Physics Letters B 748 (2015) 208–211
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Phase transition in multi-scalar-singlet extensions of the Standard
Model
A. Tofighi
∗
, O.N. Ghodsi, M. Saeedhoseini
Department of Physics, Faculty of Basic Sciences, University of Mazandaran, P.O. Box 47416-95447, Babolsar, Iran
a r t i c l e i n f o a b s t r a c t
Article history:
Received
10 February 2015
Received
in revised form 6 July 2015
Accepted
7 July 2015
Available
online 9 July 2015
Editor:
J. Hisano
Keywords:
Phase
transition
Gauge
singlet model
We propose a generalization of the Standard Model (SM) by adding two real gauge-singlets S
1
, S
2
. The
field S
1
will improve the strength of the electroweak phase transition (EWPT). Imposing a Z
2
symmetry
on the field S
2
makes this field a possible candidate for dark matter. Both singlets interact with other
observable fields through the Higgs boson. They are allowed to interact with each other as well. We find
that by introducing two different scalar fields, the model is less vulnerable to experimental constraints.
In
this paper, we consider the effects of a heavy scalar (M
1
> M
H
) on the electroweak phase transition.
And we present configurations that produce a strong first order EWPT.
© 2015 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
A solution to explain the baryon asymmetry of our universe [1]
is
based on violation of baryon number, C and CP violation as
well as a departure from thermal equilibrium. In a viable model of
electroweak baryogenesis the departure from thermal equilibrium
is realized via a strong first order phase transition [2]. But the SM
of
particle physics cannot provide a strong first order phase tran-
sition
[3]. In addition the SM does not have a candidate for dark
matter (DM) as well.
Moreover,
from the three-loop β function for the Higgs self
coupling it is found that the Higgs vacuum is no longer stable be-
yond
the scale 10
10
GeV. Hence we expect some new physics to
appear before this scale [4].
Therefore,
some new models are required to address these is-
sues.
A popular model is to couple a singlet scalar to the Higgs
boson
[5–16].
In
Ref. [17] a scheme for classifying models of the electroweak
phase transition has been presented. One may associate the forma-
tion
of gravitational waves to a strong first-order phase transition
[18–21].
But
models with an addition of one real singlet cannot address
all of the shortcomings of the SM. An interesting class of models
is the multi-singlet extensions of the SM models [22–28]. In these
*
Corresponding author.
E-mail
address: A.Tofighi@umz.ac.ir (A. Tofighi).
models there are more opportunities to satisfy the constraints im-
posed
by experimental findings [29].
In
order to study the dynamics of the electroweak phase tran-
sition
EWPT one has to resort to techniques from the domain
of thermal field theory [30–33]. An essential element is finite-
temperature
effective potential, which is a measure of the free
energy density of the system. Generally a loop-level analysis, in
conjunction with a vigorous Monte-Carlo scan of the parameter
space is needed to unravel the structure of EWPT. However in this
work we study the dynamics of the EWPT at the tree level.
The
plan of this paper is as follows:
In
Section 2 we propose a new model composed of two differ-
ent
gauge singlet scalar fields with coupling to the Higgs boson,
they can have mutual interaction as well. We impose a discrete
symmetry on only one of them. Hence this field will be a can-
didate
for dark matter. The other field will provide us astrong
first order phase transition. And we study the parameter space of
the model. In Section 3 we discuss the finite-temperature potential
and explain the origin of the strongly first-order phase transition
at the tree level. In Section 4 we discuss the phenomenological
implication of our model. And finally in Section 5 we present our
conclusions.
2. The model
We propose a new extension of the SM by addition of two real
gauge singlet scalars S
1
and S
2
. The Lagrangian of the scalar sector
of our model is given by
http://dx.doi.org/10.1016/j.physletb.2015.07.009
0370-2693/
© 2015 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
.