatible with the 0+ hypothesis. ATLAS and CMS exclude a pure pseudo-scalar nature of the
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11. Status of Higgs Boson Physics

observed boson at CLS levels of 98% and 99.8% [251].
An individual ZZ ∗ channel measurement has also been carried out with a partial Run-2 dataset
by ATLAS [258]. CMS has performed a CP -mixing analysis of a partial Run-2 dataset of 36 pb−1
combined with the full Run-1 data using the ZZ ∗ channel [262]. In this analysis the CMS experiment sets constraints on the parameters defined in the parametrisation (11.21) of the scattering
amplitude.
With the full Run-2 dataset, analyses have started exploiting in combination both the production and decay modes of the Higgs boson as exemplified by the analysis carried out by ATLAS
using the H → ZZ ∗ → 4` analysis taking advantage of the production and decay angles of theprocess and VBF production sensitive observables [263]. Very similar analyses have been carriedout in CMS as well. The analysis uses optimal observables constructed from matrix elements of
the SMEFT. These optimal observables are defined from the ratio of the interference term between
the Standard Model and the SMEFT matrix elements (normalised to the Standard Model) for
given values of the Wilson coefficients cH W̃ , cH W̃ B , and cH B̃ below Eq. (11.21). As illustrated inFig. 11.8, all measurements are in agreement with the Standard Model. ATLAS has also performeda similar analysis with the Higgs boson decaying to two photons analysing the VBF production
mode [264] which can then be used to constrain the cH W̃ parameter as shown in Fig. 11.8.
An analysis of Higgs boson anomalous couplings HV V (as well as pseudo-scalar Yukawa coupling to the top) in the H → 4` channel was also carried out by CMS [265].

Figure 11.8: The measurement of the cH W̃ Wilson coefficent based on the optimal observablesensitive to the Higgs boson production, its decay and their combination (left) for the ATLAS
H → ZZ ∗ → 4` analysis. The measurement of the cH W̃ Wilson coefficent based on optimal
observable sensitive to the Higgs boson production in the VBF channel (right) for the ATLAS
H → γγ.
ATLAS has also performed an analysis using optimal observables [266], defined as the ratioof the interference between the CP -odd and the SM contributions normalised to the SM matrix
element squared, using the Run-1 data. In this study, the CP -mixing contributions are described in
˜ found to be consistent
the framework of an effective field theory governed by a single parameter d,with its SM value of d˜ = 0 and constrained to the interval [-0.11,0.05] at the 68% CL.
CP invariance in the HV V coupling can also be probed with the VBF production process inthe H → τ + τ − channel or similarly to the D0 analysis in the VH channels. CMS has performed ananalysis in this channel and has combined its results with the aforementioned ZZ ∗ channel using
the same dataset [267].
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11. Status of Higgs Boson Physics

Finally two aditional specific measurements as for example in H → W W ∗ jj [268] by ATLAS
and using the H → τ + τ − final state [269] by CMS in several production modes have also been used
to set limits on both anomalous CP -even and CP -odd couplings.
These measurements show the complementarity of the study of production and decay modes,
separately and in combination, and underscores the importance of a synthetic approach that combines all the available information.
11.4.1.6 Probing Hf f coupling CP properties in pp → ttH production
Although EDM limits disfavour large CP -odd effects in the top Yukawa coupling of the Higgs
boson, these indirect limits are model dependent. It is therefore important to further probe theseeffects directly. This can be achieved using the pp → ttH process. The increased sensitivity to
the this process at Run 2 in particular in the channels where the Higgs boson decays to a pair ofphotons provide a good sensitivity to the CP properties of the coupling through kinematics andangular distributions between the Higgs boson and the top quarks produced in the final state.
With the full Run-2 dataset, several Higgs boson decay channels have been investigated. ATLAS [270] excludes CP -mixing angles ϕt greater than 43◦ and smaller than −43◦ at 95% confidence
level in the H → γγ channel and has recently published constraints using the H → bb channel withoa measurement of ϕt = 11o +52−73o [271].
Also using the full Run-2 dataset, CMS [272] measures the CP -odd fraction defined as follows:fCP =|κ̃t |2
× sign(κ̃t /κt )|κt |2 | + |κ̃t |2

in the diphoton channel to be fCP = 0.00 ± 0.33. CMS also derived a constraint on the CP -odd
fraction using the H → 4` channel [265]. More recently CMS has analysed the ttH multi-lepton
channel, sensitive both to the H → W W and H → τ + τ − decays, to probe the top Yukawa
CP properties [273], and combined its results with the two aforementioned channels to yield thefollowing constraint on the CP -odd fraction:+0.27|fCP | = 0.28−0.28.

Both the ATLAS and CMS experiments used multivariate analyses in order to maximize the sensitivity to the measurement of the CP properties of the Hf f coupling. Both experiments usedleptonic and hadronic decays of the top quarks.
11.4.1.7 Probing Hf f coupling CP properties in H → τ + τ − decays
As discussed in Section 11.4.1, it interesting to investigate the CP properties of the Hf fcoupling is the Higgs decay to taus through tau polarisation sensitive variables.
CMS performed a first analysis with the full Run-2 dataset [274] of the transverse spin correlations between the tau leptons in the final state which are sensitive to the CP mixing angle orrelative component of the scalar and pseudo scalar couplings of the Higgs boson to taus. Thesetransverse spin correlations are in turn related to the direction of the decay products of the taus.
In the case of the two-body decay of a tau to a charged pion and a neutrino, the transverse
momentum component of the charged pions are typically anti-aligned for the case of a scalar
decay and aligned for the pseudo-scalar case. The angle between the decay planes as illustrated
in Fig. 11.9-(left) is therefore sensitive to the CP -mixing. Given that the tau direction cannot bemeasured directly, the impact parameter direction is used instead as a proxy, where the impact
parameter direction is defined as the direction between the interaction point and the point of closest
approach of the pion track. This direction in the rest frame of the Higgs boson are denoted λ± , asshown in Fig. 11.9-(centre). In the case of three-body or more decays of the taus as for example the
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11. Status of Higgs Boson Physics

decays to a intermediate rho or an a1 (1260) vector mesons which subsequently decay to ρ → π + π 0
and a1 → π + π 0 π 0 respectively, the planes are defined as either as the (π + , π 0 ) plane as as shownin Fig. 11.9-(centre) in the case of the ρ decay, or the plane formed by the cahrged pion and a
combination of the two neutral pions in the case of the a1 decay. The discrimination obtained,showing the two extreme fully scalar and pseudo-scalar cases are illustrated in Fig. 11.9-(right).
ATLAS performed a similar analysis [275]. The results obtained are the following:
ATLAS ϕτ = 9o ± 16o (0o ± 28o ) [274]
CMS ϕτ = −1o ± 19o (0o ± 21o ) [275]

It is interesting to note that the precision reached by both experiments is already at the level thatwas foreseen for HL-LHC by initial studies [276], which yielded a precision ranging between ±18o
and ±30o .

Impact Parameter
MethodNeutral Pion
MethodFigure 11.9: Sketch of the definition of the ϕCP angle for for the decays τ ± → π ± ντ (left) andthe definition at reconstruction level of ϕCP observables (center). The distribution weighted pertau decay categories of the ϕCP observables, including the expected distributions for the expected
pure scalar or pure pseudo scalar cases.
11.4.2 Off-shell couplings of the Higgs boson
In the dominant ggF production mode with a subsequent decay of the Higgs boson into a pairof electroweak vector bosons, the production cross section of an off-shell Higgs boson is known tobe sizeable. This follows as a consequence of the enhanced couplings of the Higgs boson to thelongitudinal polarization of the massive vector bosons at high energy.
The off-shell to on-shell cross section ratio is approximately 8% in the SM [277]. This part ofthe ’off-shell’ regime corresponding to the exchange of a Higgs boson as a propagator and not as anarrow mass state is very interesting as it is sensitive to physics beyond the SM. Still, the Higgs
contribution to V V production at large invariant mass remains small compared to the background.
In addition, the difficulty in the off-shell V V analysis, beyond the small signal-to-background ratio,
is due to a large negative interference between the signal and the gg → V V background.
The resulting presence of a SM Higgs boson signal in the far off-shell domain results in a deficitof events with respect to the expectation from background only events. It is only when the off-shell
couplings of the Higgs boson are larger than expected in the SM that the presence of a signal appears
as an excess over the background expectation. One additional intricacy arises from the precisionin the prediction of the rate for gg → V V , a loop process at lowest order, and its interference withthe signal.
Besides this ’continuum’ gg → V V background with which the ’off-shell’ Higgs process interferes,the largest background comes from the qq → V V production, making this analysis very challenging.
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It is interesting to note that, in this regime, the Higgs boson is studied as a propagator andnot as a particle. The measurement of its off-shell couplings is therefore absolute and does not relyon the knowledge of the total Higgs boson width. The off-shell coupling constraints can then be
used to indirectly constrain the width of the Higgs boson, under specific assumptions detailed in
Section 11.4.3.3.
This measurement has been carried out in the H → ZZ → 4`, H → ZZ → ``νν and H →W W → `ν`ν channels, via the ggF , V BF and V H production modes. To enhance the sensitivityof the analysis, the knowledge of the full kinematics of the events is important. In particular thesignal and the background can be further distinguished by the invariant mass of the V V system,
which is more accurately accessible in the H → ZZ → 4` channel. Angular distributions also play
an important role in this analysis. For these reasons, the H → ZZ (∗) → 4` channel is significantly
more sensitive than H → W W (∗) → `ν`ν.
Limits on the off-shell rates have been reported for the two channels by ATLAS [278] andCMS [279] with Run-1 data. The combined results, assuming that the off-shell rates in the ZZ and
W W channels scale equally, are given for two different hypotheses on the VBF production rate:
fixing it to its SM value or scaling it as the gluon fusion rate. The observed (expected) limits on theoff-shell rate fraction with respect to its SM expectation is 6.7 (9.1) for ATLAS [278] with the VBF
rate fixed to its SM value and 2.4 (6.2) for CMS [279] where no assumption is made on the relative
production rates of gluon-fusion and VBF. In both cases, the custodial symmetry is assumed andthe ratio of the rates in the ZZ and W W decays are fixed to those of the SM. Results without thisassumption have also been reported in Ref. [279].
The situation using the Run-2 data has significantly changed. Both ATLAS [280] and CMS [281]have performed off-shell Higgs boson analyses to constrain the off-shell Higgs boson production
rates with the full Run-2 datasets using the H → ZZ ∗ channel. The results obtained have alreadyreached an impressive sensitivity. Both experiments have considered two independent off-shell
contributions, the first corresponding to the ggF production denoted µg,off−shell and the second
corresponding the VBF and VH denoted µV,off−shell . For simplicity we will report only the results
considering µg,off−shell = µV,off−shell = µoff−shell here.
The first striking result is that both experiments exclude the background-only hypothesisµoff−shell = 0 with a significance of 3.2σ (2.2σ) observed (expected) for ATLAS [280] and 3.6σ
for CMS [281]. This corresponds to a first evidence for the off-shell production of a Higgs boson,through the measurment of a significant deficit in the overall gg → V V production.
The measured off-shell signal strengths µoff−shell are the following:+0.9(ATLAS) µoff−shell = 1.1+0.7−0.6 (obs) [1.00−0.9 (exp)],+0.56(CMS) µoff−shell = 0.74−0.38(obs) [1.00+1.00−0.84 (exp)].

(11.24)11.4.3 The Higgs boson width
In the SM, the Higgs boson width is very precisely predicted once the Higgs boson mass isknown. For a mass of 125 GeV, the Higgs boson has a very narrow width of 4.1 MeV [40]. It is
dominated by the fermionic decays partial width at approximately 75%, while the vector boson
modes are suppressed and contribute 25% only.
At the LHC or the Tevatron, in all production modes, only the cross sections times branching
fractions can be measured.
As a consequence, the total width of the Higgs boson cannot bedirectly derived form the measurements of Higgs boson rates without additional assumptions. Direct
constraints on the Higgs boson width are much larger than the expected width of the SM Higgs
boson.
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11.4.3.1 Direct constraints
Analyses of the reconstructed mass line-shape in the two channels with a good mass resolution,
the H → γγ and H → ZZ (∗) → 4` channels, allow for a direct measurement of the width of the
SM Higgs boson. The intrinsic mass resolution in these channels is about 1–2 GeV, much larger
than the expected width of the SM Higgs boson. As a result, only upper limits on the Higgs boson
width have been set by ATLAS [282] and more recently CMS [152]. The two main challenges of
direct constraints on the width through the measurement of the line-shape are: (i) the modellingof resolution uncertainties and (ii) the modelling of the interference between the signal and thecontinuum background which can be sizeable for large widths, in particular in the range where
direct constraints are set. These challenges affect mostly the diphoton channel. Given that theseinterference effects are small with respect to the individual channels sensitivity, they are neglected
in deriving constraints on the total width. The combined constraints, however, being more precise,
could be affected by the interference. Direct lineshape measurements provide the most unambiguous access to the Higgs boson width, however constraints are still two orders of magnitude larger
than the expected SM width. The current results are fully compatible with the SM hypothesis.
The most stringent limit is obtained by CMS of 330 MeV at 95% CL [152].
Another direct constraint on the Higgs boson width can be obtained, in the H → ZZ (∗) → 4`channel, from the measurement of the average lifetime of the Higgs boson calculated from thedisplacement of the four-lepton vertex from the beam spot. This analysis has been carried out by
CMS (see references in Ref. [141]), using the measured decay length. The measured cτH is 2+25
−2 µm,
yielding an observed (and expected) limit at the 95% CL of cτH < 57(56) µm. From this upper limiton the lifetime of the Higgs boson, the 95% CL lower limit on its width is ΓH > 3.5 × 10−12 GeV.

11.4.3.2 Indirect constraints from mass shift in the diphoton channel
In the diphoton channel, it was noticed in Ref. [283], that the effect of the interference between
the main signal gg → H → γγ and the continuum irreducible background gg → γγ, taking into
account detector resolution effects, is responsible for a non negligible mass shift. The size of themass shift depends on the total width of the Higgs boson and it was suggested that measuring thismass shift could provide a constraint on the width [283]. It was further noticed that the mass shift
has a dependence also on the diphoton transverse momentum. The total width of the Higgs boson
could therefore be constrained using the diphoton channel alone.
Further studies were performed by ATLAS to estimate the size of the expected mass shift [284].
The expected shift in mass in the diphoton channel is 35±9 MeV for the SM Higgs boson. Very
preliminary studies of the sensitivity of this method to estimate the width of the Higgs boson in
the High-Luminosity regime have been made by ATLAS [285] and yield an expected 95% CL upper
limit on the total width of approximately 200 MeV from 3 ab−1 of 14 TeV data.
11.4.3.3 Indirect constraints from on-shell rate in the diphoton channel
In the diphoton channel, it was noticed in Ref. [286], that the interference between the main
signal gg → H → γγ amplitude and the continuum irreducible background gg → γγ amplitude
generates non-negligible change in the on-shell cross sections, as a result of the existence of a relative
phase between these amplitudes. The size of this on-shell interference effect depends on the total
width of the Higgs boson and it was suggested that measuring this on-shell cross section precisely
could provide a constraint on the Higgs total width. This interference effect yields a reduction ofaround 2% for the gg → H → γγ cross section measurement in the SM. The current evaluationof this interference effect is performed at NLO and has a +50%
−30% uncertainty, due to the fact thatthe large relative phase is driven by the two-loop gg → γγ background amplitude [283, 286]. This
on-shell interference effect has a dependence on the pT of the diphoton system and the photon polar
angle in the diphoton rest frame, which can be further exploited to improve the measurement to
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50

constrain the Higgs total width.
Taking the ratios of the on-shell cross section of Higgs boson to diphoton channel and thecross section of Higgs boson to four-leptons channel where the interference effect is negligible could
put a bound on the Higgs boson total width. This ratio is free from many dominant sourcesof systematic uncertainties for cross section measurements, i.e., PDF uncertainty and luminosity
uncertainty, and can be further improved by the accumulation of the LHC data. From this crosssection ratio measurement alone, a preliminary estimation of the current limit from this interference
effect with current 30% precision puts an upper bound of 800 MeV on the Higgs boson total width
and the limit improves to 60 MeV with 3 ab−1 of 14 TeV data [286, 287].
11.4.3.4 Indirect constraints from off-shell couplings
Using simultaneously on-shell and off-shell measurements in the V V channels, it was noticed [277,288] that the total width of the Higgs boson could be constrained. This can be illustrated
from the parametrisation of the signal strength measurements both on-shell (µon−shell ) and off-shell(µoff−shell ) as a function of the couplings modifiers κg and κV parameterizing the main process
gg → H → V V (see Section 11.5.1 for the definition of these coupling modifiers). The on-shell andoff-shell signal strengths can be written as:µon−shell =κ2g, on−shell κ2V, on−shell,ΓH /ΓSMµoff−shell = κ2g, off−shell κ2V, off−shell .

(11.25)

A bound on the Higgs boson width can then be obtained from the measurements of the on-shelland off-shell signal strengths. This assumes that no new physics alters the Higgs boson couplingsin the off-shell regime, i.e., that the running of its couplings in this energy range does not differ
from the Standard Model [289, 290].
Both ATLAS [278] and CMS [281] have used their very strong off-shell production analyses
described above, with kinematic event characteristics to further gain in sensitivity to discriminate
between the signal and background.
In addition, in the CMS analysis, results are also derived allowing for anomalous couplingsof the Higgs boson, therefore reducing the discriminating power of the kinematic variables usedin the analysis but reducing the model dependence. The sensitivity already reached at Run 2 isremarkable:+3.8(ATLAS) ΓH = 4.5+3.3−2.5 [4.1−3.8 (exp)] MeV,(CMS)

ΓH = 3.2+2.4
−1.7

+4.0
[4.1−3.5(exp)] MeV.

(11.26)(11.27)ATLAS and CMS have also performed a study of the prospects for measuring the Higgs boson
width mainly in the four lepton channel. Projecting to a luminosity of 3 ab−1 , it was concluded
that, within assumptions similar to the ones mentioned above and assuming the SM central value,
the width of the Higgs boson could be constrained with the following precision [118]:+0.7
ΓH = 4.1−0.8
MeV.

11.5 Probing the coupling properties of the Higgs boson(11.28)

As discussed in Section 11.2, within the SM, all the Higgs boson couplings are fixed unambiguously once all the particle masses are known. Any deviation in the measurement of the couplingsof the Higgs boson could therefore signal BSM physics.
Measuring the Higgs boson couplings without relying on the SM assumption requires a generalframework treating deviations from the SM coherently at the quantum level in order to provide
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theoretical predictions for relevant observables to be confronted with experimental data. An attempt in that direction has been formalised in the so-called κ-formalism [291], following earlier
attempts [292] and initial phenomenological studies of the first hints of the existence of the Higgs
boson [293]. In this LO-inspired approach, the SM Higgs boson couplings are rescaled by arbitrary
factors, κ’s, keeping the same Lorentz structure of the interactions. This formalism allows for
simple interpretation of the signal strengths measured in the various Higgs channels. It has beenutilised to test various physics scenarios, like the existence of additional new particles contributing
to the radiative Higgs boson production and decays, or to probe various symmetries of the SM
itself, as for example the custodial symmetry. It only compares the experimental measurements totheir best SM predictions and does not require any new BSM computations per se. And, from amore theoretical perspective, its relevance arises from the fact that it actually fully captures theleading effects in single Higgs processes of well motivated scenarios. Still, the κ-formalism has
obvious limitations and certainly does not capture the most general deformations of the SM, evenunder the assumptions of heavy and decoupling new physics. A particularly acute shortcoming at
the time Higgs physics is entering a precision era is the lack of proficiency to assert the richnessof kinematical distributions beyond simple signal strength measurements. Several extensions andalternative approaches are being developed as part of the activities of the LHC Higgs Cross Section
Working Group [43].
The Higgs Pseudo-Observable (HPO) approach [294] allows one to report the data in termsof a finite set of on-shell form factors parametrising amplitudes of physical processes subject toconstraints from Lorentz invariance and other general requirements like analyticity, unitarity, andcrossing symmetry. These form factors are expanded in powers of kinematical invariants of theprocess around the known poles of SM particles, assuming that poles from BSM particles areabsent in the relevant energy regime. A set of HPOs have been proposed to characterise boththe Higgs boson decays and the EW Higgs boson production channels, thus exploring different
kinematical regimes. Prospective studies concluded that these HPOs can be measured/bounded at
the percent level at the HL-LHC and could therefore be used to constrain some explicit models of
new physics.
Another systematic and popular approach to characterise the possible Higgs boson coupling
deviations induced by BSM physics is the use of Effective Field Theories (EFT) [295,296]. This approach assumes again that the new physics degrees of freedom are sufficiently heavy to be integrated
out, and they give rise to effective interactions among the light SM particles. By construction, an
EFT approach cannot systematically account for deviations in Higgs physics induced by light degrees of freedom unless they are added themselves as extra fields in the effective Lagrangians,
requiring to know about these light fields beforehand. In Section 11.6, several examples of models
with light degrees of freedom affecting Higgs boson production and decay rates will be presented.
Like in explicit UV models and unlike the κ-approach, the main advantage of EFTs is their prowess
to relate different observables in different sectors and at different energies to constrain a finite setof effective interactions among the SM degrees of freedom. In an EFT, the SM Lagrangian is extended by a set of higher-dimensional operators, and it reproduces the low-energy limit of a more
fundamental UV description. It will be assumed that the Higgs boson is part of a CP -even EW
doublet, Φ, and that the Lagrangian is an analytic function of the gauge invariant Φ† Φ. This scenario is commonly referred as SMEFT. Even though it is not fully established experimentally, thisset-up is motivated by the measurements of the Higgs couplings to the different SM particles thatshow an alignement with their masses, such an alignment naturally follows under this assumptionof a linear realisation of the SU(2)L × U(1)Y symmetry of the SM. General Lagrangians bypassing
this linear assumption have been explicitly written down, see for instance Ref. [297], and connections with explicit UV models made [298, 299]. They rely on a chiral expansion with a specific31st May, 2024

