Physics Letters B 746 (2015) 424–429
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Dark chiral symmetry breaking and the origin of the electroweak scale
Christopher D. Carone
∗
, Raymundo Ramos
High Energy Theory Group, Department of Physics, College of William and Mary, Williamsburg, VA 23187-8795, United Sates
a r t i c l e i n f o a b s t r a c t
Article history:
Received
15 March 2015
Received
in revised form 14 May 2015
Accepted
17 May 2015
Available
online 21 May 2015
Editor:
B. Grinstein
We study a classically scale-invariant model in which strong dynamics in a dark sector sets the scale of
electroweak symmetry breaking. Our model is distinct from others of this type that have appeared in the
recent literature. We show that the Higgs sector of the model is phenomenologically viable and that the
spectrum of dark sector states includes a partially composite dark matter candidate.
© 2015 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 Lagrangian of the standard model has precisely one dimen-
sionful
parameter, the squared mass of the Higgs doublet field. This
mass sets the scale of electroweak symmetry breaking, which is
communicated to the standard model fermions via their Yukawa
couplings. The origin and stability of the hierarchy between the
electroweak scale and the Planck scale have motivated many of
the leading proposals for physics beyond the standard model. In
this Letter, we study the phenomenology of a specific model in
which the Higgs mass squared arises as a result of strong dynam-
ics
in a dark sector. Other models of this type have been discussed
in the recent literature [1,2]; we explain how our model differs
from those proposals below.
It
is well known that the Yukawa coupling between a scalar
φ and fermions can lead to a linear term in the scalar poten-
tial
if the fermions condense. Such a term alters the potential so
that the scalar develops a vacuum expectation value (vev). If the
scalar squared mass term is absent, then the scale of the scalar vev
is set entirely by that of the strong dynamics that produced the
condensate. If these fields carry electroweak quantum numbers,
then electroweak symmetry will be spontaneously broken. A sim-
ple
model based on this idea was proposed by Carone and Georgi
in Ref. [3]. In this Letter, we consider a similar theory in which the
scalar and fermions in question do not carry electroweak charges.
The vev of φ does not break electroweak symmetry, but provides
an origin for the Higgs squared mass via the Higgs portal coupling
λ
p
φ
†
φ H
†
H. As long as λ
p
has the appropriate sign, electroweak
*
Corresponding author.
E-mail
addresses: cdcaro@wm.edu (C.D. Carone), raramos@email.wm.edu
(R. Ramos).
symmetry breaking is triggered at a scale set by the strong dy-
namics
of the dark sector.
The
choice of a classically scale-invariant scalar potential can be
justified by various arguments. We place them in two categories:
1. The
model is tuned. Dimensionful parameters might not as-
sume
natural values as a consequence of the probability distri-
bution
over the string landscape, which is poorly understood. If
one takes this point of view, it is not unreasonable to consider ex-
tensions
of the standard model that are designed to address its
deficiencies (for example, extensions that provide for viable dark
matter physics) that appear tuned but are parametrically simple
and can be easily tested in experiment. Our model is of this type
and could easily be ruled out (or supported) by upcoming dark
matter searches.
2. The
model is not tuned. If there are no physical mass scales be-
tween
the weak and Planck scales, then the only possible source
of a Higgs quadratic divergences is from the cut off of the the-
ory.
Although field theoretic completions to low-energy effective
theories lead generically to quadratic divergences proportional to
the square of the cutoff [4], this may not be the case for quantum
gravitational physics at the Planck scale [5]. As argued in Ref. [6],
a spacetime description itself may break down at this scale and
one’s intuition based on quantum field theories may be flawed.
If one takes this point of view, it is not unreasonable to assume
that a Higgs mass generated via dimensional transmutation in the
infrared is only multiplicatively renormalized [7] and to explore
the phenomenological consequences. A significant number of re-
cent
papers have adopted this perspective [1,2,8,9].
The
model we propose has a dark sector SU(2)
L
×SU(2)
R
chiral
symmetry that is spontaneously broken by a fermion condensate
triggered by strong dynamics. An SU(2)
D
subgroup of the global
symmetry is gauged, and the dark fermions have Yukawa cou-
plings
to a scalar that is a doublet under this gauge symmetry. The
http://dx.doi.org/10.1016/j.physletb.2015.05.044
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© 2015 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
.