Physics Letters B 789 (2019) 373–377
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Physics Letters B
www.elsevier.com/locate/physletb
Higgs–inflaton mixing and vacuum stability
Yohei Ema
a
, Mindaugas Kar
ˇ
ciauskas
b,∗
, Oleg Lebedev
c
, Stanislav Rusak
d
, Marco Zatta
c
a
Department of Physics, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
b
University of Jyvaskyla, Department of Physics, P.O.Box 35 (YFL), FI-40014 University of Jyväskylä, Finland
c
University of Helsinki and Helsinki Institute of Physics, P.O. Box 64, FI-00014, Helsinki, Finland
d
Nordita, KTH Royal Institute of Technology and Stockholm University, Roslagstullsbacken 23, SE-106 91 Stockholm, Sweden
a r t i c l e i n f o a b s t r a c t
Article history:
Received
14 May 2018
Received
in revised form 22 October 2018
Accepted
22 October 2018
Available
online 21 December 2018
Editor:
G.F. Giudice
The quartic and trilinear Higgs field couplings to an additional real scalar are renormalizable, gauge
and Lorentz invariant. Thus, on general grounds, one expects such couplings between the Higgs and
an inflaton in quantum field theory. We find that the often omitted trilinear interaction is only weakly
constrained by cosmology and could stabilize the electroweak vacuum by increasing the Higgs self-
coupling.
The consequent Higgs–inflaton mixing can be as large as order one making a direct inflaton
search possible at the LHC.
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license
(http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP
3
.
1. Introduction
The current data favor metastability of the electroweak (EW)
vacuum, although the result is very sensitive to the top quark mass
[1–6]. Assuming that our vacuum is indeed metastable, we face a
number of cosmological challenges including why the Universe has
chosen an energetically disfavored state and why it stayed there
during inflation despite quantum fluctuations [7,8]. Minimal solu-
tions
to these puzzles require modification of the Higgs potential
during inflation only [8], although introduction of a single extra
scalar is sufficient to make the electroweak vacuum completely
stable [9,10].
In
this Letter, we suggest another minimal option which does
not employ any extra fields beyond the usual inflaton. We show
that the Higgs mixing with an inflaton can lead to a stable EW
vacuum. A trilinear Higgs–inflaton coupling always leads to such
a mixing and it is generally present in models describing the re-
heating
stage [11]. We find that cosmological constraints on this
coupling are weak and an order one mixing is possible. In this
case, the model is effectively described by a single mass scale
of the EW size making it particularly interesting for direct LHC
searches.
*
Corresponding author.
E-mail
address: mindaugas.k@ucm.es (M. Kar
ˇ
ciauskas).
2. The set up
In quantum field theory, one should include all the couplings
that are (up to) dimension-4, gauge and Lorentz invariant. Thus,
on general grounds, we expect a quartic H
†
Hφ
2
and a trilinear
H
†
Hφ interaction between the Higgs field and an inflaton φ. The
presence of the trilinear term can be motivated by the need for re-
heating
the Universe after inflation: the inflaton transfers (at least
in part) its energy to the SM particles through decay and the rel-
evant
interactions generate the H
†
Hφ term at loop level [11]. It
can only be forbidden if the inflaton is assumed to be stable, for
instance, due to the φ →−φ symmetry, and constitutes part of
dark matter [12]. However, it is not clear whether this symmetry
remains exact in quantum gravity.
Apart
from the renormalizable QFT interactions, the Higgs dy-
namics
are affected by its coupling to gravity. Although gravity is
non-renormalizable, one may focus on the coupling of lowest di-
mension
H
†
H
ˆ
R [13], with
ˆ
R being the scalar curvature, assuming
that the effective field theory expansion applies. In any case, such
a coupling is generated radiatively [14].
Thus,
on general grounds, we expect the following lead-
ing
interactions between the Higgs and an inflaton/gravity (see
also [15]),
−L
hφ
=λ
hφ
H
†
Hφ
2
+2σ H
†
Hφ,
−
L
hR
=ξ
h
H
†
H
ˆ
R . (1)
https://doi.org/10.1016/j.physletb.2018.10.074
0370-2693/
© 2018 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by
SCOAP
3
.