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52

power-counting, effectively resumming the expansion in powers of the Higgs field, usually referred
as HEFT as opposed to SMEFT.
11.5.1 Probing coupling properties
11.5.1.1 From effective Lagrangians to Higgs observables
The κ framework, described in detail in Ref. [39, 291], facilitates the characterisation of Higgs
coupling properties in terms of a series of Higgs coupling strength modifier parameters κi , which aredefined as the ratios of the couplings of the Higgs bosons to particles i to their corresponding SM
values. The κ framework assumes a single narrow resonance so that the zero-width approximation
can be used to decompose the cross section as a product of two factors characterising the production
and the decay of the Higgs boson. The κ parameters are introduced by expressing each of the thesefactors as their SM expectation multiplied by the square of a coupling strength modifier for thecorresponding process at leading order:(σ · BR)(i → H → f ) =σiSM κ2i · ΓfSM κ2f
ΓHSM κ2H→µfi ≡κ2i · κ2f
σ · BR=,
σSM · BRSM
κ2H

(11.29)where µfi is the rate relative to the SM expectation and κ2H is an expression that adjusts the SM
Higgs width to take into account the modifications induced by the deformed Higgs boson couplings.
When all κi are set to 1, the SM is reproduced. For loop-induced processes, e.g. H → γγ, there is achoice of either resolving the coupling strength modification in its SM expectation, i.e., κγ (κt , κW )or keeping κγ as an effective coupling strength parameter.
The κ-framework is the simplest parametrisation directly related to experimental measurementsof the Higgs boson production and decay modes. For this reason, it has been widely used by thecommunity. It can also be connected to the SMEFT formalism as follows. Restricting to the EFT
directions not probed outside Higgs physics [300], the Higgs boson couplings are written in theunitary gauge as:m2Z
2m2W + −µα  2+Zµ Z µ H + κW
Wµ W H + κV V
cos θW Zµν Z µν + 2 Wµν
W −µν H
v
v
2πv
X
2α
α
mF
m2
αs a aµν
Gµν G H + κγ
Aµν Aµν H + κZγ Aµν Z µν H −κF
F F H + κ3 H H 3 + . . . .
+ κg
12πv
9πv
πv
v
2v
F
(11.30)L = κZThe exact correspondence between the effective coefficients of the dimension-6 operators and the
κ’s can be found for instance in Ref. [40]. In the SM, the Higgs boson does not couple to masslessgauge bosons at tree level, hence κg = κγ = κZγ = 0. Nonetheless, the contact operators are
generated radiatively by SM particle loops. In particular, the top quark gives a contribution to
the 3 coefficients κg , κγ , κZγ that does not decouple in the infinite top mass limit (for instance, inthat heavy limit, the top quark contribution amounts to ∆κγ = ∆κg = 1 [21, 22, 301], while the
W ± also contributes to κγ ). Depending on the nature of new physics, these effective couplings canbe generated at tree level or only at the radiative/loop level, see Refs. [295, 302–304] for further
discussions.
The coefficient for the contact interactions of the Higgs boson to the W and Z field strengths
is not independent but obeys the relation(1 − cos4 θW )κV V = sin 2θW κZγ + sin2 θW κγγ .

(11.31)This relation is a general consequence of the custodial symmetry [305], which also imposes κZ = κW
at leading order (κZ /κW − 1 is a measure of custodial symmetry breaking and, as such, is already
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11. Status of Higgs Boson Physics

constrained by electroweak precision data and the bounds on anomalous gauge couplings). When
the Higgs boson is part of an SU(2)L doublet, the custodial symmetry in the bosonic sector could←→ 2
only be broken by the OT = 21 Φ† D µ Φ operator at the level of dimension-6 operators and itis accidentally realised among the interactions with four derivatives, like the contact interactions
considered.
The coefficient κ3 is the trilinear Higgs boson self-coupling parameter which corresponds tothe more generic κλ self-coupling parameter discussed in Section 11.3.9.1. Before the associatedproduction of a Higgs boson with a pair of top quarks was observed, the Higgs boson coupling to
the top quark was only probed indirectly via the one-loop gluon fusion production or the radiative
decay into two photons. However, these two processes are only sensitive to the combinations ofcouplings (κt + κg ) and (κt + κγ ) and not to the individual couplings. Therefore a deviation in
the Higgs boson coupling to the top quark can in principle always be masked by new contact
interactions to photons and gluons (and this is precisely what is happening in minimal incarnationsof composite Higgs models [306]). The current and still limited sensitivity, of the order of 20%, in
the tt̄H channel leaves elongated ellipses in the direction κg = κγ = 1 − κt .
The operators already bounded by EW precision data and the limits on anomalous gauge
couplings modify in general the Lorentz structure of the Higgs couplings and hence induce somemodifications of the kinematical differential distributions [307]. A promising way to have a directaccess to the effective coefficients of these operators in Higgs physics is to study the V H associatedproduction with a W or a Z at large invariant mass of the V H system [308]. These differential
distributions could also be a way to test the hypothesis that the Higgs boson belongs to a SU(2)Ldoublet together with the longitudinal components of the massive electroweak gauge bosons.
11.5.1.2 Measurements of the Higgs boson coupling properties
As described in Section 11.3, a framework was developed by ATLAS and CMS [153], individually and together, to combine the very large number of exclusive categories aimed at reconstructing
the five main decay modes and the five main production modes of the Higgs boson. The general
conclusion of this combination, illustrating the compatibility of the observation with the SM expectations, is given in Section 11.3. The same framework with its master formula, Eq. (11.14),
can be used to further measure coupling properties of the Higgs boson under specific additional
assumptions.
i. Interpretations of the experimental data
The measurements of the coupling properties of the Higgs boson are entirely based on the formalismof the effective Lagrangian described above. Measurements of coupling properties in this framework
implies assessing the parameters of the model Eq. (11.30) or combinations of these parameters withdifferent sets of assumptions.
These measurements are carried out with the combination framework described in Section 11.3.6,
where the µi and µf signal strength parameters are further interpreted in terms of modifiers of the
SM couplings κk where k ∈ {Z, W, f, g, γ, Zγ} as in Eq. (11.30). The number of signal events per
category for the various production modes are typically estimated at higher orders in the analyses
but are scaled by these single LO-inspired factors, thus not taking into account possible intricacies
and correlations of these parameters through the higher-order corrections. This approximation isvalid within the level of precision of current results and their compatibility with the SM expectation.
In this formalism, further assumptions are explicitly made: (i) the signals observed in the different search channels originate from a single narrow resonance with a mass of 125 GeV; (ii) similarly
to the combination described in Section 11.3.6, the narrow width approximation is assumed (to31st May, 2024

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11. Status of Higgs Boson Physics

allow the decomposition of signal yields into products of production and decay signal strengths);(iii) the tensor structure of the couplings is assumed to be the same as that of a SM Higgs boson.
This means in particular that the observed state is assumed to be a CP -even scalar as in the SM.
Loop-level couplings such as the gg → H, H → γγ and H → Zγ can either be treated effectively,
with κg , κγ and κZγ as free parameters in the fit or these parameters can be expressed in terms of
the know SM field content and as a function of the SM coupling modifiers, in the following way [309]by either scaling cross sections (for κg given for a centre-of-mass energy of 13 TeV and a Higgs boson
mass of 125 GeV) or partial widths (for κγ and κZγ for a Higgs boson mass of 125 GeV):
κ2g (κt , κb , κc ) = 1.042 κ2t − 0.040 κt κb + 0.002 κ2b − 0.005κt κc + 0.0005κb κc + 0.00002κ2c ,
κ2γ (κt , κW ) = 1.59 κ2W − 0.66 κW κt + 0.07 κ2t ,(11.32)

κ2Zγ (κt , κW ) = 1.12 κ2V − 0.15 κV κF + 0.03 κ2F .

It should be noted that the parametrisation of the gluon coupling modifier could also be used toscale the H → gg partial width and would be different from the cross section parametrisation.
However when considered effectively, i.e., without resolving the content of the loop in terms of SM
fields, it can be assumed that the scaling behaviour of the production cross section and partial
width will be very similar.
The parametrisations are given for a Higgs boson mass hypothesis of 125 GeV (and in thelast two expressions, all the Higgs-fermion couplings are assumed to be rescaled by an universal
multiplicative factor κF ). It can be noted from the expression of κγ that the coupling of the Higgs
boson to photons is dominated by the loop of W bosons, and it is affected by the top quark loop
mostly through its interference with the W loop. The sensitivity of the current measurements to
the relative sign of the fermion and vector boson couplings to the Higgs boson is due to this large
negative interference term. The κg parameter is expressed in terms of the scaling of production crosssections and therefore also depends on the pp collisions centre-of-mass energy. The parametrisationsof κγ and κZγ are obtained from the scaling of partial widths and are only dependent on the Higgs
boson mass hypothesis. Experiments use a more complete parametrisation with the contributions
from the b-quarks, τ -leptons in the loops [39, 291].
The global fit is then performed expressing the µi and µf parameters in terms of a limited
number of κk parameters or their ratios, under various assumptions. The parametrisation for themain production modes are: (i) µggF = κ2g for the gluon fusion and an effective coupling of the Higgs
boson to the gluons; (ii) µVBF,V H = κ2V for the VBF and V H processes when the W and Z couplings
are assumed to scale equally, and µ2VBF (κW , κZ ) = (κ2W σW W H + κ2Z σZZH )/(σW W H + σZZH ), when
the couplings to the W and Z bosons are varied independently (σW W H and σZZH denote the VBF
cross sections via the fusion of a W and a Z boson respectively, the small interference term isneglected); (iii) µtt̄H = κ2t for the ttH production mode. Numerically the production modes signal
strengths as a function of the coupling modifiers to the SM fields for a centre-of-mass energy of
13 TeV and and Higgs boson mass of 125 GeV are:µggF = 1.040κ2t + 0.002κ2b − 0.038κt κb ,andµVBF = 0.73κ2W + 0.27κ2Z .

(11.33)The decay mode signal strengths are parametrised as µk = κ2k /κ2H where k ∈ {Z, W, f, g, γ, Zγ}
denotes the decay mode and κH , the overall modifier of the total width that affects all the signal
yields. κH is a priori an independent parameter. However, when it is assumed that the Higgs
boson cannot decay to new particles beyond those of the SM, κH can also be treated as an effective
parameter and expressed in terms of the coupling modifiers to the SM field content. Its general
expression is:κ2H = 0.57κ2b + 0.06κ2τ + 0.03κ2c + 0.22κ2W + 0.03κ2Z + 0.09κ2g + 0.0023κ2γ .
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11. Status of Higgs Boson Physics

The general expression of the total width of the Higgs boson can be written as follows:ΓH =κ2H ΓHSM
1 − BRBSM(11.35)where ΓHSM is the total width of the SM Higgs boson and BRBSM is the branching fraction of the
Higgs boson to new particles beyond the SM.
It is worth reminding that, in the absence of a measurement of the Higgs width wich can beaccessed through Off-Shell couplings measurements as discussed inSection 11.4.2, LHC requires
some hypotheses in order to extract the Higgs couplings from the measured Higgs signal strengths.
In particular, one can assume either (i) no BSM particles in the decay, or (ii) any BSM particles
in the decay would give rise to invisble signatures and thus be detectable through invisible Higgs
boson channels (or in other terms that there is no BSM undetected contribution), or (iii) |κV | ≤ 1.
These scenarios will be examined below.
Specific parametrisations will be made in order to address the following aspects of the coupling
properties of the Higgs boson under different assumptions, depending essentially on two assumptions
concerning either the natural width of the Higgs boson, whether it consists of partial width fromStandard Model particles only or not, or the effective couplings of the Higgs boson to photons,
gluons, Zγ and γ ∗ γ, whether these contributions are parametrised as function of the Standard
Model field content in the loops or whether these couplings are considered as effective.
Negative values of couplings are not excluded a priori, but would imply the existence of new
physics at a light scale and would also raise questions about the validity of the perturbative treatment of the SM deformations and also about the stability of the vacuum [310]. Since the results are
only sensitive to the relative sign of vector bosons with respect to fermions, by convention negative
coupling values will only be considered for vector boson couplings. Among the five main Higgs
boson decay channels, only the γγ is sensitive to the sign of κF (or κV ) through the interferenceof the W and t loops as shown in Eq. (11.32). The current global fit disfavours a negative valueof κF at more than five standard deviations. A specific analysis for the Higgs boson production inassociation with a single top quark has been proposed in order to more directly probe the sign ofκF (see references in Ref. [141]). All available experimental data show a fair agreement of the SM
prediction of the couplings of the Higgs boson to fermions and gauge bosons.
ii. Coupling measurements and probing BSM physics in loops and in the decay
Measuring Higgs boson couplings to other Standard Model fields requires either assumptions on the
total Higgs boson width, or an assumption on the coupling of the Higgs boson to vector bosons, or adirect constraint on the Higgs boson width as the one obtained from the ratio of off-shell to on-shell
Higgs boson couplings. These three cases will be discussed briefly. With the precision reached byanalyses discussed in Section 11.3.1, strong assumptions on the BSM content of the loop-induced
couplings of the Higgs boson to vector bosons as Hgg, Hγγ or HZγ are not needed and these
couplings can be considered as effective and provide a stringent probe of new fields potentiallyentering the loop.
Using the full Run-2 dataset and the formalism described in Section i., ATLAS [183] andCMS [184], have performed interpretations of the results presented in Section 11.3.6 to derivemeasurements of the Higgs boson couplings. These results are summarised in Table 11.8.
The results above are obtained under the assumption that the Higgs boson decays only to SM
particles. The degeneracy that originates from the fact that at LHC only production cross sections
times branching fractions are measured is embodied in the degeneracy between all κ factors andκH . It is interesting to note that in order to measure all couplings to be in agreement with the
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Table 11.8: Coupling modifier combined measurements assuming the absence of perceptible newphysics in the decay of the Higgs boson. No assumption is made for the loop level couplings of the
Higgs boson to gluons and photons which are considered as effective. The last column gives the
expected precision at the HL-LHC [118].
LHC Run 1 ATLAS Run 2 CMS Run 2 HL-LHC (expected)
κγ
κW

0.87 +0.14−0.09

1.01 ± 0.06

κt
κb
κτ

1.8%

1.04 ± 0.07

1.5%

1.01 ± 0.11

3.4%

0.92 ± 0.08

1.9%

1.05 ± 0.06

1.02 ± 0.08

1.7%

0.78 +0.13−0.10
1.40 +0.24−0.21
0.49 +0.27−0.15
0.84 +0.15−0.11

0.95 ± 0.07

0.92 ± 0.08

2.5%

0.89 ± 0.11

0.99 ± 0.16

3.7%

1.06 +0.25
−0.30
+0.31
1.38 −0.36

1.12 ± 0.21

4.3%

κZ −0.98 ± 0.10 0.99 ± 0.06
κg

1.10 ± 0.08

0.87 +0.13
−0.09

κµ

–

κZγ

–

0.94 ± 0.11
0.93 ± 0.07

1.65 ± 0.34

9.8%Standard Model model value requires that any deviation in the Higgs boson total width or κH be
precisely compensated by all couplings to Standard Model fields in the same fashion. This is often
referred to a flat direction, meaning that all the couplings are scaled by a factor α and the Higgs
boson width by a factor α2 . A model realising such flat direction is given in [311]. It requires theintroduction of a scalar field which decays for instance light hadrons which would not be detectablein the current experimental setups and are referred to as ’undetected’. It cannot be ’invisible’ as it
would otherwise be constrained by direct invisible Higgs boson constraints. The model parameters
would also have to lead to couplings of the Higgs to Standard Model fields to be larger than in
the Standard Model and a coupling of the Higgs boson to the scalar which will have to match thescaling of the Standard Model couplings. The former condition is exotic and the later requires a’conspiracy’.
As we have previously discussed, the flat direction can however be removed in two ways. The
first is to impose κV ≤ 1. This will induce a constraint on κH which can be seen for instance fromprocesses such as VBF Higgs production with subsequent decays to two vector bosons which areproportional to κ4V /κ2H . As was discussed, BSM scenarios yielding κV > 1 can be considered exotic.
The measurements using this constraints from the ATLAS experiment are shown in Fig. 11.10 (left).
The second is to use the Higgs boson width derived from the off-shell Higgs boson production
measurements. In this specific interpretation, the flat off-shell Higgs measurement constrain thevisible, invisible and undetected branching fractions. The ’visible’ branching fraction corresponds tothe Higgs branchings to Standard Model fields. The invisible branching fraction is constrained from’invisible’ Higgs searches. The flat direction is therefore represented by the ’undetected’ branching
fraction which is then constrained by the off-shell Higgs boson measurements. This constraint wasused in previous Higgs boson couplings measurements (see references for example the partial Run-2
combination performed in [312]).
Interpretations which are less sensitive to modelling systematic uncertainties and require no
constraints on the natural width of the Higgs bosons have been considered, either through the ratioof cross section and branching ratios (see results in Ref. [141]) or through a more generic approach to
avoid the degeneracy in the measurement of the coupling modifiers, probing the coupling properties
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11. Status of Higgs Boson Physics

57

CMS

κZ

W

1.4
1.2

Z
1.06

1.06

1.05

1.04

κ

ATLAS Run 2

κW

1.0

1.02

1.00

1

0.98

0.96

0.96

0.95

0.94

Leptons

κt

νe

κb

e

νµ
µ

0.6

Quarks

ντ

u
d

τ

c
s

b

0.92

0.9

0.9

2.6

2.0

2.8

3

3.2

3.4

3.6

3.8

4

6.6

g

γ

Z

W

H

1.0

κg

B inv. free, B u. ≥ 0, κ V ≤ 1

0.98

0.96

0.96

0.95
3

3.4

3.6

3.8

4

6.6

1.2

1.4

1.6
κ

B inv.
B u.

0.05

0.1

0.15

7.8

8

7.2

7.4

7.6

7.8

8

7.2

7.4

7.6

7.8

8

1.05

1.0

1.00

1

0.98

0.98

0.96

0.96

0.95

0.95
0.94

2.8

3

3.2

3.4

3.6

3.8

4

6.6

6.8

7

0.0

68% CL interval

0

7.6

1.02

2.6

1

7.4

1.04

1.00

0.94

0.8

7

1.06

1

0.5

κ Zγ

6.8

b
1.05
1.04

1.02

Parameter value not allowed

7.2

0.95
3.2

1.06

κ

κγ

8

0.94

2.8

t

1.5

SM prediction

7.8

1.00

1

0.98

2.6

B inv. = B u. = 0

7.6

1.02

0.94

0.0
2.0

7.4

1.04

1.00

1

0.5

κµ

7.2

1.05

1.04

1.02

κ

κτ

7

1.06

1.05

1.5

Higgs boson

6.8

g

γ
1.06

Force carriers

0.95

0.94

0.92

0.4

t

1.00

1

0.98

0.8

1.05

1.04

1.02

0.2

1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.0

95% CL limit

τ

µ
1.06

1.06

1.05

1.04

1.02

1.00

1

1.00

1

0.98

0.98

0.96

0.96

0.95

0.94

0.95

0.94

0.92

0.92

0.90

0.9

0.90

0.9

0.88

0.88

0.86

0.86

2.6

Disc

1.05

1.04

1.02

2.8

3

3.2

3.4

3.6

3.8

4

T
L
H
ove HC Ru his pa L-LHC
per
ry
n1

6.6

Obs. (stat ⊕ syst)
Proj. (stat ⊕ syst)

6.8

7

stat
syst

Figure 11.10: ATLAS [183] (left) and CMS [184] (right) combined measurements of coupling
modifiers with various assumptions. The ATLAS measurments also use the off-shell Higgs measurements.
of the Higgs boson through ratio of couplings. In the latter model, the cross section times branching
fraction of the gg → H → ZZ process is parametrised as a function of a single coupling modifier:κgZ = κg ×

κZ
.
κH

(11.36)

Then all combination signals can be parametrised with the following ratios of coupling modifiers:(i) the λZg = κZ /κg ratio which is mainly probed by the measurements of the VBF and ZH production; (ii) the λtg = κt /κg ratio constrained by the tt̄H production process; (iii) the λW Z = κW /κZ
ratio mainly probed by the W W and ZZ decay modes; (iv) the λτ Z = κτ /κZ ratio constrained bythe τ + τ − channel; (v) the λbZ = κb /κZ ratio probed mainly by the V H(bb) channels; and (vi) theλγZ = κγ /κZ ratio constrained by the diphoton channel. In this parametrisation, the ZZ channel
plays an important normalisation role (the results are discussed in detail in the previous edition ofthis review [141]).
11.5.1.3 Differential cross sections
To further characterise the production and decay properties of the Higgs boson, with the increasein size of the LHC datasets, measurements of fiducial and differential cross sections are being carriedout by ATLAS and CMS both at Run 1 (the references can be found in the previous edition of thisreview [141]) and Run 2 and in several channels [313–316]: the diphoton, the four leptons, the W W ,bb and τ + τ − channels.
The definition of a fiducial volume as close as possible to the reconstruction level selection
criteria is very important, as it will minimise the model dependence from possible variations inthe signal reconstruction efficiencies. Minimising model dependence of unfolded fiducial differential
cross section measurements is also key to ensure their usefulness to further probe and tune moreaccurate models in the future.
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While strict fiducial requirements are key to minimise model dependence, if the decay products
are part of the fiducial volume definition, these make combinations of decay channels impossible.
To gain precision in the measurement of the production properties of the Higgs boson, the fiducial
volume can be defined in terms of the Higgs boson distributions, while its decay channels andproperties are fully integrated. This has been used to combine differential cross section for instancein the transverse momentum of the Higgs boson. Such hybrid approaches are also discussed in
Section 11.5.1.5.
A large number of observables have been studied aiming at probing the accuracy of the modellingof the Higgs boson production simulations as well as measuring the properties of the Higgs boson.
The measured differential cross section in the Higgs boson transverse momentum by ATLAS
and CMS using the full Run-2 datasets are illustrated in Fig. 11.11 [314, 315, 317].
138 fb°1 (13 TeV)CMS Preliminary102

H ! ∞∞M AD G RAPH5 aMC @ NLO, NNLOPS ggH + HX
M AD G RAPH5 aMC @ NLO ggH + HX
POWHEG ggH + HX
HX = M AD G RAPH5 aMC @ NLO VBF+VH+ttH
Data, stat©syst unc.
syst unc.

