Maxi-sizing the trilinear Higgs self-coupling: how large could it be?
Eur. Phys. J. C
Maxi-sizing the trilinear Higgs self-coupling: how large could it be?
Luca Di Luzio 0
Ramona Gröber 0
Michael Spannowsky 0
0 Department of Physics, Institute for Particle Physics Phenomenology, Durham University , Durham DH1 3LE , UK
In order to answer the question on how much the trilinear Higgs self-coupling could deviate from its Standard Model value in weakly coupled models, we study both theoretical and phenomenological constraints. As a first step, we discuss this question by modifying the Standard Model using effective operators. Considering constraints from vacuum stability and perturbativity, we show that only the latter can be reliably assessed in a model-independent way. We then focus on UV models which receive constraints from Higgs coupling measurements, electroweak precision tests, vacuum stability and perturbativity. We find that the interplay of current measurements with perturbativity already excludes selfcoupling modifications above a factor of a few with respect to the Standard Model value. 1 Introduction . . . . . . . . . . . . . . . . . . . . . . 2 Theoretical constraints on Higgs self-couplings . . . . 2.1 EW symmetry breaking with d = 6 operators . . 2.2 Vacuum instabilities . . . . . . . . . . . . . . . . 2.2.1 Large-field-value instability: h¯ . . . . 2.2.2 Low-scale instability: h¯ = 0 . . . . . . . . 2.3 Perturbativity bounds . . . . . . . . . . . . . . . 2.3.1 Partial-wave unitarity . . . . . . . . . . . . 2.3.2 Loop-corrected vertices . . . . . . . . . . . 3 UV complete models . . . . . . . . . . . . . . . . . . 3.1 Tree-level custodially symmetric cases . . . . . . 3.1.1 Indirect bounds . . . . . . . . . . . . . . . 3.1.2 Results . . . . . . . . . . . . . . . . . . . 3.2 Tree-level custodially violating cases . . . . . . . 3.2.1 Indirect bounds . . . . . . . . . . . . . . . 3.2.2 Results . . . . . . . . . . . . . . . . . . .
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Contents
The recent discovery of the Higgs boson at the Large Hadron
Collider (LHC) [1, 2] marks a milestone event for
highenergy physics. Yet, the Higgs boson is only a remnant
of the underlying mechanism of spontaneous electroweak
(EW) symmetry breaking, the so-called Brout–Englert–
Higgs mechanism [3, 4]. In order to improve our
understanding of the dynamics initiating EW symmetry breaking, a key
ingredient is the global structure of the scalar potential that
triggers the spontaneous breaking of SU (
2
)L × U (
1
)Y →
U (
1
)QED. While the ongoing LHC program, focussing on
precise measurements of Higgs and gauge boson masses and
couplings, will continue to improve our understanding of the
potential’s local structure in the vicinity of the EW
minimum, information on the shape of the vacuum in a
modelindependent way is experimentally very difficult to obtain.1
However, if one specifies the degrees of freedom and
interactions in the scalar sector, one can calculate the form of the
scalar potential. After EW symmetry breaking such
potential gives rise to multi-scalar interactions, i.e. at lowest order
cubic and quartic Higgs self-interactions. While the former
can be probed directly in searches for multi-Higgs final states
[7–29], indirectly via their effect on precision observables
[30, 31] or loop corrections to single Higgs production [32–
1 The energy scale of non-perturbative phenomena, e.g. the mass of the
SU (
2
)L sphalerons [5], could potentially allow one to probe the scalar
potential away from the EW minimum [6].
36], the latter are inaccessible at the LHC or a future linear
collider [37–39]. Thus, to obtain a glimpse at the shape of
the scalar potential we have to focus on the cubic scalar
selfcoupling.
If new light degrees of freedom contribute to the Higgs
potential, they typically dominate the multi-Higgs
phenomenology. On the other hand, if new degrees of freedom
are heavy, it is widely argued that the effective field theory
(EFT) approach is most suitable to study deformations of
the Standard Model (SM) Higgs potential in a rather
modelindependent and predictive way. Thus, in the latter case,
where we assume that no light states below the cutoff scale
v ≡ 246 GeV exist, it is tempting to introduce an
operator |H |6 (where H denotes the usual Higgs doublet) and
connect the (global) properties of the vacuum, e.g. whether the
EW minimum is a local or global one, with the cubic Higgs
self-coupling. In particular, one could consider using
vacuum stability arguments to infer model-independent bounds
on the triple Higgs coupling.
In this work, we show that this approach is flawed. In
particular, there can be two kinds of instabilities
corresponding to the possible emergence of new minima either at large
field values v h¯ or at h¯ = 0 (where h¯ denotes the
background field of the effective Higgs potential, whose
minimum determines the ground state of the theory). The former,
is shown to be spurious since the very expansion of the scalar
potential in powers of h¯/ in the vicinity of an instability
leads to the brea (...truncated)