Physics Letters B 773 (2017) 121–124
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Strong CMB constraint on P -wave annihilating dark matter
Haipeng An
∗
, Mark B. Wise, Yue Zhang
Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, CA 91125, United States
a r t i c l e i n f o a b s t r a c t
Article history:
Received
26 September 2016
Received
in revised form 7 August 2017
Accepted
10 August 2017
Available
online 16 August 2017
Editor:
S. Dodelson
We consider a dark sector consisting of dark matter that is a Dirac fermion and a scalar mediator. This
model has been extensively studied in the past. If the scalar couples to the dark matter in a parity
conserving manner then dark matter annihilation to two mediators is dominated by the P -wave channel
and hence is suppressed at very low momentum. The indirect detection constraint from the anisotropy
of the Cosmic Microwave Background is usually thought to be absent in the model because of this
suppression. In this letter we show that dark matter annihilation via bound state formation occurs
through the S-wave and hence there is a constraint on the parameter space of the model from the
Cosmic Microwave Background.
© 2017 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 Standard Model (SM) has no acceptable dark matter (DM)
candidate. As its name implies DM must be uncharged and various
direct detection as well as astrophysical and cosmological con-
straints
exist on its couplings to ordinary matter as well as its self
interactions. These constraints motivate a class of very simple ex-
tensions
of the SM that contain a dark sector with particles that
carry no SM gauge quantum numbers. For thermal DM the mini-
mal
dark sector model consists of the DM and a mediator that the
DM annihilates into in the early universe. There are various possi-
bilities
for the Lorentz quantum numbers of the DM and mediator.
Two well studied examples are a Dirac fermion with a mediator
that is either a new massive U (1)
D
gauge boson (the dark photon)
or a massive scalar. In the first case communication with the SM
degrees of freedom occurs through the vector portal (via kinetic
mixing between the U(1)
D
and U(1)
Y
field strength tensors) and
in the latter case through the Higgs portal.
Constraints
on the parameter space of these models occur from
the so-called indirect detection signals. Annihilation of DM in the
early universe at the time of recombination injects energy into
the plasma of SM particles elongating the recombination process
and changing expectations for the cosmic microwave background
(CMB) radiation anisotropy. Annihilation of DM today in our galaxy
contributes to electromagnetic and charged particle astrophysical
spectra observed, for example, by the Fermi satellite.
*
Corresponding author.
E-mail
address: anhp@caltech.edu (H. An).
In a recent paper [1], we have highlighted the role that DM
bound state formation can play on indirect detection signals from
DM annihilation in our galaxy when the mediator is a dark photon
(there bound state formation was not important for the CMB con-
straint).
In this letter, we again consider the influence of DM bound
state formation on indirect signals but focus on the case where the
mediator is a real scalar and on the CMB constraint. We impose a
parity symmetry on the dark sector with the real scalar mediator
having even parity. Then, the Lagrange density for the DM sector
is,
L = i
¯
χγ
μ
∂
μ
χ −m
D
¯
χχ − g
¯
χχφ +
1
2
∂
μ
φ∂
μ
φ −
1
2
m
2
φ
φ
2
, (1)
where χ and φ are the DM and the dark mediator and the Higgs
portal couplings are omitted. This model has been well studied for
various reasons [2–19]. For DM heavier than 5–10 GeV, direct de-
tection
experiments [20] and the requirement that φ decays before
BBN set the lower bound, m
φ
> 2m
μ
0.2GeV. In our calcula-
tions
below, we assume a thermal DM relic density, which fixes
the value of α
D
= g
2
/(4π) as a function of the DM mass, m
D
.
The
most often considered DM annihilation process in this
model is χ
¯
χ → φφ. The parity of a 2φ system must be even
and so does the χ
¯
χ system because parity is conserved by the
Lagrange density in Eq. (1). Therefore this annihilation is mostly
P -wave for slow DM and anti-DM particles.
1
With the P -wave
1
If parity was not conserved S-wave annihilation would be possible.
http://dx.doi.org/10.1016/j.physletb.2017.08.010
0370-2693/
© 2017 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
.