100

p-value(SM): 0.236

æf id (pT > 450.0 GeV) /100.0 GeV¢æf id/¢pT(fb/GeV)

101

10°1

10°2

Ratio to prediction

10°3

2

0
0

100

200

300

400

500

pT(GeV)

Figure 11.11: (Left) Fiducial differential cross sections in Higgs boson transverse momentum inthe H → γγ channel from the CMS experiment [315]. (Right) Partially fiducial combined crosssections using the H → γγ and H → 4` channels from the ATLAS experiment [314].
The Higgs boson transverse momentum distribution is of particular importance to probe newphysics in the Higgs production. An example of interpretations that can be made using thesemeasurements is the constraints on the b and charm quark Yukawa couplings through their impact
on the production, both via the loop-level gluon fusion contribution or the gg → bbH, ccH processes. These results are also combined with the direct search for the V H(bb) process and shownin Fig. 11.12. It is interesting to compare the constraint, |κc | < 8.5, from the V H(cc) production
analysis alone and the limit obtained using only the differential distribution which is approximately
the double of the direct search limit as well as the limit that also uses the normalisation which yields|κc | < 2.3. The latter indirect limits assume that κb = 1. This shows the already good strengthof the shape analysis as well as the limit coming from the parametrisation of the normalisationin the H → γγ, 4` decay channels. The constraint coming from the normalisation is due to themodification of the total width from from the charm and b quark couplings [314].
11.5.1.4 Constraints on non-SM Higgs boson interactions in an effective Lagrangian
An example of the possible use of differential cross sections in constraining non-SM Higgs
boson couplings in an EFT is given by ATLAS [318]. In this analysis, differential cross section
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11. Status of Higgs Boson Physics

Figure 11.12: Measured likelihood contours for the κb and κc parameters from a simultaneous fitof the direct search for V H(bb, cc) analyses and the measurement of the differential cross section
in transverse momentum in the H → γγ, 4` channels, using the overall normalisation of the crosssections parametrised as a function of the κb and κc couplings and assuming no non-Standard Modelcontributions to the total width of the Higgs boson (left) and using only the differential shape intransverse momentum [314].
measured in the diphoton channel are used to constrain an effective Lagrangian where the SM is
supplemented by dimension six CP -even operators of the Strongly Interacting Light Higgs (SILH)
formulation [295] and corresponding CP -odd operators. The diphoton differential cross sections aremainly sensitive to the operators that affect the Higgs boson interactions with gauge bosons. CMS
has also recently analysed [313] the Higgs boson transverse momentum distribution to constrain
the Higgs boson couplings to top, bottom, and charm quarks as well as the effective coupling togluons. This analysis is, however, not performed in an EFT framework.
The differential distributions used in this combination are: (i) the transverse momentum of the
Higgs boson, (ii) the number of reconstructed jets produced in association with the diphoton pair,(iii) the invariant mass of the diphoton system and (iv) the difference in azimuthal angle of theleading and sub-leading jets in events with two or more jets. This analysis shows how differential
information significantly improves the sensitivity to dimension-6 operators.
11.5.1.5 Simplified Template Cross Sections (STXS)
An overarching subject of discussion between the theory and experimental communities in thefield of Higgs physics has been how experimentalists could best communicate their results to be
most efficiently used by others for further interpretation. The commonly used practice is that
results are given at particle level within a well-defined fiducial volume of phase space. The fiducial
volume is usually defined close enough to the experimental reconstruction to minimise the possible
variations of the reconstruction efficiency within the particle level fiducial volume. In this way,results minimise their dependence on theoretical uncertainties.
ATLAS and CMS have produced fiducial and unfolded cross sections based on all objects reconstructed in the events. These measurements could be used for further interpretation. However,
performing a proper combination of channels taking into account all experimental systematic uncertainties is non trivial and given the number of channels, combinations are very involved. A
proposal [40, 319] was made by the LHC Higgs Working Group to produce results in each decay
channel with a well defined fiducial phase space of the Higgs boson (and not its decay products)
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and for other associated objects pertaining to all channels, such as jets and missing transverse
momentum (MET). The definition of the fiducial regions is motivated by maximising the experimental sensitivity, isolating possible BSM effects, and minimising the dependence on theoreticaluncertainties. The number of regions is also minimised to avoid the loss of experimental sensitivity.
The observables that are measured in this approach are still the standard production cross sections(the gluon fusion, the vector boson fusion, the V H and tt̄H associated production modes) within
the defined fiducial volumes.
This approach is hybrid. It is fiducial on specific objects to reduce the theory dependence
and inclusive in the Higgs kinematics in order to allow for a more straightforward combination.
This approach also allows the use of multivariate techniques to enhance the sensitivity within given
fiducial regions, at the expense of a greater extrapolation and therefore increased model dependence.
The currently used Simplified Template Cross Sections (STXS) scheme covers, with a limited
number of bins, the ggF process in four categories in number of jets (0, 1, 2 and 2 VBF-likejets, where VBF-like means a selection of two high invariant mass jets with large pseudo rapidity
difference) further subdivided in four transverse momentum categories covering the full spectrumwith the last bin being inclusive for pT > 200 GeV. The V H process is subdivided in two categories
depending on the number of reconstructed charged leptons corresponding to the decays of either aW boson or a Z boson, and two bins in transverse momentum. VBF and hadronic V H categories
are defined using jet cuts and two bins in transverse momentum.
Measurements in this framework have been made in various decay channels. The first measurements have been performed in the main Higgs boson discovery channels. ATLAS and CMS haveproduced measurements of the diphoton and the 4` channels with Run-2 data [258, 314, 320–325].
The ATLAS and CMS collaborations have also performed measurements of the STXS in the
H → W + W − decay channel [326, 327].
CMS has also carried out a measurement of the STXS in the H → τ + τ − decay channel targetingthe high transverse momentum of the Higgs boson [156], in particular in the channel where the
Higgs boson is produced with one jet of transverse energy in excess of 200 GeV.
ATLAS [328] has made a measurement of the STXS aiming at the VH production mode in the
H → bb decay mode at high transverse momentum of the vector boson above 250 GeV, where thediscrimination of the background further increases.
A combination of STXS across decay channels has also been carried out by ATLAS with thefull Run-2 dataset [183, 329, 330].
11.5.2 Effective Lagrangian framework
The SMEFT has the same field content and it respects the same linearly-realised SU(3)C ×
SU(2)L ×U(1)Y local symmetry as the SM. The difference is the presence of operators with canonicalmass-dimension d larger than 4. These are organised in a systematic expansion in d, where eachconsecutive term is suppressed by a larger power of a high mass scale. Assuming baryon and lepton
number conservation, the most general Lagrangian takes the form
Leff = LSM +X (6) (6)
i

ci Oi

+

X (8) (8)jcj Oj + · · · .

(11.37)The contribution of the higher order operators of dimension d to physical amplitudes is suppressedby (E/Λ)d−4 , where E is the relevant energy scale of the process and Λ is the energy scale sup(d)pressing the higher-dimensional operators. The Wilson coefficients ci encode the virtual effectsof the heavy new physics in low-energy observables. Their precise forms in terms of masses andcouplings of the new particles can be obtained via matching with the ultraviolet (UV) completionof the SM [331–334], or inferred using specific power-counting rules [295, 335].
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Figure 11.13: Simultaneous combined measurement of simplified template cross sections assuming SM branching fractions of the Higgs boson [183].
The list of dimension-6 operators was first classified in a systematic way in Ref. [336] after theworks of Ref. [337]. Subsequent analyses pointed out the presence of redundant operators, and aminimal and complete list of operators was finally provided in Ref. [338]3 . For a single family offermions, there are 76 real ways to deform the SM generated by 59 independent operators. Withthe 3 families of fermions of the SM, flavour indices can be added to these 59 operators, andfurthermore, new operator structures, that have been dismissed by means of Fierz transformationsin the single family case, have to be considered, for a total of 2499 real deformations [341].
The numbers of operators to constrain can be reduced by imposing suitable flavour assumptions. Inspired by flavour physics, a U(2)q × U(2)u × U (2)d × U(3)l × U(3)e symmetry can be
enforced to impose a flavour symmetry in the first two quark generations and all three lepton
generations. ATLAS performed a detailed analysis of Higgs and EW data from LEP/SLD and
LHC. Under the previous flavour assumption, 22 operators are affecting Higgs observables alone,
22 operators are affecting EW precision observables alone and 11 operators are affecting both setsof observables simultaneously. Dedicated samples representing SM, linear, and quadratic effects ofdimension-six operators are generated at leading order using MadGraph5_aMC@NLO and SMEFTsim.
Events are interfaced to Pythia 8 to simulate parton shower and hadronization. The decays ofbottom and charm hadrons are performed by EvtGen. For the loop-induced processes, calculations
are performed with SMEFTatNLO, which allows for the calculation of NLO QCD corrections, insteadof SMEFTsim. Effects of dimension-six operators on background processes are usually not taken
into account except in the analysis of VBF Z measurement and of WW production. The results
are displayed in Fig. 11.14 [342]. The current measurements cannot currently constrain simultaneously all SMEFT Wilson coefficients as numerous degrees of freedom are not contrained by thedata. One option is to fit a limited (typically one) coefficient while fixing the others. Another3
Complete enumerations of d=8 operators have been obtained [339] and some preliminary constraints on peculiar
subsets of these operators have been derived from experimental measurements [340]. Still, in this review, the EFT
Lagrangians will be truncated at the level of dimension-6 operators.

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approach as shown in Fig. 11.14 is to perform a Principal Component Analysis (PCA) which

Figure 11.14: Constraints on Wilson coefficients from the combined LHC+EWPO analysis, presented in four blocks with different x-axis ranges. Right-hand side panel shows the contribution ofeach input measurement group to the eigenvector constraint in the Gaussian approximation.
will identify the sensitive and the flat directions of the likelihood and compute a modified basis
corresponding to a linear combination of the SMEFT coefficients [342]. For this reason the results
displayed in Fig. 11.14 illustrate coefficients with several indices, which correspond to the main
Wilson coefficients represented in a given direction of the PCA analysis. The superscript represent a numbering of different linear combinations with similar coefficients. These results show theexcellent agreement between measurements and the Standard Model expectations projected onto
[4]
SMEFT sensitive directions. The largest discrepancy is observed for the cHV V,V f f coefficient which

is driven by the longstanding discrepancy in the A0,b
F B measurements at LEP. In this paper [342],
ATLAS has performed both fits in the linear and quadratic parametrisations of SMEFT effects
corresponding to taking into account the interference between SM and SMEFT only or the entire
SMEFT effect (including the quadratic SMEFT contributions) respectively.
Phenomenological studies [343, 344] have also combined Higgs, diboson, and top quark pro31st May, 2024

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duction and decay measurements from the LHC and LEP to produce global fit of SMEFT at thedimension-6 order. Automated codes like or Matchete [334] or Matchmakereft [333] allows one
to match explicit UV models onto SMEFT and hence to interpret the global EFT fit to directly
constrain these UV models.

11.6 New physics models of EWSB in the light of the Higgs boson discovery

The discovery of a light scalar with couplings to gauge bosons and fermions that are consistent
with SM predictions, together with the slow running of the Higgs boson self-coupling at highenergies allow one to consider the SM as a valid perturbative description of nature all the way to
the Planck scale. This picture is admittedly very attractive, but it posits that the Higgs boson isan elementary scalar field, whose mass has quantum sensitivity to possible new physics scales. This
EW/Higgs naturalness problem [6] has become much more definite after the Higgs boson discovery.
There are two broad classes of models addressing the naturalness problem4 . One is based on
SUSY [7] (for recent reviews, see Refs. [8, 9]). This is a weakly coupled approach to EWSB, maintaining the perturbativity of the SM, and, the Higgs boson remains elementary and the corrections
to its mass are screened at the scale at which SUSY is broken so the value of the weak scale remains
insensitive to the details of the physics at higher scales. These theories predict at least three neutral
Higgs particles and a pair of charged Higgs particles [23]. One of the neutral Higgs bosons, mostoften the lightest CP -even one, has properties that can resemble those of the SM Higgs boson (atleast in some regions of the parameter space referred to as the alignment limit [346, 347], whichin the case of sufficiently heavy additional Higgs bosons is dubbed the decoupling limit [348, 349]).
Such scalar is referred to as a SM-like Higgs boson, meaning that its couplings are close to the ones
predicted in the SM. The other approach invokes the existence of strong interactions at a scale ofthe order of one TeV or above and these new interactions induce the breaking of the electroweak
symmetry [350]. In the original incarnation, dubbed technicolor, the strong interactions themselves
trigger EWSB without the need of a Higgs boson. Another possibility, more compatible with the
ATLAS and CMS discovery, is that the strong interactions produce four light resonances identified
with the Higgs doublet and EWSB proceeds through vacuum misalignment [10] (see Refs. [11, 12]
for recent reviews). In that case, the Higgs boson itself has a finite size and thus never feels the UV
degrees of freedom that would otherwise have dragged its mass to much higher scales. The Higgs
boson could also correspond to the Goldstone boson associated with the spontaneous breaking ofscale invariance, see Ref. [351] and references therein. However, this dilaton/radion scenario now
requires a jumbled model-building to be consistent with the constraints from the coupling measurements. All these BSM scenarios can have important effects on the phenomenology of the Higgs
boson. Also, in each case, the role of the Higgs boson in the unitarisation of scattering amplitudes
is shared by other particles which remain targets of experimental searches.
The realisation of SUSY at low energies has many good qualities that render it attractive as amodel of new physics. First of all since, for every SM degree of freedom, there is a superpartner ofdifferent spin but of equal mass and effective coupling to the SM-like Higgs boson, in the case ofexact SUSY, an automatic cancellation of quantum corrections to the Higgs mass parameter holds.
In practice, it is known that SUSY must be broken since no superpartners of the SM particles havebeen observed so far. The mass difference between the precise value of the mass of any particle
and that of its corresponding superpartner is proportional to the correlated soft SUSY breaking
parameter, generically called MSUSY . The quantum corrections to the Higgs boson mass parameter2
are proportional to MSUSY, and provided MSUSY is of order of a few TeV, the low energy mass
parameters of the Higgs sector become insensitive to physics at the GUT or Planck scale. Anotherinteresting feature of SUSY theories is related to the dynamical generation of EWSB [352]. In
4

Another solution to the naturalness problem is to lower the fundamental scale of quantum gravity, like for
instance in models with large extra-dimensions, see Ref. [345].
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the SM, a negative Higgs mass parameter, m2 , needs to be inserted by hand to induce EWSB,
see Eq. (11.1). In SUSY, instead, even if the relevant Higgs mass parameter is positive in theultraviolet, it may become negative and induce EWSB radiatively through the strong effect of the
top quark-Higgs boson coupling in its renormalisation group evolution [352].
In the following, the Higgs sector will be explored in specific SUSY models. In all of them, it
is often possible to find regions of the parameter space that accommodate one neutral Higgs bosonwith properties that resemble those of the SM Higgs boson, whereas additional neutral and charged
Higgs bosons are also predicted and are intensively being sought for at the LHC (see Section 11.6.7).
In the simplest SUSY model, accommodating a SM-like Higgs boson mass of about 125 GeV resultsin constraints on the stop sector, with at least one stop mass in the few TeV mass range. In
non-minimal SUSY extensions of the SM (details and related references can be found in the 2018
edition of this review [141]), a SM-like Higgs boson with mass of 125 GeV can be accommodatedwith less restrictions on the stop sector. While naturalness dictates relatively light stops and - at
the two loop level - also gluinos, the first and second generation of squarks and sleptons couple
weakly to the Higgs sector and may be heavy. Moreover, small values of the µ parameter andtherefore light Higgsinos, the fermionic superpartners of the Higgs bosons, would be a signature ofa natural realization of electroweak symmetry breaking [353]. Such SUSY spectra, consisting of TeV
range stop masses and light Higgsinos, continue to be under intense scrutiny by the experimental
collaborations [354], in order to understand if such natural SUSY scenarios endure and can explain
why the Higgs boson remains light.
In the context of weakly coupled models of EWSB, one can also consider multiple Higgs SU(2)Ldoublets as well as additional Higgs singlets, triplets or even more complicated multiplet structures,with or without low energy SUSY. In general, for such models, one needs to take into accountexperimental constraints from precision measurements and flavour changing neutral currents. The
LHC signatures of such extended Higgs sectors are largely shaped by the role of the exotic scalar
fields in EWSB.
The idea that the Higgs boson itself could be a composite bound state emerging from a newstrongly-coupled sector has been reconsidered thanks to the insights gained from the AdS/CFT
duality. The composite Higgs boson idea is an incarnation of EWSB via strong dynamics thatsmoothly interpolates between the standard technicolor approach and the true SM limit. To avoid
the usual conflict with EW data, it is sufficient, if not necessary, that a mass gap separates the Higgs
resonance from the other resonances of the strong sector. Such a mass gap can naturally follow
from dynamics if the strongly-interacting sector exhibits a global symmetry, G, broken dynamicallyto a subgroup H at the scale f , such that, in addition to the three Nambu–Goldstone bosons ofSO(4)/SO(3) that describe the longitudinal components of the massive W and Z, the coset G/Hcontains a fourth Nambu–Goldstone boson that can be identified with the physical Higgs boson.
Simple examples of such a coset are SU(3)/SU(2) or SO(5)/SO(4), the latter being favoured since it
is invariant under the custodial symmetry. It is also possible to have non-minimal custodial cosetswith extra Goldstone bosons leading to additional Higgs bosons in the spectrum, see for instanceRef. [355]. Modern incarnations of composite Higgs models have been recently investigated in theframework of 5D warped models where, according to the principles of the AdS/CFT correspondence,
the holographic composite Higgs boson then originates from a component of a gauge field along the
5th dimension with appropriate boundary conditions.
A last crucial ingredient in the construction of viable composite Higgs boson models is the concept of partial compositeness [356], i.e., the idea that there are only linear mass mixings between
elementary fields and composite states. After diagonalisation of the mass matrices, the SM particles, fermions and gauge bosons, are admixtures of elementary and composite states and thus theyinteract with the strong sector, and in particular with the Higgs boson, through their composite
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65

component. This setup has important consequences on the flavour properties, chiefly the suppression of large flavour changing neutral currents involving light fermions. It also plays an importantrole in dynamically generating a potential for the would-be Goldstone bosons. Partial compositeness also links the properties of the Higgs boson to the spectrum of the fermionic resonances, i.e.,
the partners of the top quark. As in the MSSM, these top partners are really the agents that trigger
the EWSB and also generate the mass of the Higgs boson that otherwise would remain an exact
Goldstone boson and hence massless. The bounds from the direct searches for the top partners,
in addition to the usual constraints from EW precision data, force the minimal composite Higgs
models into some unnatural corners of their parameter spaces [357].
11.6.1 Higgs bosons in the minimal supersymmetric standard model (MSSM)
The particle masses and interactions in a SUSY theory are uniquely defined as a function of thesuperpotential and the Kähler potential [9]. A fundamental theory of SUSY breaking, however, is
unknown at this time. Nevertheless, one can parametrise the low-energy theory in terms of the mostgeneral set of soft SUSY-breaking operators [9]. The simplest realistic model of low-energy SUSY
is the minimal SUSY extension of the SM (MSSM) [9,358], that associates a SUSY partner to eachgauge boson and chiral fermion of the SM, and provides a realistic model of physics at the weak
scale. However, in this minimal model, with the most general set of soft SUSY-breaking terms,
more than 100 new parameters are introduced. Nevertheless, only a subset of these parameters
impact the Higgs boson phenomenology either directly at tree-level or through quantum effects.
The MSSM contains the particle spectrum of a two-Higgs-doublet model (2HDM) extension of
the SM and the corresponding SUSY partners. Two Higgs doublets, Φ1 and Φ2 , with hypercharge
Y = −1 and Y = 1, respectively, are required to ensure an anomaly-free SUSY extension of the
SM and to generate mass for down-type quarks/charged leptons (Φ1 ) and up-type quarks (Φ2 ) [23].
The Higgs potential reads
V =m21 Φ†1 Φ1 + m22 Φ†2 Φ2 − m23 (ΦT1 iσ2 Φ2 + h.c.)1
1+ λ1 (Φ†1 Φ1 )2 + λ2 (Φ†2 Φ2 )2 + λ3 (Φ†1 Φ1 )(Φ†2 Φ2 ) + λ4 |ΦT1 iσ2 Φ2 |2(11.38)
2
2
h
i
h
i
1
+ λ5 (ΦT1 iσ2 Φ2 )2 + h.c. + [λ6 (Φ†1 Φ1 ) + λ7 (Φ†2 Φ2 )]ΦT1 iσ2 Φ2 + h.c. ,2where m2i = µ2 + m2Hi (i = 1, 2), with µ being the supersymmetric Higgsino mass parameter andmHi the soft supersymmetric breaking mass parameters of the two Higgs doublets; m23 ≡ Bµ is
associated to the B-term soft SUSY breaking parameter; and λi , for i = 1 to 7, are all the Higgs
quartic couplings.
After the spontaneous breaking of the electroweak symmetry, five physical Higgs particles areleft in the MSSM spectrum: one charged Higgs pair, H ± , one CP -odd neutral scalar, A, and two
CP -even neutral states, H and h, with h being the lightest.5 The Higgs sector at tree level depends
on the electroweak gauge coupling constants and the vacuum expectation value v – or equivalently
the Z gauge boson mass – and is determined by only two free parameters: tan β - the ratio of thetwo Higgs doublets’ vacuum expectation values v2 /v1 - and one Higgs boson mass, conventionallychosen to be the CP -odd Higgs boson mass, mA . The other tree-level Higgs boson masses are thengiven in terms of these parameters. The tree level value of mh is maximised not only for mA  mZbut also for tan β  1. For mA  mZ it acquires a maximum value mh = mZ cos 2β.
5Observe that in the SM sections of this review, H denotes the SM Higgs boson, whereas in the sections about
SUSY, or extensions of the SM with two Higgs doublets, H is used for the heaviest CP -even Higgs boson, since this is
the standard notation in the literature, and the 125 GeV SM-like light Higgs boson will be denoted by h. Generically,in the MSSM, the lightest CP -even Higgs boson is indeed SM-like and thus it is naturally identified with the 125 GeV
Higgs boson discovered by ATLAS and CMS, while in general 2HDM extensions, with or without SUSY, there could
still be lighter scalar states below 125 GeV.
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66

