Physics Letters B 748 (2015) 316–322
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Communication with SIMP dark mesons via Z
-portal
Hyun Min Lee
a
, Min-Seok Seo
b,∗
a
Department of Physics, Chung-Ang University, Seoul 156-756, Republic of Korea
b
Center for Theoretical Physics of the Universe, Institute for Basic Science (IBS), Daejeon 305-811, Republic of Korea
a r t i c l e i n f o a b s t r a c t
Article history:
Received
15 April 2015
Received
in revised form 8 June 2015
Accepted
5 July 2015
Available
online 10 July 2015
Editor:
G.F. Giudice
We consider a consistent extension of the SIMP models with dark mesons by including a dark U(1)
D
gauge symmetry. Dark matter density is determined by a thermal freeze-out of the 3 → 2self-
annihilation
process, thanks to the Wess–Zumino–Witten term. In the presence of a gauge kinetic mixing
between the dark photon and the SM hypercharge gauge boson, dark mesons can undergo a sufficient
scattering off the Standard Model particles and keep in kinetic equilibrium until freeze-out in this SIMP
scenario. Taking the SU(N
f
) × SU(N
f
)/SU(N
f
) flavor symmetry under the SU(N
c
) confining group, we
show how much complementary the SIMP constraints on the parameters of the dark photon are for
current experimental searches for dark photon.
© 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
Various evidences of dark matter (DM) imply that fundamen-
tal
particles and interactions need to be extended beyond the
Standard Model (SM) [1]. One of the appealing suggestions is
the thermal DM scenario, where the DM relic density is deter-
mined
through the freeze-out of the DM number changing process.
Weakly Interacting Massive Particle (WIMP) provides the most
popular thermal DM scenario, in which the annihilation of a DM
pair into a pair of SM particles is responsible for the freeze-out.
Since WIMP mass is of order weak scale for the effective cou-
pling
of α
eff
∼ O(10
−2
), ‘WIMP miracle’ has been the mainstream
for thermal DM studies, corroborating the expectation of finding
new physics at the weak scale in the solutions for gauge hierarchy
problem.
Another
interesting proposal for thermal (pseudo-)scalar DM
has been recently made under the name of Strongly Interacting
Massive Particle (SIMP) [2–4], explaining DM relic density through
the freeze-out of 3 → 2 self-annihilation. The DM self-interaction
is motivated by potential small-scale problems [5], although it is
strongly constrained by bullet cluster [6] and simulations on halo
shape [7]. As a result, the SIMP scenario predicts dark matter with
dimensionless self-interacting coupling of order one and mass in
the 0.1–1 GeV range, which has not been explored seriously so
far.
*
Corresponding author.
E-mail
addresses: hminlee@cau.ac.kr (H.M. Lee), minseokseo@ibs.re.kr
(M.-S. Seo).
The SIMP scenario requires the interaction between dark and
SM sectors in the form of scattering for dark matter to be in
kinetic equilibrium with the SM particles, without altering the
structure formation [8]. Since such an inter-sector interaction also
leads to the DM annihilation into SM particles, the inter-sector in-
teraction
strength is bounded from above for the dominance of
3 → 2 self-annihilation, if combined, resulting in n
DM
σ v
ann
<
n
2
DM
σ v
2
3→2
< n
SM
σ v
scatt
, at the freeze-out temperature. Tak-
ing
other constraints from ground-based experiments into account
in addition, we can make quite a concrete prediction on the pa-
rameters
of a specific SIMP model.
In
this article, we consider a SIMP model with dark mesons
suggested in Ref. [3], where the 5-point interactions between dark
mesons for 3 → 2 annihilation come from the leading interactions
of the Wess–Zumino–Witten (WZW) term [9,10]. From the model
point of view, the WZW term is interesting because it encodes var-
ious
aspects on dark sector, namely, the WZW term exists only
for a specific flavor symmetry of light dark quarks, depending on
its spontaneous breaking pattern [11], and it contains color num-
ber
as a topological index [10]. As an inter-sector interaction, we
consider the hidden valley scenario [12], that some heavy dark sec-
tor
particle has a renormalizable coupling to the mediator particle
that communicates between DM and SM particles. Higgs-portal in-
teraction
would be a natural candidate, but it is not enough for
a sufficiently large DM–SM particle scattering at freeze-out tem-
perature
due to small Yukawa couplings of the light SM fermions.
Thus, we study the case with a gauge kinetic mixing [13], that
is the renormalizable and gauge invariant interaction between SM
hypercharge U(1)
Y
and dark sector U(1)
D
with a dimensionless
coupling. When the dark U(1) gauge coupling is not too tiny, dark
http://dx.doi.org/10.1016/j.physletb.2015.07.013
0370-2693/
© 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
.