Figure 11.15: Values of the SUSY mass scale MSUSY = MS versus the stop mixing parameternormalised by the SUSY mass scale Xt /MSUSY , for fixed tan β = 20, µ = 200 GeV and At = Ab =Aτ . The solid black line corresponds to mh = 125 GeV while in the grey band mh varies by ±1 GeV.
The red dotted lines are iso-values of the stop mass in GeV. This figure is based on Ref. [360].
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Radiative corrections have a significant impact on the values of Higgs boson masses and couplings in the MSSM. The dominant radiative effects to the SM-like Higgs boson mass arise fromthe incomplete cancellation between top and scalar-top (stop) loops and at large tan β also fromsbottom and stau loops. The stop, sbottom and stau masses and mixing angles depend on the
SUSY Higgsino mass parameter µ and on the soft-SUSY-breaking parameters [9, 358]: MQ , MU ,MD , ML , ME , and At , Ab Aτ . The first three of these are the left-chiral and the right-chiral top
and bottom scalar quark mass parameters. The next two are the left-chiral stau/sneutrino andthe right-chiral stau mass parameters, and the last three are the trilinear parameters that enterin the off-diagonal squark/slepton mixing elements: Xt ≡ At − µ cot β and Xb,τ ≡ Ab,τ − µ tan β.
At one-loop, the electroweak gauginos yield a small contribution to the Higgs boson mass, and at
the two-loop level, the masses of the gluinos also enter in the calculations. Radiative corrections
to the Higgs boson masses have been computed using a number of techniques, with a variety of
approximations, see Ref. [359] for a recent review.
The discovered SM-like Higgs boson, if interpreted as the lightest MSSM Higgs boson with amass of about 125 GeV, provides information on the possible MSSM parameter space, see Fig. 11.15.
The phenomenology of the Higgs sector depends on the couplings of the Higgs bosons to gaugebosons and fermions. At tree-level, the couplings of the two CP -even Higgs bosons to W and Z
bosons are given in terms of the angles α, that diagonalises the CP -even Higgs boson squared-mass
matrix, and β
ghV V = gV mV sin(β − α), gHV V = gV mV cos(β − α),(11.39)where gV ≡ 2mV /v, for V = W or Z (gV mV is the SM hV V coupling). Observe that in the limitcos(β − α) → 0, the lightest CP -even Higgs boson h behaves as the SM Higgs boson. This situation
is called alignment and is achieved in specific regions of parameter space for mA ≥ mZ [348] or
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11. Status of Higgs Boson Physics

in the large mA  mZ limit, in which alignment is achieved through decoupling [348, 349]. There
are no tree-level couplings of A or H ± to V V . The couplings of the Z boson to two neutral Higgs
bosons are given by gφAZ (pφ − pA ), where φ = H or h, the momenta pφ and pA point into thevertex, andghAZ = gZ cos(β − α)/2, gHAZ = −gZ sin(β − α)/2 .
(11.40)The expressions of the couplings between a charged Higgs boson, a neutral Higgs boson and the Wboson as well as the expressions of the four-point couplings of vector bosons and Higgs bosons canbe found in Ref. [23].
The tree-level Higgs boson couplings to fermions obey the following property: the neutralcomponents of one Higgs doublet, Φ1 , couple exclusively to down-type fermion pairs while theneutral components of the other doublet, Φ2 , couple exclusively to up-type fermion pairs [23].
This Higgs-fermion coupling structure defines the Type-II 2HDM. In the MSSM, fermion masses
are generated when both neutral Higgs components acquire a vacuum expectation value, and therelations between Yukawa couplings and fermion masses are (in third-generation notation)√√hb,τ = 2 mb,τ /(v cos β), ht = 2 mt /(v sin β) .
(11.41)
The couplings of the neutral Higgs bosons to f f¯, relative to their SM values, g mf /(2mW ), aretherefore given byhbb̄ : − sin α/ cos β,htt̄ : cos α/ sin β ,(11.42)
Hbb̄ : cos α/ cos β,Htt̄ : sin α/ sin β ,Abb̄ : γ5 tan β,Att̄ : γ5 cot β .
In each relation above, the factor listed for √bb̄ also pertains to τ + τ − . The charged Higgs boson
couplings to fermion pairs, normalised to g/( 2mW ), are given bygH − tb̄ : mt cot β

1 + γ51 − γ5+ mb tan β,22gH − τ + ν : mτ tan β

1 − γ5.
2(11.43)The non-standard neutral Higgs bosons have significantly enhanced couplings to down-type fermionsat sizeable tan β. Radiative corrections can modify significantly the values of the Higgs boson
couplings to fermion pairs and to vector boson pairs, through a radiatively-corrected value forcos(β − α) as well as from the one-loop vertex corrections to tree-level Higgs-fermion Yukawa
couplings, see Ref. [9] and references therein, for a detailed discussion.
11.6.1.1 MSSM Higgs boson phenomenology
The MSSM parameters have to be arranged such that the mass, the CP properties, the decay
and production properties of one of the neutral Higgs bosons agree with the LHC Higgs data.
Given that present data allows only for moderate departures from the SM predictions, it implies
that some degree of alignment is necessary.
The SM-like branching ratios of h can be modified if decays into SUSY particles are kinematically allowed, and, in particular, decays into a pair of the lightest SUSY particles – i.e., the lightest
neutralinos, χ̃01 – can become dominant and would be invisible if R-parity is conserved [361]. Moreover, if light superpartners exist and couple to photons and/or gluons, the h loop-induced couplingto gg and γγ could deviate sizeably from the corresponding SM predictions (see for instance thereview [362]), and would be in conflict with present data (see Section 11.3). For the heavier Higgs
states, there are two possibilities to be considered6 :6
In very special regions of the parameter space, there is still the possibility that the heavier CP -even Higgs state is
identified with the 125 GeV Higgs boson discovered by ATLAS and CMS, see for instance the discussion in Ref. [363]125
and the benchmark MH
defined in Ref. [364].

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11. Status of Higgs Boson Physicsi) Alignment triggered by decoupling, hence mA ≥ several hundred GeV: The HW W and HZZ
couplings are very small. The dominant H, A decay branching ratios strongly depend on
tan β. The decay modes H, A → bb̄, τ + τ − dominate when tan β is large (this holds evenaway from decoupling). For small tan β, the tt̄ decay mode dominates above its kinematicthreshold. For the charged Higgs boson, H + → tb̄ dominates.
ii) Some degree of alignment without decoupling, hence mA ≤ a few hundred GeV: The maindifference with the previous case is that, in the low tan β regime (tan β ≤ 5), additional decay
channels may be allowed which involve decays into the lightest SM-like Higgs boson; A → Zh,
H → hh as well as H → W W/ZZ decay modes are available (they are suppressed in the strictalignment limit). When kinematically open, the decays A/H → tt̄ become relevant or evendominant for sufficiently small tan β. For the charged Higgs boson, H + → τ + ντ dominates
below the tb̄ threshold, and also H ± → W ± h may be searched for.

In both cases i) and ii), the heavier Higgs states, H, A and H ± , are roughly mass degenerate(with masses ± 20 GeV or less apart). If kinematically allowed, the heavy Higgs boson decays into
charginos, neutralinos and third-generation squarks and sleptons can be important [365].
At hadron colliders, the dominant neutral Higgs boson production mechanism at moderatevalues of tan β is gluon fusion, mediated by loops containing heavy top and bottom quarks andthe corresponding SUSY partners. The effect of light stops that may contribute to the gluon
fusion production can be partially cancelled by mixing effects. Higgs boson radiation off bottom
quarks becomes important for large tan β, where at least two of the three neutral Higgs bosons
have enhanced couplings to bottom-type fermions [366, 367]. Detailed discussions of the impact
of radiative corrections in these search modes are presented for instance in Ref. [368]. The vectorboson fusion and Higgs-strahlung production of the CP -even Higgs bosons as well as the associatedproduction of neutral Higgs bosons with top quark pairs have lower production cross sections by atleast an order of magnitude with respect to the dominant ones, depending on the precise region of
MSSM parameter space [37–40]. Higgs boson pair production of non-standard MSSM Higgs bosons
has been studied in Ref. [369]. For a discussion of charged Higgs boson production at LHC, see
Refs. [38, 39, 370].
Strong production of a heavy neutral Higgs boson followed by its decay into top-quark pairs is achallenging channel, only most recently being searched for by ATLAS and CMS. Interference effects
between the signal and the SM tt̄ background need to be carefully taken into account [371, 372].
Summarising, the additional Higgs bosons are sought for mainly via the channels:
pp → A/H → τ + τ − (inclusive),bb̄A/H, A/H → τ + τ − (with b-tag),bb̄A/H, A/H → bb̄ (with b-tag),pp → tt̄ → H ± W ∓ bb̄, H ± → τ + ντ (τ − ν̄τ ) or tb̄ (bt̄) ,gb → H − t or g b̄ → H + t̄, H ± → τ + ντ (τ − ν̄τ ) or tb̄ (bt̄) .

(11.44)After the Higgs boson discovery, updated MSSM benchmarks scenarios have been defined to highlight interesting conditions for the MSSM Higgs boson searches [39, 364] and are scrutinised by the
LHC Higgs Working Group [373]. The latest benchmark scenarios update [364], partly based in
MSSM parameter space discussions in Ref. [374], considers six benchmarks to illustrate different
aspects of Higgs phenomenology in the MSSM. They include one case with complex parameters, butthey all assume R-parity conservation and no flavour mixing. Each scenario contains one CP -evenscalar with mass around 125 GeV and SM-like couplings. These scenarios include a Mh125 scenario
with relatively heavy superparticles, so the Higgs phenomenology at the LHC resembles that of a
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11. Status of Higgs Boson Physics

2HDM with MSSM-inspired Higgs boson couplings. Other two scenarios are characterised by someof the superparticles – staus or electroweakinos – being relatively light, that in turn is of relevancefor heavy neutral Higgs boson searches. In particular, the traditional A/H → τ + τ − search channel
varies depending on the values of µ and M2 , that may enable the A/H decays into electroweakinos.
Another two scenarios are characterised by the phenomenon of alignment without decoupling, inwhich one of the two neutral CP -even scalars has SM-like couplings independently of the mass
spectrum of the remaining Higgs bosons, hence allowing for all the Higgs bosons to have relatively
low mass values (about few hundred GeV). Finally, there is one scenario which incorporates CP
violation in the Higgs sector and gives rise to a strong admixture of the two heavier neutral states.
All the above scenarios assume all parameters in the mass range from 1 to a few TeV, hence they
are not applicable for values of tan β of order a few, for which a Higgs boson mass value of 125 GeV
is out of reach. An additional study [375], relying on an EFT approach in the MSSM, focusses on
two scenarios specifically designed for the low tan β region and ensures a 125 GeV Higgs boson massin almost the entire parameter space by employing a flexible supersymmetric mass scale, reachingvalues of up to 1016 GeV.
An alternative approach to reduce the large number of parameters relevant to the Higgs sector
is to consider that, in the Higgs basis, the only important radiative corrections are those affecting
the Higgs boson mass [376]. This approximation is called hMSSM and works well in large regions ofparameter space but it breaks down for sizeable values of µ and At , and moderate values of tan β,
for which the radiative corrections to the mixing between the two CP even eigenstates become
relevant. The effect of such radiative corrections is to allow for alignment for small to intermediate
values of tan β, independent of the specific value of mA [346]. In addition, the hMSSM assumptionthat the right value of the Higgs boson mass may be obtained for all values of mA and tan β
is in conflict with the MSSM predictions for the Higgs boson mass for small values of mA andtan β ' O(1). The recent Mh125 [364] and EFTMSSM benchmarks [375], are designed to address
the limitations of the hMSSM, in particular the low tan β region for the EFTMSSM.
The compatibility between the predicted and measured Higgs boson mass sets stringent constraints on the parameter space of BSM models. The predictions are illustrated in Fig. 11.16 fortwo concrete scenarios. Note that to use the predicted Higgs boson mass as a constraint (exclusion
at nearly constant tan β at high MA in the (MA ,tan β) plane), it is important to account for thetheoretical uncertainty on the prediction which is in excess of an order of magnitude larger thanthe experimental uncertainty on the measured mass of the Higgs boson. The theoretical uncertainty depends itself on the specific SUSY spectrum for a given MSSM parameter set and shouldbe estimated accordingly, however, a more generic estimate of ±3 GeV is made and found to be aconservative choice [359].
Reviews of the properties and phenomenology of the Higgs bosons of the MSSM can be foundfor example in Refs. [9, 362, 378]. Future precision measurements of the Higgs boson couplings tofermions and gauge bosons together with information on heavy Higgs boson searches will provide
powerful information on the SUSY parameter space [379].
Improvements in our understanding of B-physics observables put indirect constraints on additional Higgs bosons in mass ranges that would be accessible in direct LHC searches. In particular,BR(Bs → µ+ µ− ), BR(b → sγ), and BR(Bu → τ ν) play an important role within minimal flavourviolating (MFV) models [380], in which flavour effects proportional to the CKM matrix elements
are induced as in the SM [381].
11.6.2 Supersymmetry with singlet extensions
The Higgs mass parameter µ is a SUSY parameter, and as such, it should naturally be of order
MGU T or MP lanck . The fact that phenomenologically it is required that µ be at the electroweak/TeV
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11. Status of Higgs Boson Physics

70
Mh125 scenario

Mh [GeV]

60

50

50

40

40
tan β

tan β

60

30

Mh125(χ̃) scenario

Mh [GeV]

7
12

30

20

125

20

10

124
122

10

126

500

1000
MA [GeV]

1500

2000

125
124
122

500

1000
MA [GeV]

1500

2000

Figure 11.16: The 95% CL exclusion contours in the (MA , tan β) parameter space for the Mh125(right) and Mh125 (χ̃)(left) benchmark scenarios [377]. The Mh125 benchmark assumes that superpartners are heavy, so that the phenomenology of the observed Higgs boson is not altered except
in its couplings due to the existence of another doublet. The Mh125 (χ̃) scenario on the other handconsiders light electroweakinos and therefore the heavy Higgs bosons H and A can have sizeable
decay rates to charginos and neutralinos, consequently suppressing the τ + τ − decay rate. The
nearly vertical dotted line illustrates the lower limit on the mass of the A boson from precision
measurements of the Higgs boson couplings and the close-to horizontal dotted line represents thelimit on tan β from the compatibility of the measured mass of the observed Higgs boson and theprediction using radiative corrections (mostly from the stop sector).
scale is known as the µ problem [382]. SUSY models with additional singlets can provide a solution
to the µ problem, by promoting the µ parameter to a dynamical singlet superfield S that onlyinteracts with the MSSM Higgs doublets through a coupling λS at the level of the superpotential.
An effective µ is generated when the real scalar component of S acquires a vacuum expectation
value vS , yielding µeff = λS vS . After the minimization of the Higgs potential, the vacuum state
relates the vacuum expectation values of the three CP -even neutral scalars, v1 , v2 and vS , to thescalar doublet and singlet soft SUSY breaking masses, hence, one expects that these VEVs should
all be of order MSUSY and therefore the µ problem is solved.
The addition of a singlet superfield to the MSSM may come along with additional symmetries
imposed to the theory. Depending on such symmetries, different models with singlet extensions of
the MSSM (xMSSM) have been proposed, see Ref. [383] for a general review. Among the moststudied examples are the NMSSM with an additional discrete Z3 symmetry (first introduced inR
Ref. [384]), the Nearly-Minimal SUSY SM (nMSSM), with additional discrete ZR
5 , and Z7 symmetries [385], and the U(1)0 -extended MSSM (UMSSM) [386]. A Secluded U(1)0 -extended MSSM
(sMSSM) [387] contains three singlets in addition to the standard UMSSM Higgs boson singlet;
this model is equivalent to the nMSSM in the limit that the additional singlet VEV’s are large,
and the trilinear singlet coupling, λS , is small [388]. The non-zero neutrino masses provide also a
motivation for a particular extension of the MSSM, µνSSM [389], which also happens to address
the mu problem. The computation of the Higgs boson spectrum in these various models has beenreviewed in Ref. [359].
A singlet extended SUSY Higgs sector opens new avenues for discovery. Since the singlet
pseudoscalar particle may be identified as the pseudo-Goldstone boson of a spontaneously broken
Peccei–Quinn symmetry, it may become naturally light [390]. Generally, there is mixing of the
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11. Status of Higgs Boson Physics

singlet sector with the MSSM Higgs sector, and for a sufficiently light, singlet-dominated scalar or
pseudoscalar, hS or AS , respectively, the SM-like Higgs boson h may decay to pairs of hS or AS .
The light scalar and/or pseudoscalar may subsequently decay to τ τ or bb̄ pairs. Such cascade decays
are more difficult to detect than in standard searches due to the potentially soft decay products.
There is also a rich phenomenology for the decays of the heavy CP -even and CP -odd doublets, H
and A into two lighter Higgs bosons such as H → hhS , hh, hS hS or A → AS hS , AS h as well as
into a light Higgs boson and a gauge boson: H → AS Z; A → hS Z, hZ. If kinematically allowed,
the heavy Higgs bosons decay into tt̄. If the singlet-dominated scalar or pseudoscalar are somewhat
heavier, the decays hS → W W or AS → hS Z will be allowed.
In addition, the light singlet scenario in the NMSSM or nMSSM is typically associated with alight singlino-dominated neutralino. The 125 GeV SM-like Higgs boson can then decay to pairs of
this neutralino [391], opening an invisible decay mode that is not excluded by present data. All of
the Higgs bosons can decay into electroweakinos depending on kinematics and on the singlino or
Higgsino composition of the electroweakinos.
In models with extended singlets, at low tan β, it is possible to trade the requirement of alarge stop mixing by a sizeable trilinear Higgs-singlet Higgs coupling λS , rendering more freedomon the requirements for gluon fusion production. As in the MSSM, mixing in the Higgs sector –additionally triggered by the extra new parameter λS – can produce variations in the Higgs–bb̄ and
Higgs–τ − τ + couplings that can alter the Higgs to ZZ/W W and to diphoton rates. Light charginos
at low tan β can independently contribute to enhance the di-photon rate, without altering any otherof the Higgs boson decay rates, see for instance Ref. [392].
There is much activity in exploring the NMSSM phenomenology in the light of the 125 GeV
Higgs boson as well as in defining benchmark scenarios with new topologies including Higgs decay
chains, see Refs. [40, 393] and references therein. An analytic understanding of the alignment condition in the NMSSM is presented in Ref. [347]. The NMSSM with a Higgs boson of mass 125 GeV
can be compatible with stop masses of order of the electroweak/TeV scale, thereby reducing thedegree of fine-tuning necessary to achieve electroweak symmetry breaking. Interestingly, the alignment conditions point toward a more natural region of parameter space for electroweak symmetry
breaking, while allowing for perturbativity of the theory up to the Planck scale and yielding a richand interesting Higgs boson phenomenology at the LHC.
11.6.3 Supersymmetry with extended gauge sectors
In the MSSM, the tree-level value of the lightest CP -even Higgs boson mass originates from the
D-term dependence of the scalar potential that comes from the SUSY kinetic terms in the Kähler
potential. The D-terms lead to tree-level quartic couplings which are governed by the squares of
the gauge couplings of the weak interactions, under which the Higgs boson has non-trivial charges.
Hence, the lightest Higgs mass is bounded to be smaller than MZ . In the presence of new gaugeinteractions at the TeV scale, and if the Higgs fields had non-trivial charges under them, new Dterm contributions would lead to an enhancement of the tree-level Higgs boson mass value. Since
the low energy gauge interactions reduce to the known SU(3)c × SU(2)L × U(1)Y ones, in orderfor this mechanism to work, the extended gauge and Higgs sectors should be integrated out in a
non-SUSY way. This means that there must be SUSY breaking terms that are of the order of, orlarger than, the new gauge boson masses. The tree-level quartic couplings would then be enhanced
through their dependence on the square of the gauge couplings of the extended Higgs sector. Thiseffect will be suppressed when the heavy gauge boson masses are larger than the SUSY breaking
scale and will acquire its full potential only for large values of this scale.
One of the simplest possibilities is to extend the weak interactions to a SU(2)1 × SU(2)2 sector,
such that the known weak interactions are obtained after the spontaneous breaking of these groups
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to SU(2)L [394]. This example is briefly summarised in the previous editions of this review [141].
Assuming SUSY breaking terms of the order of the new gauge boson masses, enhancements oforder 50% of the MSSM D-term contribution to the Higgs boson mass may be obtained. Suchenhancements are sufficient to obtain the measured Higgs mass value without the need for very
heavy stops or large stop mixing parameters. This gauge extension leads to new, heavy gauge andHiggs bosons, as well as new neutralinos and charginos, that depending on the region of parameter
space can induce novel phenomenology at the LHC. Gauge extensions including new Abelian gauge
groups have also been considered.
Gauge extensions of the MSSM can also lead to an enhancement of the Higgs boson mass value
by modifying the renormalisation group evolution of the Higgs quartic coupling to low energies. In
the MSSM, the evolution of the quartic coupling is governed by the top-quark Yukawa interactions
and depends on the fourth power of the top-quark Yukawa coupling. The neutralino and chargino
contributions, which depend on the fourth power of the weak gauge couplings, are small due tothe smallness of these couplings. Depending on the values of the soft SUSY breaking parametersin the gaugino and Higgsino sectors, the SU(2)1 gauginos may become light, with masses of theorder of the weak scale. Since the SU(2)1 coupling may be significantly larger than the SU(2)L
one, for small values of the Higgsino mass parameter µ, the associated charginos and neutralinos
may modify the evolution of the quartic coupling in a significant way [395]. This may lead to asignificant increase of the lightest CP -even Higgs boson mass, even for small values of tan β ' 1for which the D-term contributions become small. Radiative corrections should be properly taken
into account in this scenario as they might modify the tree-level result.
11.6.4 Effects of CP violation
SUSY scenarios with CP -violation (CP V ) phases are theoretically appealing, since additional
CP V beyond that observed in the K, D, and B meson systems is required to explain the observed
cosmic matter-antimatter asymmetry. In the MSSM, CP -violation effects in the Higgs sector appear
at the quantum level, while in singlet extensions of the MSSM CP -violation effects can already beeffective at tree level. In general, CP -violation effects in the Higgs sector have significant constraints
from electric dipole moments data [396].
In the MSSM, the gaugino mass parameters (M1,2,3 ), the Higgsino mass parameter, µ, thebilinear Higgs squared-mass parameter, m212 , and the trilinear couplings of the squark and slepton
fields to the Higgs fields, Af , may carry non-trivial phases. The two parameter combinations
arg[µAf (m212 )∗ ] and arg[µMi (m212 )∗ ] are invariant under phase redefinitions of the MSSM fields [397,398]. Therefore, if one of these quantities is non-zero, there would be new sources of CP -violation
affecting the Higgs sector through radiative corrections, see Ref. [399] and references therein. The
mixing of the neutral CP -odd and CP -even Higgs boson states is no longer forbidden. Hence, mA
is no longer a physical parameter. However, the charged Higgs boson mass mH ± is still physicaland can be used as an input for the computation of the neutral Higgs boson spectrum of thetheory. For large values of mH ± , corresponding to the decoupling limit, the properties of thelightest neutral Higgs boson state approach those of the SM Higgs boson. In particular, the upperbound on the lightest neutral Higgs boson mass takes the same value as in the CP -conservingcase [398]. Nevertheless, there still can be significant mixing between the two heavier neutral mass
eigenstates. For a detailed study of the Higgs boson mass spectrum and parametric dependence of
the associated radiative corrections, see Ref. [399] and references therein.
Major variations to the Higgs boson phenomenology occur in the presence of explicit CP V
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11. Status of Higgs Boson Physics

states, Hi (i = 1, 2, 3), with couplings
gHi V V = cos β O1i + sin β O2i ,gHi Hj Z = O3i (cos β O2j − sin β O1j ) − O3j (cos β O2i − sin β O1i ) ,(11.45)where the gHi V V couplings are normalised to the analogous SM coupling and the gHi Hj Z have beennormalised to gZSM /2. The orthogonal matrix Oij , only defined in the p2 → 0 limit, is relating the
weak eigenstates to the mass eigenstates. It has non-zero off-diagonal entries mixing the CP -evenand CP -odd components of the weak eigenstates. Moreover, CP V phases imply that all neutral
Higgs bosons can couple to both scalar and pseudoscalar fermion bilinear densities. The couplingsof the mass eigenstates Hi to fermions depend on the loop-corrected fermion Yukawa couplings(similarly to the CP conserving (CP C) case), on tan β and on Oji [400].
The production processes of neutral MSSM Higgs bosons in the CP V scenario are similar to
those in the CP C scenario. Regarding the decay properties, the lightest mass eigenstate, H1 ,predominantly decays to bb̄ if kinematically allowed, with a smaller fraction decaying to τ + τ − . If
kinematically allowed, a SM-like neutral Higgs boson, H2 or H3 can decay predominantly to H1 H1leading to many new interesting signals both at lepton and hadron colliders; otherwise it will decay
preferentially to bb̄.
The discovery of a 125 GeV Higgs boson has put strong constraints on the realisation of the
CP V scenario within the MSSM. This is partly due to the fact that the observed Higgs boson rates
are close to the SM values, and a large CP -violating component would necessarily induce a large
variation in the rate of the SM-like Higgs boson decays into the weak gauge bosons W ± and Z. The
measured Higgs mass imposes additional constraints on the realisation of this scenario. Once all
effects are considered, the CP -odd Higgs boson A component of the lightest Higgs boson tends tobe smaller than about 10% [401]. This restriction can be alleviated in the NMSSM or more general
two Higgs doublet models. CP -violating effects can still be significant in the heavy Higgs sector.
For instance, the Higgs bosons H2 and H3 may be admixtures of CP -even and CP -odd scalars,
and therefore both may be able to decay into pairs of weak gauge bosons. The observation of suchdecays would be a clear signal of CP -violation. In the MSSM, the proximity of the masses of H2and H3 makes the measurement of such effect quite challenging, but in generic two Higgs doublet
models, the mass splitting between the two heavy mass eigenstates may become larger, facilitating
the detection of CP -violating effects at collider experiments [402].
11.6.5 Non-supersymmetric extensions of the Higgs sector
There are many ways to extend the minimal Higgs sector of the SM. In the preceding sections thephenomenology of SUSY Higgs sectors is considered, which at tree level implies a constrained typeII 2HDM (with restrictions on the Higgs boson masses and couplings). In the following discussion,
more generic 2HDM’s are presented (for some comprehensive reviews, see the reviews [403]). Thesemodels are theoretically less compelling since they do not provide an explanation for the SM
Higgs naturalness problem, but can lead to different patterns of Higgs-fermion couplings, hence, todifferent phenomenology. It is also possible to consider models with a SM Higgs boson and one ormore additional scalar SU(2) doublets that acquire no VEV and hence play no role in the EWSB
mechanism. Such models are dubbed Inert Higgs Doublet Models (IHD) [404]. Without a VEV
associated to it, a Higgs boson from an inert doublet has no tree-level coupling to gauge bosons andhence cannot decay into a pair of them. Moreover, imposing a Z2 symmetry that prevents themfrom coupling to the fermions, it follows that, if the lightest inert Higgs boson is neutral, it becomesa good DM candidate with interesting associated collider signals. Various studies of IHD models
in the light of a 125 GeV Higgs boson have been performed, see for instance Ref. [405], showing aninteresting interplay between collider and direct DM detection signals.
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An interesting type of 2HDMs are those in which an Abelian flavour symmetry broken at theelectroweak scales creates the fermion mass hierarchies and mixing angles [406]. This idea is basedon the Froggatt–Nielsen model [407], where a flavon field couples differently to the SM fermions ofdifferent flavour charges. Such flavon acquires a vacuum expectation value, breaking the flavour
symmetry but leaving both the flavour breaking and the new physics scales undetermined. In
Refs. [408], it was proposed to relate the flavour breaking scale to the electroweak scale by identifying the flavon with the modulus square of the Higgs field. A 2HDM, however, provides a morecompelling realisation of the electroweak scale flavour breaking idea. In the most ambitious constructions of two Higgs doublet flavour models (2HDFM), the textures of the Yukawa couplings area result of an Abelian flavour symmetry that only allows renormalisable Yukawa couplings of the
top quark to the Higgs bosons. All other Yukawa couplings are generated by higher dimensional
operators that produce hierarchical entries of the Yukawa matrices, explaining the observed quark
masses and mixing angles. Flavour observables, LHC Higgs signal strength measurements, electroweak precision measurements, unitarity and perturbativity bounds, as well as collider searches
for new scalar resonances result in precise predictions for the parameters of these 2HDFMs. In particular, correlated departures from SM Higgs boson couplings, as well as additional Higgs bosons
with masses < 700 GeV must be observed at the LHC. Other incarnations of 2HDFMs can aim atonly partially explaining the fermion mass hierarchies but are therefore less restrictive.
Other extensions of the Higgs sector can include multiple copies of SU(2)L doublets [409],
additional Higgs singlets [410], triplets or more complicated combinations of Higgs multiplets. It isalso possible to enlarge the gauge symmetry beyond SU(2)L ×U(1)Y along with the necessary Higgs
field structure to generate gauge boson and fermion masses. There are two main experimental
constraints on these extensions: (i) precision measurements which constrain ρ = m2W /(m2Z cos2 θW )to be very close to 1 and (ii) flavour changing neutral current (FCNC) effects. In electroweakmodels based on the SM gauge group, the tree-level value of ρ is determined by the Higgs multiplet
structure. By suitable choices for the hypercharges, and in some cases the mass splitting between the
charged and neutral Higgs sector or the vacuum expectation values of the Higgs fields, it is possible
to obtain a richer combination of singlets, doublets, triplets and higher multiplets compatible with
precision measurements. Concerning the constraints coming from FCNC effects, the Glashow–
Weinberg (GW) criterion [411] states that, in the presence of multiple Higgs doublets, the tree-level
FCNC’s mediated by neutral Higgs bosons will be absent if all fermions of a given electric charge
couple to no more than one Higgs doublet. An alternative way of suppressing FCNC in a two Higgs
doublet model has been considered in Ref. [412], where it is shown that it is possible to have treelevel FCNC completely fixed by the CKM matrix, as a result of an Abelian symmetry.
There is a lot of activity on the study of non-supersymmetric models with an extended Higgs
sector with an intense collaboration between theorists and experimentalists, in particular inside the
LHC Higgs Working Group [373].
11.6.5.1 Two-Higgs-doublet models
General two Higgs doublet models [403] can have a more diverse Higgs-fermion coupling structure than in SUSY, and can be viewed as a simple extension of the SM to realise the spontaneous breakdown of SU(2)L × U(1)Y to U(1)em . Quite generally, if the two Higgs doublets contain opposite hypercharges, the scalar potential will contain mixing mass parameters of the kindm212 ΦT1 iσ2 Φ2 + h.c.. √In the presence√ of such terms, both Higgs doublets will acquire vacuum expectation values, v1 / 2 and v2 / 2, respectively,qand the gauge boson masses will keep their SM

expressions with the Higgs VEV v replaced by v12 + v22 . Apart from the mass terms, the mostgeneric renormalisable and gauge invariant scalar potential for two Higgs doublets with opposite
hypercharges contains seven quartic couplings, as presented in Eq. (11.38).
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Just as in the MSSM case, after electroweak symmetry breaking and in the absence of CP violation, the physical spectrum contains a pair of charged Higgs bosons H ± , a CP -odd Higgs
boson A and two neutral CP -even Higgs bosons, h and H. The angles α and β diagonalise theCP -even, and the CP -odd and charged Higgs sectors, respectively. The complete 2HDM is defined
only after considering the interactions of the Higgs fields to fermions. Yukawa couplings of thegeneric form
− haij Ψ̄Li Ha ΨRj + h.c.
(11.46)
may be added to the renormalisable Lagrangian of the theory. Contrary to the SM, the two√ Higgsadoublet structure does not ensure the alignment of the fermion mass terms mij = hij va / 2 with
the Yukawa couplings haij . This implies that quite generally the neutral Higgs boson will mediate
flavour changing interactions between the different mass eigenstates of the fermion fields. Suchflavour changing interactions should be suppressed in order to describe properly the Kaon, D and
B meson phenomenology. Based on the Glashow–Weinberg criterion, it is clear that the simplest
way of avoiding such transitions is to assume the existence of a symmetry that ensures the couplingsof the fermions of each given quantum number (up-type and down-type quarks, charged and neutral
leptons) to only one of the two Higgs doublets. Different models may be defined depending on whichof these fermion fields couple to a given Higgs boson, see Table 11.9. Models of type-I are thosein which all SM fermions couple to a single Higgs field. In type-II models, down-type quarks andcharged leptons couple to a common Higgs field, while the up-type quarks and neutral leptons
couple to the other. In models of type-III (lepton-specific), quarks couple to one of the Higgs
bosons, while leptons couple to the other. Finally, in models of type-IV (flipped), up-type quarks
and charged leptons couple to one of the Higgs fields while down-quarks and neutral leptons couple
to the other.
Table 11.9: Higgs boson couplings to up, down and charged lepton-type
SU (2)L singlet fermions in the four discrete types of 2HDM models thatsatisfy the Glashow–Weinberg criterion.
Model 2HDM I 2HDM II 2HDM III 2HDM IV
u
Φ2
Φ2
Φ2
Φ2
d
Φ2
Φ1
Φ2
Φ1
e
Φ2
Φ1
Φ1
Φ2
The two Higgs doublet model phenomenology depends strongly on the size of the mixing angle
α and therefore on the quartic couplings. For large values of mA , sin α → − cos β, cos α → sin β,cos(β − α) → 0, and the lightest CP -even Higgs boson h behaves as the SM Higgs boson. The
same behaviour is obtained if the quartic couplings are such that M212 sin β = −(M211 − m2h ) cos β.
The latter condition represents a situation in which the couplings of h to fermions and weak gaugebosons become the same as in the SM, without decoupling the rest of the non-standard scalars andit is of particular interest due to the fact that the discovered Higgs boson has SM-like properties.
This situation will be referred to as alignment, as in the MSSM case.
In analogy to the effects of CP violation in the SUSY 2HDM, some parameters of the Higgs
potential can be complex and one has a model that is explicitly CP violating. The three neutral
mass eigenstates mixed with each other and the Higgs phenomenology is analogous to the one
described for the SUSY case above, with the caveat that when considering the neutral Higgs boson
couplings to the scalar and pseudoscalar fermion bilinear densities, the proper weight should beconsidered for the respective 2HDM’s.
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In type-II Higgs doublet models, at large values of tan β and moderate values of mA , the nonstandard Higgs bosons H, A and H ± couple strongly to bottom quarks and τ leptons. Hence, thedecay modes of the non-standard Higgs bosons tend to be dominated by the b-quark and τ -lepton
modes, including top quarks or neutrinos in the case of the charged Higgs boson. However, forlarge and negative values of λ4 , the charged Higgs boson mass may be sufficiently heavy to allow
on-shell decays H ± → W ± + (H, A), via a trilinear couplinggH ± W ∓ H,A 'MW
sin(β − α)(pH + − pH,A ) ,v(11.47)

where pH + and pH,A are the charged and neutral scalar Higgs boson momenta pointing into thevertex. On the other hand, for large and positive values of λ5 , the above charged Higgs boson decay
into a W ± and the CP -odd Higgs boson may be allowed, but the heavy Higgs boson H may besufficiently heavy to decay into a CP -odd Higgs boson and an on-shell Z, H → Z + A, via
gHZA 'MZ
sin(β − α)(pH − pA ).
v(11.48)The decay H ± → W ± + H, on the other hand may be allowed only if λ4 < −λ5 . The couplings controlling all the above decay modes are proportional to sin(β − α) and therefore they areunsuppressed in the alignment limit. Moreover, these could still be the dominant decay modes atmoderate values of tan β, offering a way to evade the current bounds obtained assuming a dominant
decay into b-quarks or τ -leptons.
The quartic couplings are restricted by the condition of stability of the effective potential aswell as by the restriction of obtaining the proper value of the lightest CP -even Higgs boson mass.
Close to the alignment limit, the lightest CP -even Higgs boson mass becomesm2h ' v 2 (λ1 cos4 β + λ2 sin4 β + 2λ̃3 v 2 cos2 β sin2 β + 4λ6 cos3 β sin β + 4λ7 sin3 β cos β) ,(11.49)where λ̃3 = λ3 + λ4 + λ5 .
The stability conditions imply the positiveness of all masses, as well as the avoidance of run-away
solutions to large negative values of the fields in the scalar potential. These conditions imply
λ1 ≥ 0, λ2 ≥ 0, λ3 + λ4 − |λ5 | ≥ − λ1 λ2 , λ3 ≥ − λ1 λ2 , 2|λ6 + λ7 | <pp

λ1 + λ2+ λ̃3 , (11.50)
2where the first four conditions are necessary and sufficient conditions in the case of λ6 = λ7 = 0,
while the last one is a necessary condition in the case all couplings are non-zero. Therefore, toobtain the conditions that allow the decays H ± → W ± H, A and H → ZA, λ3 should take large
positive values in order to compensate for the effects of λ4 and λ5 . For more detailed discussions
about 2HDM phenomenology, see for example Refs. [40, 403].
11.6.5.2 Higgs triplets
Electroweak triplet scalars are the simplest non-doublet extension of the SM that can participate
in the spontaneous breakdown of SU(2)L × U(1)Y to U(1)em . Two types of model have beendeveloped in enough detail to make a meaningful comparison to LHC data: the Higgs triplet model(HTM) [413] and the Georgi–Machacek model (GM) [414].
The Higgs triplet model extends the SM by the addition of a complex SU(2)L triplet scalar field∆ with hypercharge Y = 2, and a general gauge-invariant renormalisable potential V (Φ, ∆) for ∆and the SM Higgs doublet Φ. The components of the triplet field can be parameterised as√ ++ !
1∆+
2∆.
(11.51)∆= √−∆+2 v∆ + δ + iξ
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where ∆+ is a singly-charged field, ∆++ is a doubly-charged field, δ is a neutral CP -even scalar,ξ is a neutral CP -odd scalar, and v∆ is the triplet VEV. The general scalar potential mixes the
doublet and triplet components. After electroweak symmetry breaking there are seven physicalmass eigenstates, denoted H ±± , H ± , A, H, and h.
A distinguishing feature of the HTM is that it violates the custodial symmetry of the SM; thus
the ρ parameter deviates from 1 even at tree level. Letting x denote the ratio of triplet and doublet
VEVs, the tree level expression is
1 + 2x2
ρ=.
(11.52)
1 + 4x2
The measured value of the ρ parameter then limits the triplet VEV to be quite small, x . 0.03, orv∆ < 8 GeV. This constraint severely limits the role of the triplet scalar in the EWSB mechanism.
The small VEV of the Higgs triplet in the HTM is a virtue from the point of view of generating
neutrino masses without the necessity for introducing right-handed neutrino fields. The gauge
invariant dimension four interactionhνij `Ti C −1 iσ2 ∆ `j ,(11.53)where `i are the lepton doublets, C is the charge conjugation matrix, and hνij is a complex symmetric coupling matrix, generates a Majorana mass matrix for the neutrinos:√mνij = 2hνij v∆ .
(11.54)This can be combined with the usual neutrino seesaw to produce what is known as the type-II
seesaw [415].
The HTM suggests the exciting possibility of measuring parameters of the neutrino mass matrix
at the LHC. If the doubly-charged Higgs boson is light enough and/or its couplings to W + W + are+
sufficiently suppressed, then its primary decay is into same-sign lepton pairs: H ++ → `+i `j ; from
Eq. (11.53) and Eq. (11.54), it is apparent that these decays are in general lepton-flavour violatingwith branchings proportional to elements of the neutrino mass matrix [416].
Precision electroweak data constrain the mass spectrum as well as the triplet VEV of the
HTM [417]. These constraints favour a spectrum where H ++ is the lightest of the exotic bosons,and where the mass difference between H + and H ++ is a few hundred GeV. The favoured triplet
VEV is a few GeV, which also favours H ++ decays into W + W + over same-sign dileptons.
The GM model addresses the ρ parameter constraint directly by building in a custodial symmetry (it was however argued that large corrections to ρ = 1 are generated at one-loop [418], requiring
some fine-tuning to preserves agreement with EW precision data). Writing the complex scalar doublet of the SM as a (2, 2) under SU(2)L × SU(2)R , it is obvious that the next simplest construction
respecting custodial symmetry is a scalar transforming like a (3, 3) [419]. These nine real degrees of
freedom correspond to a complex electroweak triplet combined with a real triplet, with the scalarpotential required to be invariant under SU(2)R . Under the custodial SU(2)L+R , they transformas 1 ⊕ 3 ⊕ 5, with a CP -even neutral scalar as the custodial singlet (thus matching the SM Higgs
boson), a CP -odd neutral scalar in the custodial triplet, and another CP -even neutral scalar in
the custodial 5-plet.
The scalar components can be decomposed asχ∗3ξ 1 χ1∗Ξ = −χ2 ξ2 χ2  ,χ∗1 −ξ1∗ χ3


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(11.55)

78

11. Status of Higgs Boson Physics

where ξ2 is a real scalar and the others are complex scalars. Linear combinations of these scalars
account for the neutral custodial singlet, a neutral and singly-charged field making up the custodial
triplet, and neutral, singly-charged, and doubly-charged fields making up the custodial 5-plet.
When combined with the usual SM doublet field Φ, the electroweak scale v is now related tothe doublet and triplet VEVs by2v 2 = vΦ2 + 8vΞ
.
(11.56)Note that the GM triplets by themselves are sufficient to explain electroweak symmetry breaking
and the existence of a 125 GeV neutral boson along with a custodial triplet of Goldstone bosons;the complex doublet field in the GM model is required to generate fermion masses via the usual
dimension four Yukawa couplings. This raises the question of whether one can rule out the possibility that the 125 GeV boson is the neutral member of a custodial 5-plet rather than a custodial
singlet, without invoking decays to fermions. A conclusive answer is given by observing that theratio of the branching fractions to W versus Z bosons is completely determined by the custodial
symmetry properties of the boson. For a custodial 5-plet, the ratio of the signal strength to W W
over that to ZZ is predicted to be 1/4 that of a SM Higgs boson [419], and thus already ruled out
by the experimental results presented in Section 11.5.
Another interesting general feature of Higgs triplet models is that, after mixing, the SM-likeneutral boson can have stronger couplings to W W and ZZ than predicted by the SM [420]; this is
in contrast to mixing with additional doublets and singlet, which can only reduce the W W and ZZ
couplings versus the SM. This emphasises that LHC Higgs data cannot extract model independent
coupling strengths for the Higgs boson [291].
Because of the built-in custodial symmetry, the triplet VEV in the GM model can be large
compared to the doublet VEV. The custodial singlet neutral boson from the triplets mixes with theneutral boson from the doublet. Two interesting special cases are (i) the triplet VEV is small andthe 125 GeV boson is SM-like except for small deviations, and (ii) the 125 GeV boson is mostly thecustodial singlet neutral boson from the electroweak triplets. The phenomenology of the doublycharged and singly-charged bosons is similar to that of the HTM. The constraints on the GM modelfrom precision electroweak data, LEP data, and current LHC data are summarised in Ref. [40].
11.6.6 Composite Higgs models
Within the SM, EWSB is posited but has no dynamical origin. Furthermore, the Higgs boson
appears to be unnaturally light. A scenario that remedies these two catches is to consider the Higgs
boson as a bound state of new dynamics becoming strong around the weak scale. The Higgs boson
can be made significantly lighter than the other resonances of the strong sector if it appears as a
pseudo-Nambu–Goldstone boson, see Refs. [11] for reviews.
11.6.6.1 Little Higgs models
The idea behind the Little Higgs boson models [421] is to identify the Higgs doublet as a (pseudo)
Nambu–Goldstone boson while keeping some sizeable non-derivative interactions, in particular alargish Higgs quartic interaction. By analogy with QCD where the pions π ±,0 appear as Nambu–
Goldstone bosons associated to the breaking of the chiral symmetry SU(2)L × SU(2)R /SU(2),switching on some interactions that break explicitly the global symmetry will generate masses
for the would-be massless Nambu–Goldstone bosons of the order of gΛG/H /(4π), where g is thecoupling of the symmetry breaking interaction and ΛG/H = 4πfG/H is the dynamical scale of the
global symmetry breaking G/H. In the case of the Higgs boson, the top Yukawa interaction or thegauge interactions themselves will certainly break explicitly (part of) the global symmetry since
they act non-linearly on the Higgs boson. Therefore, obtaining a Higgs boson mass around 125 GeV
would demand a dynamical scale ΛG/H of the order of 1 TeV, which is known to lead to too large
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11. Status of Higgs Boson Physics

oblique corrections. Raising the strong dynamical scale by at least one order of magnitude requires
an additional selection rule to ensure that a Higgs boson mass is generated at the 2-loop level only
m2H =

g2 2
g12 g22
ΛG/H → m2H =
Λ2 .
2
16π
(16π 2 )2 G/H(11.57)

The way to enforce this selection rule is through a “collective breaking” of the global symmetry:
L = LG/H + g1 L1 + g2 L2 .

(11.58)Each interaction L1 or L2 individually preserves a subset of the global symmetry such that the
Higgs boson remains an exact Nambu–Goldstone boson whenever either g1 or g2 is vanishing. A
mass term for the Higgs boson can be generated only by diagrams involving simultaneously bothinteractions. At one-loop, such diagrams are not quadratically divergent, so the Higgs boson mass
is not UV sensitive. Explicitly, the cancellation of the SM quadratic divergences is achieved by aset of new particles around the Fermi scale: gauge bosons, vector-like quarks, and extra massive
scalars, which are related, by the original global symmetry, to the SM particles with the same spin.
Contrary to SUSY, the cancellation of the quadratic divergences is achieved by same-spin particles.
These new particles, with definite couplings to SM particles as dictated by the global symmetriesof the theory, are perfect goals for the LHC.
The simplest incarnation of the collective breaking idea, the so-called littlest Higgs boson model,
is based on a non-linear σ-model describing the spontaneous breaking SU(5) down to SO(5). A
subgroup SU(2)1 × U(1)1 × SU(2)2 × U(1)2 is weakly gauged. This model contains a weak doublet,that is identified with the Higgs doublet, and a complex weak triplet whose mass is not protectedby collective breaking. Other popular little Higgs models are based on different coset spaces:
minimal moose (SU(3)2 /SU(3)), the simplest little Higgs (SU(3)2 /SU(2)2 ), the bestest little Higgs(SO(6)2 /SO(6)). For comprehensive reviews, see Ref. [422].
Generically, oblique corrections in Little Higgs models are reduced either by increasing thecoupling of one of the gauge groups (in the case of product group models) or by increasing themasses of the W and Z partners, leading ultimately to a fine-tuning of the order of a few percents(see for instance Ref. [423] and references therein). The compatibility of Little Higgs models
with experimental data is significantly improved when the global symmetry involves a custodial
symmetry as well as a T -parity [424] under which, in analogy with R-parity in SUSY models, theSM particles are even and their partners are odd. Such Little Higgs models would therefore appear
in colliders as jet(s) with missing transverse energy [425] and the ATLAS and CMS searches forsquarks and gluinos can be recast to obtain limits on the masses of the heavy vector-like quarks.
The T -even top partner, with an expected mass below 1 TeV to cancel the top loop quadratic
divergence without too much fine-tuning, would decay dominantly into a t + Z pair or into a b + W
pair or even into t+H. The latest CMS and ATLAS direct searches [426] for vector-like top partners
put a lower bound around 1.1–1.3 TeV (for various branching fraction combinations), excluding themost natural region of the parameter space of these models, i.e., imposing a fine-tuning below thepercent level.
The motivation for Little Higgs models is to solve the little hierarchy problem, i.e., to push theneed for new physics (responsible for the stability of the weak scale) up to around 10 TeV. Per se,
Little Higgs models are effective theories valid up to their cutoff scale ΛG/H . Their UV completions
could either be weakly or strongly coupled.
11.6.6.2 Models of partial compositeness
Even in composite models, the Higgs boson cannot appear as a regular resonance of the strong
sector without endangering the viability of the setup when confronted to data. The way out is that
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80

the Higgs boson appears as a pseudo Nambu–Goldstone boson: the new strongly coupled sector
is supposed to be invariant under a global symmetry G spontaneously broken to a subgroup H at
the scale f (the typical mass scale of the resonances of the strong sector is mρ ∼ gρ f with gρ thecharacteristic coupling of the strong sector). To avoid conflict with EW precision measurements,
the strong interactions themselves should better not break the EW symmetry. Hence the SM gauge
symmetry itself should be contained in H. See Table 11.10 for a few examples of coset spaces.
Table 11.10: Global symmetry breaking patterns and the corresponding
Goldstone boson contents of the SM, the minimal composite Higgs model,
the next to minimal composite Higgs model, and the minimal composite
two Higgs doublet model. Note that the SU(3) model does not have acustodial invariance. a denotes a CP -odd scalar while h and H are CP even scalars.
Model
SM
–
MCHM
NMCHM
MC2HM

Symmetry Pattern
SO(4)/SO(3)SU(3)/SU(2)×U(1)SO(5)/SO(4)SO(6)/SO(5)SO(6)/SO(4)×SO(2)Goldstones
WL , ZL
WL , ZL , H
WL , ZL , H
WL , ZL , H, a
WL , ZL , h, H, H ± , a

The SM (light) fermions and gauge bosons cannot be part of the strong sector itself since LEP
data have already put stringent bounds on the compositeness scale of these particles far above
the TeV scale. The gauge bosons couple to the strong sector by a weak gauging of a SU(2)×U(1)subgroup of the global symmetry G. Inspiration for the construction of such models comes from the
AdS/CFT correspondence: the components of a gauge field along an extra warped space dimension
can be interpreted as the Goldstone bosons resulting from the breaking of global symmetry of
the strong sector. The couplings of the SM fermions to the strong sector could a priori take twodifferent forms:(i) a bilinear coupling of two SM fermions to a composite scalar operator, O, of the form L =y q̄L uR O + h.c., in simple analogy with the SM Yukawa interactions. This is the way fermion
masses were introduced in technicolor theories and it generically comes with severe flavour
problems and calls for extended model-building gymnastics [12] to circumvent them;(ii) a linear mass mixing with fermionic vector-like operators: L = λL q̄L QR + λR ŪL uR . Q and U
are two fermionic composite operators of mass MQ and MU .
Being part of the composite sector, the composite fermionic operators can have a direct coupling ofgeneric order Y∗ to the Higgs boson. In analogy with the photon-ρ mixing in QCD, once the linear
mixings are diagonalised, the physical states are a linear combination of elementary and composite
fields. Effective Yukawa couplings are generated and read for instance for the up-type quarky = Y∗ sin θL sin θR(11.59)2
where sin θi = λi / MQ,U
+ λ2i , i = L, R, measure the amount of compositeness of the SM leftand right-handed up-type quark. If the strong sector is flavour-anarchic, i.e., if the couplings ofthe Higgs boson to the composite fermions does not exhibit any particular flavour structure, therelation Eq. (11.59) implies that the light fermions are mostly elementary states (sin θi  1),while the third generation quarks need to have a sizable degree of compositeness. The partialq

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compositeness paradigm offers an appealing dynamical explanation of the hierarchies in the fermion
masses. In fact, assuming the strong sector to be almost conformal above the confinement scale, thelow-energy values of the mass-mixing parameters λL,R are determined by the (constant) anomalous
dimension of the composite operator they mix with. If the UV scale at which the linear mixings are
generated is large, then O(1) differences in the anomalous dimensions can generate naturally large
hierarchies in the fermion masses via renormalisation group running [427]. While the introductionof partial compositeness greatly ameliorated the flavour problem of the original composite Higgs
models, nevertheless, it did not solve the issue completely, at least in the case where the strong sector
is assumed to be flavour-anarchic [428]. While the partial compositeness set-up naturally emerges
in models built in space-times with extra dimensions, no fully realistic microscopic realisation ofpartial compositeness has been proposed in the literature.
Another nice aspect of the partial compositeness structure is the dynamical generation of the
Higgs potential that is not arbitrary like in the SM. The Higgs boson being a pseudo-Nambu–
Goldstone boson, its mass does not receive any contribution from the strong sector itself but it
is generated at the one-loop level via the couplings of the SM particles to the strong sector sincethese interactions are breaking the global symmetries under which the Higgs doublet transforms
non-linearly. Obtaining v  f , as required phenomenologically, requires some degree of tuning,which scales like ξ ≡ v 2 /f 2 . A mild tuning of the order of 10% (ξ ≈ 0.1) is typically enough tocomply with electroweak precision constraints. This is an important point: in partial compositenessmodels, the entire Higgs potential is generated at one loop, therefore the separation between v andf can only be obtained at a price of a tuning. This marks a difference with respect to the Little
Higgs models which realise a parametric hierarchy between the quartic and mass terms throughthe collective symmetry breaking mechanism. In fact in Little Higgs models, the quartic coupling
is a tree-level effect, leading to a potential
V (H) ≈

2gSM
2
m2 H 2 + gSM
H 4,
16π 2 ρ(11.60)where gSM generically denotes the SM couplings. The minimisation condition reads v 2 /f 2 ∼gρ2 /(16π 2 ), therefore v is formally loop suppressed with respect to f . This is the major achievementof the Little Higgs constructions, which however comes at the price of the presence of sub-TeV vectors carrying EW quantum numbers and therefore giving rise generically to large oblique corrections
to the propagators of the W and the Z gauge bosons.
After minimisation, the dynamically generated potential leads to an estimate of the Higgs boson
mass asm2H ≈ gρ3 yt 2π 2 v 2 .
(11.61)

It follows that the limit f → ∞, i.e., ξ → 0, is a true decoupling limit: all the resonances of thestrong sector become heavy but the Higgs boson whose mass is protected by the symmetries of
the coset G/H. When compared to the experimentally measured Higgs boson mass, this estimate
puts an upper bound on the strength of the strong interactions: gρ . 2. In this limit of not solarge coupling, the Higgs potential receives additional contributions. In particular, the fermionic
resonances in the top sector which follow from the global symmetry structure of the new physics
sector can help raising the Higgs boson mass. Using some dispersion relation techniques, the massof the Higgs is connected to the resonance masses. In the minimal SO(5)/SO(4) model, it was
shown [429] that a 125 GeV mass can be obtained if at least one of the fermionic resonances islighter than ∼ 1.4 f . As in SUSY scenarios, the top sector is playing a crucial role in the dynamics
of EWSB and can provide the first direct signs of new physics. The direct searches for these top
partners, in particular the ones with exotic electric charges 5/3, are already exploring the naturalparameter spaces of these models [430].
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82

The main physics properties of a pseudo Nambu–Goldstone Higgs boson can be captured ina model-independent way by a small number of higher-dimensional operators. Indeed, the strong
dynamics at the origin of the composite Higgs boson singles out a few operators among the complete
list discussed earlier in Section 11.5: these are the operators that involve extra powers of the Higgs
doublets, and they are therefore generically suppressed by a factor 1/f 2 as opposed to the operatorsthat involve extra derivatives or gauge bosons that are suppressed by a factor 1/(gρ2 f 2 ). The relevant
effective Lagrangian describing a strongly interacting light Higgs boson is:
LSILH =

2cH∂µ Φ† Φ
2f 2




+

2

←
→
cT
Φ† D µ Φ
2f 2


−

c λ
6

f2

3

Φ† Φ



X cf yf+Φ† Φf¯L ΦfR + h.c. .
ff2(11.62)

Typically, these new interactions induce deviations in the Higgs boson couplings that scale likeO(v 2 /f 2 ). Hence, the measurements of the Higgs boson couplings can be translated into someconstraints on the compositeness scale, 4πf , of the Higgs boson. The peculiarity of these composite
models is that, due to the Goldstone nature of the Higgs boson, the direct couplings to photons
and gluons are further suppressed and generically the coupling modifiers scale like
κW,Z,f ∼ 1 + O

v2
f2

!

,

κZγ ∼ O

v2
f2

!

,

κγ,g ∼ Ov2
yt2
×f 2 gρ2!

,(11.63)where gρ denotes the typical coupling strength among the states of the strongly coupled sector
and yt is the top Yukawa coupling, the largest interaction that breaks the Goldstone symmetry.
The κZγ,γ,g coupling modifiers are not generated by the strong coupling operators of Eq. (11.62)
but by some subleading form-factor operator generated by loops of heavy resonances of the strong
sector. The coupling modifiers also receive additional contributions from the other resonances ofthe strong sector, in particular the fermionic resonances of the top sector that are required tobe light to generate a 125 GeV Higgs boson mass. Some indirect information on the resonancespectrum could thus be inferred by a precise measurement of the Higgs boson coupling deviations.
However, it was realised, see in particular Ref. [306], that the task is actually complicated by thefact that, in the minimal models, these top partners give a contribution to both κt (resulting froma modification of the top Yukawa coupling) and κγ and κg (resulting from new heavy particles
running into the loops) and the structure of interactions is such that the net effect vanishes forinclusive quantities like σ(gg → H) or Γ (H → γγ) as a consequence of the Higgs low energy
theorem [21, 22, 301]. So, one would need to rely on differential distribution, like the Higgs boson
pT distribution discussed in Section 11.2.4.1, to see the top partner effects in Higgs data [431]. The
off-shell channel gg → H ∗ → 4` [290] and the double Higgs boson production gg → HH [432] canalso help to resolve the gluon loop and separate the top and top-partner contributions.
11.6.6.3 Minimal composite Higgs models
The minimal composite Higgs models (MCHM) are concrete examples of the partial compositeness paradigm. The Higgs doublet is described by the coset space SO(5)/SO(4) where a subgroup
SU(2)L × U(1)Y is weakly gauged and under which the four Goldstone bosons transform as a doublet of hypercharge 1. There is some freedom on how the global symmetry is acting on the SM
fermions: in MCHM4 the quarks and leptons are embedded into spinorial representations of SO(5),while in MHCM5 they are part of fundamental representations (it might also be interesting phenomenologically to consider larger representations like MCHM14 [433] with the SM fermions insidea representation of dimension 14). It is also possible to consider that fermions of different chirality
and flavour are in different representations of SO(5), leading to a more varied phenomenology [434].
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The non-linearly realised symmetry acting on the Goldstone bosons leads to general predictions of
the coupling of the Higgs boson to the EW gauge bosons. For instance, it can be shown that thequadratic terms in the W and Z bosons readm2W (H)

1
Wµ W +Zµ Z µ ,2 cos2 θWµ(11.64)H
with mW (H) = gf
2 sin f . Expanding around the EW vacuum, the expression of the weak scale isv = f sin(hHi/f ). And the values of the modified Higgs boson couplings to the W and Z become:2m2V qgHV V =
1 − v 2 /f 2 ,v

gHHV V =2m2V(1 − 2v 2 /f 2 ) .
v2(11.65)Note that the Higgs boson couplings to gauge bosons is always suppressed compared to the SM
prediction. This is a general result [435] that holds as long as the coset space is compact.
The Higgs boson couplings to the fermions depend on the representation which the SM fermionsare embedded into. The most commonly used embeddings consider all fermion doublets and singlets
in the same representations. While, in MCHM4 and MCHM5, the modifications of the couplings
depend only on the Higgs boson compositeness scale, in MCHM14 the leading corrections depend
also on the mass spectrum of the resonances [433]. This is due to the fact that more than one
SO(5) invariant gives rise to SM fermion masses. The (κV , κf ) experimental fit of the Higgs boson
couplings can be used to derive a lower bound on the Higgs boson compositeness scale 4πf & 9 TeV,
which is less stringent than the indirect bound obtained from EW precision data, 4πf & 15 TeV [436]but more robust and less subject on assumptions [437].
11.6.6.4 Twin Higgs models
In all composite models presented above, the particles responsible for canceling the quadratic
divergences in the Higgs boson mass are charged under the SM gauge symmetries. In particular, thetop partner carries color charge, implying a reasonably large minimal production cross section at the
LHC. An alternative scenario, which is experimentally quite challenging and might explain the null
result in various new physics searches, is the case nowadays referred to as “neutral naturalness” [13,14], where the particles canceling the 1-loop quadratic divergences are neutral under the SM. The
canonical example for such theories is the Twin Higgs model of Ref. [13]. This is an example of apseudo-Goldstone boson model with an approximate global SU(4) symmetry broken to SU(3). The
Twin Higgs model is obtained by gauging the SU(2)A × SU(2)B subgroup of SU(4), where SU(2)A
is identified with the SM SU(2)L , while SU(2)B is the twin SU(2) group. Gauging this subgroupbreaks the SU(4) symmetry explicitly, but quadratically divergent corrections do not involve the
Higgs boson when the gauge couplings of the two SU(2) subgroups are equal, gA = gB . The SU(4)→SU(3) breaking will also result in the breaking of the twin SU(2)B group and, as a result, threeof the seven Goldstone bosons will be eaten, leaving 4 Goldstone bosons corresponding to the SM
Higgs doublet. In fact, imposing the Z2 symmetry on the full model will ensure the cancellationof all 1-loop quadratic divergences to the Higgs boson mass. Logarithmically divergent terms can,however, arise for example from gauge loops, leading to a Higgs boson mass of order g 2 f /4π, which
is of the order of the physical Higgs boson mass for f ∼ 1 TeV. The quadratic divergences fromthe top sector can be eliminated if the Z2 protecting the Higgs boson mass remains unbroken by
the couplings that result in the top Yukawa coupling. This can be achieved by introducing top
partners charged under a twin SU(3)C . In this case, the quadratic divergences are cancelled by top
partners that are neutral under the SM gauge symmetries.
Twin Higgs models are low-energy effective theories valid up to a cutoff scale of order Λ ∼4πf ∼ 5–10 TeV, beyond which a UV completion has to be specified. The simplest such possibility
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is to also make the Higgs boson composite, and to UV complete the twin Higgs model via gauge
and top partners at masses of the order of a few TeV. A concrete implementation is the holographic
twin Higgs model [438], which also incorporates a custodial symmetry to protect the T -parameterfrom large corrections. It is based on a warped extra dimensional theory with a bulk SO(8) gauge
group, which incorporates the SU(4) global symmetry discussed above enlarged to contain theSU(2)L ×SU(2)R custodial symmetry. In addition, the bulk contains either a full SU(7) group or
an SU(3) × SU(3) × U(1) × U(1) × Z2 subgroup of it to incorporate the QCD, its twin, and thehypercharge local symmetries. The breaking on the UV brane is to the SM symmetries and their
twin symmetries, while on the IR brane SO(8) → SO(7), giving rise to the 7 Goldstone bosons,three of which will be again eaten by the twin W, Z. The main difference compared to ordinary
composite Higgs models is that, in composite twin Higgs models, the cancellation of the one-loop
quadratic divergences is achieved by the twin partners. They have a mass of order 700 GeV–1 TeV
and they are uncharged under the SM gauge group. This allows the IR scale of the warped extra
dimension to be raised to the multi-TeV range without reintroducing the hierarchy problem. The
role of the composite partners is to UV complete the theory, rather than to cancel the one-loop
quadratic divergences. For more details about the composite twin Higgs models, see Refs. [439].
11.6.7 Searches for signatures of extended Higgs sectors
The measurements described in Sections 11.3 to 11.5 have established the existence of one stateof the electroweak symmetry breaking sector, compatible with a SM Higgs boson, but not that itis the only one. As was discussed above, several classes of models beyond the SM require extended
Higgs sectors. The searches are typically designed to be as model-independent as possible7 and canbe categorised in the classes summarised as follows:(i) the search for an additional CP -even state mostly in the high mass domain decaying to vectorbosons, which would correspond either to the heavy CP -even state in a generic 2HDM where
the light state would be the discovered Higgs boson at 125 GeV or to a generic additional
singlet;(ii) the search for a state in the high mass domain decaying to pairs of fermions, which would
correspond to the CP -odd A or the heavy CP -even state H in a generic 2HDM;(iii) the search for charged Higgs bosons, which also appear in generic 2HDMs;(iv) the search for a CP -odd state a in the low mass region which appears in the NMSSM in avariety of final states, e.g., with one or two a bosons decaying to pairs of photons, muons,taus, and b-quarks;(v) the search for doubly charged Higgs bosons which are expected in extensions of the Higgs
sector with triplets.
Below is a concise description of the most recent searches performed at the LHC and elsewhere.
A summary of these searches in terms of final states is given in Table 11.11 where the correspondingreferences are given for more details.
11.6.7.1 Searches for an additional CP -even state(a) Exclusion limits from LEP
The searches for the SM Higgs boson at LEP provided an absolute lower limit of 114 GeV on its
mass. These searches are also relevant for non-SM Higgs bosons. These searches were interpreted
as 95% CL upper bounds on the ratio of the coupling gHZZ to its SM prediction as a functionof the Higgs boson mass [139, 523]. These results have an impact on MSSM benchmarks such as
7
Still, most non-SUSY models are likely to include further states and dynamics above the weak scale to stabilise
the scalar sector and this new and unknown physics may influence the searches described in this section in a way
difficult to estimate.

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85

Table 11.11: Summary of references to the searches for additional statesfrom extended Higgs sectors. (BBr) denotes the BaBar experiment and(TeV), the Tevatron experiments. V denotes either the W or the Z boson.
Only Run-2 searches references are indicated except when searches havebeen carried out using Run-1 data only. References for Run-1 searches areavailable in Ref. [141].
ATLAS
CMS
CP -even H
H → γγ[440, 441]
[442, 443]
H → γγ (low mass)
[444]
[445]
H → Zγ[446, 447]
[448]
H → ZZ → 4`
[449]
[450]
H → ZZ → ``νν
[449]
[451]
H → W Z → ```ν
—
[452]
[453]
[454, 455]
H → ZZ → ``qq
H → ZZ → ννqq[456]—
H → W W → `ν`ν
[457]
[458]
H → W W → `νqq 0
[459]
[458]
[460, 461]—
H → V V → qq 0 qq 0 (JJ)
H → V V combination[462]—
H → hh → bbτ τ, bbγγ, 4b,[463–465] [455, 466, 467]
γγW W ∗ , bbW W ∗ , W W ∗ W W ∗ , bbZZ ∗CP -odd A (and/or CP -even H)

Other experiments
—
—
—
—
—
—
—
—
—
—
—
—
—

[468]

[469, 470]

A → τ + τ − (low mass)—
H, A → µ+ µ−[475]
H → µτ, eτ LFV
bjµ+ µ− (low µ+ µ− mass)[478]
H, A → tt[461, 480]
H, A → bb[482]
A → hV → bbqq 0 , bb`ν, bb``, ``τ τ, ννbb [486, 487]
A → ZH[490]
H → ZA → bb`+ `−[213]
Charged H ±H ± → τ ±ν[493, 494]
H ± → cs[496]
H ± → tb
[498]
H ± → W ±Z[500]
H ± → W ±A—
H ± → HW ±—H ± → cb—
CP -odd aa → µ+ µ−
[506]

[474]
[476]
[477]
[479]
[481]
[483]
[488, 489]
[491]
[492]

[471, 472] (TeV)[473] (LHCb)
—
—
—
—
—
[484, 485] (TeV)
—
—
—

[495]
[497]
[499]
[501, 502]
[503]
[504]
[505]

—
—
—
—
—
—
—

[507]

—
[513] (LEP)

H, A → τ + τ −h → aa → 4µ, 4τ, 2µ2τ, 4γ[514] (TeV) h → aa → bbµµ, bbτ τ, 4b
Υ1s,3s → aγ
Doubly charged H ±±[508]

[509–512][515, 516]—
[521]

[517, 518]—
[502, 522]

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86

the low-mH scenario where the heavy CP -even Higgs boson is the discovered 125 GeV boson [374],
which is also nearly ruled out by current direct constraints and charged Higgs boson limits from
LHC. These results also impact scenarios of light CP -even Higgs boson of the NMSSM which areconstrained to project predominantly onto the EW singlet component. Additional interest for thesescenarios is due to the slight excess observed at LEP [139] at a Higgs boson mass hypothesis ofapproximately 98 GeV, bolstered by a possible excess in the diphoton channel at 96 GeV in Run-2
data of CMS [445].
(b) Searches at the LHC
At the LHC, the searches for the SM Higgs boson before the 2012 discovery covered a wide
range of mass hypotheses up to approximately 1 TeV. After the discovery, the SM Higgs boson
searches have been reappraised to search for a heavy CP -even state, extending progressively thesearch mass range beyond 1 TeV. This state could be the heavy CP -even Higgs boson of a 2HDM,
or a generic additional singlet. In both cases, the natural width of the additional H state can bevery different from that of the SM Higgs boson. To preserve unitarity of the longitudinal vectorboson scattering and the longitudinal vector boson scattering into fermion pairs, the couplings ofthe additional CP -even Higgs boson to gauge bosons and fermions should not be too large andshould constrain the natural width to be smaller than that of a unique Higgs boson at high mass
with couplings to fermions and gauge bosons as predicted by the SM (and provided that trilinear
and quartic couplings are not too large and that no new state affects the heavy state total width).
It is therefore reasonable to consider total widths for the high mass CP -even state smaller thanthe equivalent SM width. Two specific cases have been considered: (i) the SM width using thecomplex pole scheme (CP S), and (ii) the narrow width approximation. For the sake of generality,
these searches are now done as a function of the Higgs boson mass and total width.
Searches for the Higgs boson in the channels H → γγ, H → Zγ, H → W W (∗) leptonic andsemi-leptonic, and in the H → ZZ (∗) searches in the 4`, ``qq and ``νν channels have also been
done, but some of them are simple reinterpretations of the SM Higgs boson search in the CP S
scheme. References for these searches are summarised in Table 11.11.
(c) Searches for an additional resonance decaying to a pair of Higgs bosons
In addition to the rare and expected Higgs boson pair production mode, high mass CP -even
Higgs bosons can be searched for in the resonant double Higgs boson mode. Searches for suchprocesses, where the Higgs boson is used as a tool for searches for BSM phenomena, have been
carried out in a variety of distinct modes depending on the subsequent decays of each Higgs bosons.
ATLAS and CMS have searched for the H → hh → bbτ τ , bbγγ, H → hh → 4b, H → hh →γγW W ∗ , H → hh → bbW W ∗ , H → hh → W W ∗ W W ∗ and H → hh → bbZZ ∗ final states. For
mass hypotheses of an additional Higgs boson below 500 GeV, the two dominant search channels
are the bbγγ and the bbτ τ channels. For masses above 500 GeV, the most powerful search is withthe 4b final state. As illustrated in Fig. 11.17, these searches provide useful limits in the low tan β
and high mass domain. The list of references for these searches is given in Table 11.11.
(d) Searches for an additional state with the presence of the Higgs boson
In the post-discovery era, analyses searching for additional Higgs bosons need to take into account the presence of the 125 GeV Higgs boson. For searches with sufficiently high mass resolution
to disentangle the additional states which are not degenerate in mass, the strength of the observed
state and limits on the signal strength of a potential additional state can be set independently, as
discussed in the next section. However, in some cases where channels do not have a sufficiently
fine mass resolution to resolve states nearly degenerate in mass, specific analyses need to be designed. There are two examples of such analyses: (i) the search for an additional state in the
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11. Status of Higgs Boson Physics

H → W W (∗) → `ν`ν channel in ATLAS, and (ii) the search for nearly degenerate states in the
H → γγ channel with the CMS detector.
In the H → W W (∗) → `ν`ν channel, the search for an additional state is done using a boosted
decision tree combining several discriminating kinematic characteristics to separate both the signal
from the background and a high mass signal H from the lower mass state h [524]. A simultaneous
fit of the two states h and H is then made to test the presence of an additional state. In this case,the usual null hypothesis of background includes the SM signal.
The CMS search for nearly degenerate mass states decaying to a pair of photons [525] is moregeneric and could for instance apply to CP -odd Higgs bosons as well. It consists of a fit to thediphoton mass spectrum using two nearly degenerate mass templates.
(e) Type I 2HDM and fermiophobia
The measurements of coupling properties of the 125 GeV Higgs boson directly establish its
couplings to fermions. However, the presence of an additional fermiophobic state, as predicted byType I 2HDMs, is not excluded. Prior to the discovery, ATLAS and CMS have performed searches
for a fermiophobic Higgs boson, i.e., produced through couplings with vector bosons only (VBF andV H) and decaying in two photons. CMS has further combined these results with searches in the
W + W − and ZZ channels, assuming fermiophobic production and decay. This way, CMS excluded
a fermiophobic Higgs boson in the range 110 GeV < mH < 188 GeV at the 95% CL. References forthese Run-1 measurements can be found in Ref. [141]11.6.7.2 Searches for additional neutral states (φ ≡ h, H, A) decaying to fermions(a) Exclusion limits from LEP

In e+ e− collisions, around the centre-of-mass energies reached by LEP, the main production
mechanisms of the neutral MSSM Higgs bosons were the Higgs-strahlung processes e+ e− → hZ,
HZ and the pair production processes e+ e− → hA, HA, while the vector boson fusion processes
played a marginal role. Higgs boson decays to bb̄ and τ + τ − were used in these searches.
The searches and limits from the four LEP experiments are described in Refs. [526]. The
combined LEP data did not contain any excess of events which would imply the production of a
Higgs boson. Combined limits were derived [523]. For mA  MZ , the limit on mh is nearly that), theof the SM searches, as sin2 (β − α) ≈ 1. For high values of tan β and low mA (mA ≤ mmaxhe+ e− → hA searches become the most important, and the lightest Higgs boson h is non SM-like.
In this region, the 95% CL mass bounds are mh > 92.8 GeV and mA > 93.4 GeV. In the mmaxhscenario [527], values of tan β from 0.7 to 2.0 are excluded taking mt = 174.3 GeV, while a muchlarger tan β region is excluded for other benchmark scenarios such as the no-mixing one.
A flavour-independent limit for Higgs bosons in the Higgs-strahlung process at LEP has also
been set at 112 GeV [528].
Neutral Higgs bosons may also be produced by Yukawa processes e+ e− → f f φ, where the
Higgs particle φ ≡ h, H, A, is radiated off a massive fermion (f ≡ b or τ ± ). These processes
can be dominant at low masses, and whenever the e+ e− → hZ and hA processes are suppressed.
The corresponding ratios of the f f h and f f A couplings to the SM coupling are − sin α/ cos β andtan β, respectively. The LEP data have been used to search for bb̄ bb̄, bb̄τ + τ − , and τ + τ − τ + τ − final
states [529]. Regions of low mass and high enhancement factors are excluded by these searches.
The searches for the Higgs boson at LEP also included the case where it does not predominantly
decay to a pair of b quarks. All four collaborations conducted dedicated searches for the Higgs
boson with reduced model dependence, assuming it is produced via the Higgs-strahlung process,and not addressing its flavour of decay, a lower limit on the Higgs boson mass of 112.9 GeV is set
by combining the data of all four experiments [528].
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Using an effective Lagrangian approach and combining results sensitive to the hγγ, hZγ andhZZ couplings, an interpretation of several searches for the Higgs boson was made and set a lower
limit of 106.7 GeV on the mass of a Higgs boson that can couple anomalously to photons [528].
(b) Searches at the Tevatron and the LHC
The best sensitivity is in the regime with low to moderate mA and with large tan β which
enhances the couplings of the Higgs bosons to down-type fermions. The corresponding limits on
the Higgs boson production cross section times the branching ratio of the Higgs boson into downtype fermions can be interpreted in MSSM benchmark scenarios [530]. The most promising channels
at the Tevatron are the inclusive pp̄ → φ → τ + τ − process (φ = A, H, h), with contributions fromboth gg → φ and bb̄φ production, and bb̄φ, φ → τ + τ − or φ → bb̄, with bτ τ or three tagged b-jetsin the final state, respectively. Although the Higgs boson production via gluon fusion has a higher
cross section in general than via associated production, it cannot be used to study the φ → bb̄
decay mode since the signal is overwhelmed by the QCD background.
CDF and D0 have searched for neutral Higgs bosons produced in association with bottom
quarks and which decay into bb̄ [484, 485], or into τ + τ − [471, 472]. The most recent searches in thebb̄φ channel with φ → bb̄ analyse approximately 2.6 fb−1 (CDF) and 5.2 fb−1 (D0) of data, seeking
events with at least three b-tagged jets. The cross section is defined such that at least one b quark
not from φ decay is required to have pT > 20 GeV and |η| < 5. The invariant mass of the twoleading jets as well as b-tagging variables are used to discriminate the signal from the backgrounds.
The QCD background rates and shapes are inferred from data control samples, in particular, thesample with two b-tagged jets and a third, untagged jet. Separate-signal hypotheses are tested andlimits are placed on σ(pp̄ → bb̄φ) × BR(φ → bb̄). A local excess of approximately 2.5σ significancehas been observed in the mass range of 130–160 GeV, but D0’s search is more sensitive and setsstronger limits. The D0 result had a O(2σ) local upward fluctuation in the 110 to 125 GeV mass
range. These results have been superseded by the LHC searches and the excess seen by D0 has notbeen confirmed elsewhere.
A substantially larger sensitivity in the search for the φ → τ + τ − is obtained with the ATLAS
and CMS analyses. The higher centre-of-mass energy reached at the Run 2 brings a substantial,
though not excessively large, increase in sensitivity due to the intermediate masses probed. BothATLAS and CMS have reported the result of their searches in this important channel with thefull 2016 dataset. The searches are performed in categories of the decays of the two tau leptons:eτhad , µτhad , eµ, and µµ, where τhad denotes a tau lepton which decays to one or more hadrons
plus a tau neutrino, e denotes τ → eνν, and µ denotes τ → µνν. The dominant background comesfrom Z → τ + τ − decays, although tt̄, W +jets and Z+jets events contribute as well. Separating
events into categories based on the number of b-tagged jets improves the sensitivity in the MSSM.
The bb̄ annihilation process and radiation of a Higgs boson from a b quark gives rise to events inwhich the Higgs boson is accompanied by a bb̄ pair in the final state. Requiring the presence of one
or more b-jets reduces the background from Z+jets. Data control samples are used to constrain
background rates. The rates for jets to be identified as a hadronically decaying tau lepton aremeasured in dijet samples, and W +jets samples provide a measurement of the rate of events that,with a fake hadronic tau, can pass the signal selection requirements. Lepton fake rates are measured
using samples of isolated lepton candidates and same-sign lepton candidates. Constraints from the
ATLAS searches are shown in Fig. 11.17 (left) in the hMSSM approximation defined in Ref. [376].
The neutral Higgs boson searches consider the contributions of both the CP -odd and CP -even
neutral Higgs bosons with enhanced couplings to bottom quarks, similarly to was done for theTevatron results. In Fig. 11.17, decays of the charged Higgs boson into τ ν and decays of the heavy
Higgs boson into a pair of SM-like Higgs bosons or gauge bosons, or decays of A into hZ are also
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11. Status of Higgs Boson Physics

being constrained. In addition, decays of the neutral Higgs bosons into muon pairs are also being
explored. In the mmod+
scenario, the region of tan β lower than 5 does not allow for a Higgs bosonhmass mh close to 125 GeV. For the hMSSM scenario, instead, the SM-like Higgs boson mass is fixed
as an input and hence the requirement that it is close to 125 GeV is always fulfilled, although thismay imply other limitations as discussed in Section 11.6.1.1.
A search for φ → µ+ µ− has also been performed by ATLAS [475] and CMS [476] and no
significant deviations from the SM expectation were observed, allowing to set model-independent
limit on the product of the branching fraction for the decay into a muon pair and the cross section
for the production of a scalar neutral boson, either via gluon fusion, or in association with b quarks,
in the mass range from 130 to 1000 GeV.

Figure 11.17: The 95% CL exclusion contours in the (MA , tan β) parameter space for: (left) asummary of CMS Run-2 searches in the hMSSM and (right) in the Mh125 scenario.
Finally, searches for a resonance decaying to a top quark pair were done by ATLAS [480,531] andCMS [481, 532]. These searches were interpreted as searches for scalar resonances by ATLAS [480],
however, an important component of these searches is an accurate treatment of the interference
effects between the signal and the continuum background. These effects can yield a dip and peakstructure instead of a simple peak [372]. ATLAS has performed a search for a high mass state
decaying to a pair of top quarks taking into account the deformation in mass shape of the signal
in the presence of the continuum background [533].
The LHC has the potential to explore a broad range of SUSY parameter space through the search
for non-SM-like Higgs bosons. As illustrated in Fig. 11.17, the parameter space corresponding tolarge tan β values and large masses of the A boson are covered mostly by the searches in theA, H → τ + τ − channel. A projection of the combined sensitivity of ATLAS and CMS at the HLLHC has been performed in Ref. [118], showing that, compared to the current sensitivity, the full
HL-LHC luminosity can expand the exclusion domain by nearly 1 TeV. In the low tan β limit, theparameter space spanning large A boson masses is best excluded indirectly from the observed Higgs
boson measurements. This is illustrated in the Mh125 scenario by the nearly horizontal exclusion
which is due to the compatibility of the Higgs boson mass measurement with its prediction fromradiative corrections (mostly from the stop sector). Nevertheless, Fig. 11.17 (right) shows a broad
region with intermediate tan β and large values of mA that is not accessed by current searches, andin which the most promising channel is the very difficult search for tt decays with its aforementioned
intricacies [379]. In this region of parameter space, it is possible that only the SM-like Higgs boson
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can be within the LHC’s reach. If no other state of the EWSB sector than the 125 GeV state is
discovered, it may be challenging to determine only from the Higgs sector whether there is a SUSY
extension of the SM in nature.
11.6.7.3 Searches for a CP -odd state decaying to hZ
Similarly, to the search for a CP -even high mass Higgs boson decaying to a pair of Higgs bosons,the search for a CP -odd states decaying to hZ was carried out at the LHC by ATLAS and CMS
in various channels: (i) (Z → ``)(h → bb), (ii) (Z → νν)(h → bb), (iii) (Z → ``)(h → τ τ ), and(iv) (Z → ``)(h → τ τ ). The searches where the A boson decays to a pair of b quarks have been
performed both in the regime where both b-jets are resolved and in the boosted regime where thetwo b-jets are merged in a single larger radius jet. These searches have been used to constrain theparameter space of 2HDMs. In the MSSM, these searches place limits on small values of tan β formasses of A between 220 GeV and 360 GeV.
11.6.7.4 Searches for low mass states
Searches for pseudo-scalar Higgs boson at intermediate to low masses, below the Z mass (inthe 25 GeV to 80 GeV mass range) have been performed by CMS both in the τ + τ − [534] and theµ+ µ− [535] decay channels. A light pseudo-scalar in this mass range is excluded by current direct
constraints in the MSSM but not in general 2HDMs [536]. These searches are done in the decay
channels where the pseudo-scalar Higgs boson is produced in association with a pair of b-quarks
and decays into a pair of taus or muons.
CMS has also reported an anomaly observed in the search for µ+ µ− resonances produced with
one jet tagged as containing a b-hadron and a forward jet in the Run-1 data. A mild excess appearedin the di-muon mass distribution at approximately 28 GeV. Another very mild excess was then also
found in the 2016 Run-2 data [479]. ATLAS then performed a similar analysis with the full Run-2
dataset corresponding to an integrated luminosity of approximately 139 fb−1 , and no significant
excess was found [478].
Searches for low mass Higgs bosons were also performed in the diphoton channel by both ATLAS
and CMS [537,538] at Run 1. ATLAS and CMS have updated the results of this search with Run-2
data [440, 442]. A modest excess has been observed by CMS at a mass of 95.4 GeV with a local
significance of 2.9σ (the corresponding global significance is 1.3σ). A slight excess was also seen
by ATLAS at the same mass of 95.4 GeV with a local significance of 1.7σ. No significant excess
has been observed in this region by ATLAS at Run 1. This mildly significant excess also coincides
in mass with the excess observed at LEP and discussed in Section 11.6.7.1. It is interesting tonote that the sensitivity of searches at masses very near that of the Z boson, require a very strong
rejection of events where electrons are misidentified as photons. Dedicated experimental methods
have been developped to reduce the vulnerability of the analysis in this specific mass region to thisbackground. It has therefore raised interest and speculations on its possible nature, see for instanceRef. [539] and references therein.
11.6.7.5 Searches for charged Higgs bosons H ±At e+ e− colliders, charged Higgs bosons can be pair produced in the s-channel via γ or Z
boson exchange. This process is dominant in the LEP centre-of-mass energies range, i.e., up to
209 GeV. At higher centre-of-mass energies, other processes can play an important role such as the
production in top quark decays via t → b + H + if mH ± < mt − mb or via the one-loop processe+ e− → W ± H ∓ [540, 541], which allows the production of a charged Higgs boson with mH ± >√s/2, even when H + H − production is kinematically forbidden. Other single charged Higgs boson
production mechanisms include tb̄H − / t̄bH + production [123], τ + νH − / τ − ν̄H + production [542],
and a variety of processes in which H ± is produced in association with a one or two other gauge
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and/or Higgs bosons [543].
At hadron colliders, charged Higgs bosons can be produced in several different modes dependingon the value of its mass with respect to the top-quark mass. For light values of the charged
Higgs boson mass, defined by Higgs boson masses smaller than the mass of the top quark (withexperimental analyses typically considering masses up to mH ± ≤ 160 GeV), the top-quark decayt → Hb is allowed and the charged Higgs boson is light enough so that top-quark off-shell effects canbe neglected. The cross section for the production of a light charged Higgs boson is simply given by
the product of the top-pair production cross section and the branching ratio of a top quark into acharged Higgs boson. The top-pair production cross section is known up to NNLO in perturbative
QCD [544], and relevant QCD and SUSY-QCD including NLO corrections to the branching ratio
for t → H + b have been computed in the literature, see Refs. [545–547] and references therein.
At present, the theoretical accuracy for the production of a light charged Higgs boson is at the
few percent level. For the intermediate mass range, values of mH ± near mt , the finite top-width
effects as well as the interplay between top-quark resonant and non-resonant diagrams cannot be
neglected. Hence, the full process pp → H ± W ∓ bb̄ (with massive b-quarks) must be considered toperform a reliable perturbative calculation of the charged Higgs boson production cross section [547].
For heavy charged Higgs boson scenarios, with charged Higgs boson masses larger than the topquark mass (typically above 180 GeV), the dominant charged Higgs boson production channel isthe associated production with a top quark/antiquark and a (possibly low transverse momentum)
bottom antiquark/quark. Theoretical calculation at NLO have been computed both at the inclusiveand fully-differential level in the five-flavour scheme and in the four-flavour scheme, see Ref. [40]and references therein. Charged Higgs bosons can also be produced via associated production with
W ± bosons through bb annihilation and gg-fusion annihilation [548].
For charged Higgs boson production cross section predictions for the Tevatron and the LHC,
see Refs. [38, 39, 370].
(a) Exclusion limits from LEP
Charged Higgs bosons have been searched for at LEP, where the combined data of the four
experiments, ALEPH, DELPHI, L3, and OPAL, were sensitive to masses of up to about 90 GeV [523]in two decay channels, τ ν and cs. The combined LEP data exclude, at 95% CL, charged Higgs
bosons with mass below 80 GeV (Type II scenario) or 72.5 GeV (Type I scenario) [549].
(b) Exclusion limits from Tevatron
Compared to the mass domain covered by LEP searches, the Tevatron covered a complementary
range of charged Higgs boson masses. CDF and D0 have also searched for charged Higgs bosons
in top quark decays with subsequent decays to τ ν or to cs̄ [550]. For the H + → cs̄ channel, thelimits on BR(t → H + b) from CDF and D0 are ≈ 20% in the mass range 90 GeV < mH + < 160 GeV
and assuming a branching fraction of 100% in this specific final state. H + → τ + ντ channel, D0’s
limits on BR(t → H + b) are also ≈ 20% in the same mass range and assuming a branching fractionof 100% in this final state. These limits are valid in general 2HDMs, and they have also beeninterpreted in terms of the MSSM [550].
(c) Exclusion limits from LHC
Similarly, to the Tevatron, at the LHC, light charged Higgs bosons can be searched for in the
decays of top quarks. The main initial production mode for light charged Higgs bosons (mH ± <mt − mb ) is top pair production. The subsequent decay modes of the charged Higgs boson forthese searches are τ ν and cs. More recently, ATLAS and CMS have also searched for higher
mass charged Higgs bosons (mH ± > mt + mb ) in H + → tb. The main production modes are theassociated production of a charged Higgs boson in association with a top and a bottom quark or
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in association with a top quark only.
The decay H + → τ + ντ is searched typically in three final state topologies:(i) lepton+jets: with tt̄ → b̄W H + → bb̄(q q̄ 0 )(τlep ν), i.e., the W boson decays hadronically and thetau decays into an electron or a muon, with two neutrinos;(ii) τ +lepton: with tt̄ → b̄W H + → bb̄(lν)(τhad ν), i.e., the W boson decays leptonically (with` = e, µ) and the tau decays hadronically;(iii) τ +jets: tt̄ → b̄W H + → bb̄(q q̄ 0 )(τhad ν), i.e., both the W boson and the τ decay hadronically.

CMS has also searched for the charged Higgs boson in the decay products of top quark pairs:tt̄ → H ± W ∓ bb̄ and tt̄ → H + H − bb̄ as well. Three types of final states with large missing transverse
energy and jets originating from b-quark hadronisation have been analysed: the fully-hadronic
channel with a hadronically decaying tau in association with jets, the dilepton channel with ahadronically decaying tau in association with an electron or muon and the dilepton channel with
an electron-muon pair. The results of the searches at the LHC are illustrated in Figure 11.17.
Both ATLAS and CMS have also searched for high mass charged Higgs bosons decaying to a
top and bottom quarks. The main production mode for this search is the associated production
with one top quark (5-flavour scheme) or a top quark and and bottom quark (4-flavour scheme) in
the final state. The s-channel production mode where the charged Higgs boson is produced alone in
the final state at tree level is also considered. This search is particularly intricate and it is sensitive
to the modelling of the top pair production background produced in association with additional
partons and in particular b-quarks. No excess was found and the results are expressed in terms of
exclusion limits of cross section times branching fractions.
ATLAS and CMS have also searched for charged Higgs bosons in top quark decays assuming
BR(H + → cs̄) = 100% [496, 551], and sets limits of ≈ 20% on BR(t → H + b) in the 90 GeV< mH + < 160 GeV mass range.
In 2HDMs, the decay of the charged Higgs boson to a W and a Z boson is allowed only at
loop level and is therefore suppressed. However the H ± → W ± Z decay channel is allowed in Higgs
triplet models. ATLAS [500] has searched for such decays, requiring that the charged Higgs bosonis produced through the fusion of vector bosons. No excess with respect to the SM backgrounds has
been observed in this channel, and the results are interpreted in the Georgi–Machacek model [414]discussed in Section 11.6.5.2.
At the LHC, various other channels still remain to be explored, in particular searches involving
additional neutral scalars in particular in the W H, W A channels (A is the pseudo-scalar MSSM
Higgs boson), and in the W a channel (a is the light CP -odd scalars of the NMSSM).
11.6.7.6 Interpretation of the measurements of the coupling properties of the Higgs boson
The 125 GeV Higgs boson being part of any hypothetically extended EWSB sector, it can beused through the compatibility of its measured couplings and mass with those predicted in specificmodels to provide constraints on these specific models parameters.
As discussed in Section 11.6.1.1, the mass of the Higgs boson limits drastically the MSSM
parameter space and can be used to set limits on specific MSSM benchmarks. This is the case for
the Mh125 scenario as illustrated in Fig. 11.16 and in Fig. 11.17, corresponding approximately toa lower limit on tan β in this model [118].
The measurements of the Higgs boson couplings, discussed in Section 11.5, can be interpreted
in the framework of a constrained model where the couplings of the Higgs boson to vector bosons,up-type quarks, down-type quarks and leptons, are varied. In 2HDMs, these couplings are functionsof the mixing angle α between the observed Higgs boson and the heavy CP -even neutral scalar,and of the ratio of the vacuum expectation values of the two doublets, tan β. In the case of the
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MSSM, the two parameters are the A boson mass and tan β (the sole two parameters needed todescribe the MSSM Higgs sector at tree level). The coupling measurements have been interpreted
both by ATLAS [312] and CMS [552] in specific MSSM benchmarks and in 2HDMs. The exclusion
contour in the hMSSM for the ATLAS combination [312] is illustrated in Fig. 11.17.
11.6.7.7 Searches for a light CP -odd Higgs boson
A light pseudo-scalar boson a is present in any two Higgs doublet model enhanced with anadditional singlet field. A prominent example is the NMSSM. The theoretical motivations for
singlet extensions of the MSSM are discussed in Section 11.6.2. There is also a variety of othermodels with light additional spin-0 bosons such as two Higgs doublet models with a scalar, Little
Higgs models or light scalar mediator to a dark sector.
In the framework of the NMSSM, the searches now focus on the low a mass region for several
reasons:(i) in the NMSSM, the light pseudo-scalar a boson can, as a pseudo-Goldstone boson, be a natural
candidate for an axion;(ii) scenarios where ma > 2mb and a CP -even state h decaying to a pair of a (mh > 2ma ) areexcluded by direct searches at LEP in the four b’s channel [514, 523, 553];(iii) in the pre-discovery era, LEP limits on a CP -even Higgs boson resulted in fine-tuning MSSM
constraints [554] which could be evaded through non standard decays of the Higgs boson toaa;(iv) in the NMSSM, a CP -odd a boson with a mass in the range 9.2–12 GeV can also accountfor the difference observed between the measured anomalous muon magnetic moment and its
prediction [555].
The benchmark scenarios have also changed in the light of the Higgs boson discovery. The
125 GeV state could be the lightest or the next-to-lightest of the three CP -even states of the
NMSSM. Light pseudo-scalar scenarios are still very interesting in particular for the potential
axion candidate. There are three main types of direct searches for the light a boson:(i) for masses below the Υ resonance, the search is for radiative decays Υ → aγ at B-factories;(ii) the inclusive search in high energy pp collisions at the LHC;(iii) the search for decays of the observed CP -even Higgs h boson into a pair of a bosons;Radiative decays Υ → aγ have been searched for in various colliders, the most recent results aresearches for radiative decays of the Υ (1s) to aγ with a subsequent decay of the a boson to a pairof taus at CLEO [556], and the radiative decays of the Υ (1s, 2s, 3s) to aγ with subsequent decays
to a pair of muons or taus by BaBar [519, 520].
Direct inclusive searches for the light pseudo scalar a boson were performed in the a → µµ
channel at the Tevatron by D0 [514] and by ATLAS [506], CMS [507], and LHCb [164] at the LHC.
Finally, searches for the decays of the Higgs boson to a pair of a bosons were performed withsubsequent decays to four photons, in the four muons final state, in the two muons and two taus
final state, and in the four taus final state.
No significant excess in the searches for a light CP -odd a boson was found and limits on the
production times branching fractions of the a boson have been set.
References for all these searches are summarised in Table 11.11.
11.6.7.8 Searches in Higgs decays
Dark-photons or axion-like particles searches can also be carried out within the decays of the
Higgs boson to four leptons through dilepton pair resonances. Such search has been carried out by
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ATLAS and CMS [557]. Alternatively signatures of dark photons escaping detection with misingtransverse momentum signatures have also been searched for by ATLAS [558].
11.6.7.9 Searches for doubly charged Higgs bosons H ±±As discussed in Section 11.6.5, the generation of small neutrino masses via the standard EWSB
mechanism described in Section 11.2 requires unnaturally small Yukawa couplings, provided thatneutrinos are Dirac-type fermions. A Majorana mass term with a see-saw mechanism for neutrinos,
would allow for naturally small masses and would also yield a framework for the appealing scenario
of leptogenesis. However, within the SM, Majorana mass terms correspond to (non-renomalizable)
dimension-5 operators. Such effective interactions can be generated via renormalisable interactions
with an electroweak triplet of complex scalar fields (corresponding to a type-II see-saw mechanism).
Other models such as the Zee–Babu model, with the introduction of two SU(2)L singlets, also
generate Majorana mass terms. The signature of such models would be the presence of doubly
charged Higgs bosons H ±± .
The main production mechanisms of H ±± bosons at hadron colliders are the pair production in
the s-channel through the exchange of a Z boson or a photon and the associated production with acharged Higgs boson through the exchange of a W boson. Various searches for doubly charged Higgs
bosons have been performed by ATLAS and CMS at Run 1 [559] and Run 2 [521, 522]. Typically,
these searches aim at low values of the Higgs triplet vacuum expectation for which the doubly
charged Higgs boson will decay mostly to leptons (for high values, the decay to W bosons will
become predominant). These searches assume that the coupling to W bosons is negligible and thatthe main production mode is through the Drell–Yan process.
11.6.7.10 Searches for non-standard production processes of the Higgs boson
The discovery of the Higgs boson has also allowed for searches of BSM processes involving
standard decays of the Higgs boson. One example directly pertaining to the search for additional
states of the EWSB sector is the search for Higgs bosons in the cascade decay of a heavy CP even Higgs boson decaying to charged Higgs boson and a W boson, and the charged Higgs boson
subsequently decaying to H and another W boson. This search has been performed by ATLAS inbb decays of the 125 GeV Higgs boson [560].
11.6.7.11 Outlook on searches for additional states
The LHC program of searches for additional states covers a large variety of decay and production
channels. Since the Higgs boson discovery, many new channels have been explored at the LHC,
e.g., the searches for additional states decaying into hh or V h or ZA. The search for charged Higgs
bosons has been extended to include the W Z, W A and the very difficult tb decay channel.

11.7 Summary and outlook

Summary– The discovery of the Higgs boson is a major milestone in the history of particle
physics as well as an extraordinary achievement of the LHC machine and the ATLAS and CMS
experiments. Eleven years after the discovery, substantial progress in the field of Higgs boson
physics has been accomplished and a significant number of measurements probing the nature ofthis unique particle have been made. They are revealing an increasingly precise profile of the Higgs
boson.
The LHC has concluded its Run 2 in 2018, delivering a dataset of 13 TeV pp collisions corresponding to an integrated luminosity of more than 150 fb−1 of data collected by ATLAS and
CMS. The Run 3 started in 2022 at 13.6 TeV and more than 70 fb−1 of additional data were delivered. First cross section measurements at this new centre-of-mass energy have been presented
and are reported herein. With the substantial increase in production rates at the higher center-ofmass energy (mostly from Run 1 to Run 2) and the larger datasets, new landmark results in Higgs
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physics have been achieved. They are highlighted in the 10th anniversary papers of the Higgs boson
discovery [183, 184].
Three new results of fundamental importance have been achieved with Run-2 datasets by ATLAS and CMS independently: (i) the clear and unambiguous observation of the Higgs boson decay
to taus; (ii) the clear and unambiguous observation of the Higgs boson decay to a pair of b quarks;(iii) the clear and unambiguous observation of the production of the Higgs boson through the tt̄H
process. These results provide direct evidence for the Yukawa coupling of the Higgs boson tofermions of the third generation: taus, bottom quarks and top quarks, at rates compatible withthose expected in the SM. In addition, the evidence for the decay of the Higgs boson to muons
is being consolidated. These, and all other experimental measurements, are consistent with the
EWSB mechanism of the SM.
New theoretical calculations and developments in Monte-Carlo simulations pertaining to Higgs
physics are still occurring at a rapid pace. For example, the theoretical prediction for the dominant
gluon fusion production mode now includes the latest N3LO result at the inclusive and differential
levels, which is twice as precise as previous N2LO calculations. With these improvements in thestate-of-the-art theory predictions and the increase in luminosity and center-of-mass energy, Higgs
physics has definitively entered a precision era. Its impact can already be seen on the latest Run-2
combined measurements of the Higgs boson couplings (see Section 11.5).
Since the discovery of the Higgs boson, new ideas have emerged to probe its rare decays andproduction modes, as well as to indirectly measure the Higgs boson width through the study of its
off-shell couplings, or via on-shell interference effects. The Higgs boson has now become part ofthe standard toolkit in searches for new physics, with Higgs measurements being used in SMEFT
global fits.
Many extensions of the SM at higher energies call for an enlargement of the EWSB sector.
Hence, direct searches for additional scalar states can provide valuable insights on the dynamics
of the EWSB mechanism. The ATLAS and CMS experiments have searched for additional Higgs
bosons in the Run-2 data, and have imposed constraints in broad ranges of mass and couplings forvarious scenarios with an extended Higgs sector.
The landscape of Higgs physics has been scrutinized extensively since its discovery. The current
precisions on the measurements of the couplings of the Higgs boson to gauge bosons and third
generation fermions are typically of the order of 10–20%. The uncertainty on the Higgs boson
coupling to the muon shrank below 50%, and the upper limits on the branching fraction to newinvisible particles are approximately 10%. Sensitivity to the Higgs boson self-coupling has notreached the SM value yet, and there is no information on how the Higgs field acquired its VEV in
the early times of the Universe. However, significant progress in being made through exploration of
di-Higgs production, including new analyses based on machine learning algorithms. This situation
allows for new challenges to ultimately increase further the reach in precision and it also widens thepossibilities of unveiling the true nature and the dynamics of the electroweak symmetry breaking
mechanism.
Outlook– The unitarisation of the vector boson scattering (VBS) amplitudes, dominated at highenergies by their longitudinal polarisation, has been the basis of the no lose theorem at the LHC,
and was a determining consideration in the building of the accelerator and detectors. It motivatedthe existence of a Higgs boson or the observability of manifestations of strong dynamics at theTeV scale. Now that a Higgs boson has been found and its couplings to gauge bosons are - withincurrent accuracy - consistent with the SM predictions, perturbative unitarity is preserved to a large
extent with the sole exchange of the Higgs boson, and without the need for any additional states.
VBS remains still an important channel to further investigate in order to better understand thenature of the Higgs sector and the possible completion of the SM at the TeV scale. In association
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with the double Higgs boson production channel by vector boson fusion, VBS could, for instance,
confirm that the Higgs boson is part of a weak doublet and also establish whether it is an elementary
object or a composite state that could emerge as a pseudo-Nambu–Goldstone boson from a newunderlying broken symmetry.
The fermion-Higgs boson couplings are not governed by local gauge symmetry. Thus, in addition to a new particle, the LHC has also discovered a new force, different in nature from the otherfundamental interactions since it is non-universal and distinguishes between the three families ofquarks and leptons. The existence of the Higgs boson embodies the problem of an unnatural cancellation among the quantum corrections to its mass if new physics is present at scales significantly
higher than the EW scale. The non-observation of additional states which could stabilise the Higgs
boson mass is a challenge for natural scenarios like Supersymmetry or models with a new strong
interaction in which the Higgs boson is not a fundamental particle. This increasingly pressing
paradox starts questioning the principle of naturalness and it also inspires new solutions tied to thecosmological evolution of the Universe.
The search for the Higgs boson has occupied the particle physics community for the last 50
years. Its discovery has shaped and sharpened the physics programs of the LHC and of prospective
future accelerators [126, 561]. With respect to current data, at the HL-LHC the precision will
improve by a factor of approximately 5–10 depending on the observables considered. Table 11.8
displays the expected sensitivities in the characterization of the Higgs boson at HL-LHC: in thistable, the parameters κi specify by how much the coupling of the Higgs boson to a given particle
i deviates from the SM expectation. The only channels which are expected to be limited by data
statistics are the rare decays to muons and Zγ. In all other cases, the experimental systematic
uncertainties are similar to the statistical uncertainties, but the dominant source of uncertainty
arises from theory, and this remains the case even after assuming that, by the end of the HL-LHC
run, the theory uncertainties can be reduced by a factor two compared to the current uncertainties,a hypothesis that appears realistic but still requires dedicated and concerted work [118]. For both
hadron and lepton colliders, some theoretical progress is crucial to fully exploit and capitalise on theexperimental data. In particular, the expected HL-LHC data together with rapid ongoing progressin theoretical calculations are defining a new era of precision Higgs boson measurements.
Acknowledgements
We would like to thank many of our colleagues for proofreading this review, for useful criticism
and for their input in general: W. Altmannshofer, J. de Blas, G. Branco, G. Buchalla, J. Campbell,
F. Caola, F. Cerutti, C. Csáki, R. Contino, J. Conway, N. Craig, A. David, S. Dawson, J.B. De Vivie,
J. D’Hondt, G. Durieux, C. Englert, J.R. Espinosa, A. Falkowski, L. Fayard, W. Fischer, S. Forte,
S. Gori, M. Grazzini, J. Gu, H. Haber, B. Heinemann, S. Heinemeyer, J. Hubisz, A. Korytov,
B. Jäger, H. Ji, T. Junk, P. Langacker, J. Lykken, F. Maltoni, M.L. Mangano, B. Mansoulié,
M. McCullough, R. Mishra, M. Mühlleitner, B. Murray, M. Neubert, A. Nisati, Y. Paul, G. Perez,
G. Petrucciani, A. Pomarol, E. Pontón, R. Rattazzi, D. Rebuzzi, L. Reina, F. Riva, R. Salerno, J.
Santiago, E. Salvioni, N. Shah, G. Shaughnessy, M. Spira, A. Strumia, K. Tackmann, R. Tanaka,
J. Terning, A. Vartak, C. Wagner, N. Wardle, A. Weiler, A. Wulzer, and G. Zanderighi. We arealso most grateful to the ATLAS, CDF, CMS and D0 collaborations for their help with this review.
M.C. is supported by Fermilab, that is operated by Fermi Research Alliance, LLC under Contract No. DE–AC02–07CH11359 with the United States Department of Energy. C.G. is supportedby the Helmholtz Association and by the Deutsche Forschungsgemeinschaft under Germany’s Excellence Strategy – EXC 2121 “Quantum Universe” – 390833306. V.S. is supported by the grant
DE–SC0009919 of the United States Department of Energy.
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