Physics Letters B 760 (2016) 807–815
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Dark matter and global symmetries
Yann Mambrini
a
, Stefano Profumo
b
, Farinaldo S. Queiroz
b,c,∗
a
Laboratoire de Physique Theorique, Université Paris-Sud, F-91405 Orsay, France
b
Department of Physics and Santa Cruz Institute for Particle Physics, University of California, Santa Cruz, CA 95064, USA
c
Max-Planck-Institut für Kernphysik, Postfach 103980, 69029 Heidelberg, Germany
a r t i c l e i n f o a b s t r a c t
Article history:
Received
19 May 2016
Received
in revised form 22 July 2016
Accepted
29 July 2016
Available
online 3 August 2016
Editor: A.
Ringwald
General considerations in general relativity and quantum mechanics are known to potentially rule out
continuous global symmetries in the context of any consistent theory of quantum gravity. Assuming the
validity of such considerations, we derive stringent bounds from gamma-ray, X-ray, cosmic-ray, neutrino,
and CMB data on models that invoke global symmetries to stabilize the dark matter particle. We compute
up-to-date, robust model-independent limits on the dark matter lifetime for a variety of Planck-scale
suppressed dimension-five effective operators. We then specialize our analysis and apply our bounds
to specific models including the Two-Higgs-Doublet, Left–Right, Singlet Fermionic, Zee–Babu, 3-3-1 and
Radiative See-Saw models. Assuming that (i) global symmetries are broken at the Planck scale, that
(ii) the non-renormalizable operators mediating dark matter decay have O(1) couplings, that (iii) the
dark matter is a singlet field, and that (iv) the dark matter density distribution is well described by a
NFW profile, we are able to rule out fermionic, vector, and scalar dark matter candidates across a broad
mass range (keV–TeV), including the WIMP regime.
© 2016 The Author(s). 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
Particle physics models achieve stability for dark matter (DM)
particle candidates by advocating the presence of either discrete
or continuous global symmetries. Discrete symmetries arise, for ex-
ample,
from broken gauge (local) symmetries, which are respected
at the Planck scale [1,2]. Continuous global symmetries, instead,
are generically violated at the Planck scale, leading to important
implications on the dark matter phenomenology of the associated
models.
There
are several reasons why continuous global symmetries
are not expected to be present in a consistent theory of quan-
tum
gravity, which rely on general facts in gravity and quantum
mechanics:
(i)
No-Hair Theorem: Since local U (1) symmetries are effec-
tively
identical to Gauss’s law, any observer outside a Black Hole
(BH) horizon can determine the BH charge. However, if there ex-
isted
continuous global symmetries, when a charged particle gets
trapped inside the BH there would be no way to assess this from
*
Corresponding author.
E-mail
addresses: yann.mambrini@th.u-psud.fr (Y. Mambrini), profumo@ucsc.edu
(S. Profumo),
farinaldo.queiroz@mpi-hd.mpg.de (F.S. Queiroz).
outside the horizon. Thus the charge would appear to be “deleted”,
in contradiction to its conservation [3].
(ii)
Hawking Radiation: The main problem with continuous
global symmetries has to do with Hawking radiation [4]. Since
there are no gauge interactions associated with continuous global
symmetries, one could throw a large amount of charged particles
into a BH and increase its charge (Q ) indefinitely [4,5]. However,
the theory of Hawking radiation indicates that until T
Hawking
> m,
where m is the mass of the lightest charged particle pair, the BH
does not radiate charge. Combining this with the bound on the BH
mass, namely Qm ≤ M
BH
≤ M
2
pl
/m, where M
pl
= 1.22 × 10
19
GeV
is
the Planck mass, we find Q ≤ M
2
pl
/m
2
. This limit can however
be violated by making Q sufficiently large. Hence, if Q were con-
served
we could have identical BHs with an infinite number of
states labeled by Q M
2
pl
/m
2
.
(iii)
Entropy: Since an external observer cannot infer a global
charge, in order to assign an entropy to a given BH one would have
to count all micro-states of all charges, finding an entropy of order
∼ log(Q ). Now, taking Q indefinitely large, one would violate the
Bekenstein–Hawking formula, which says that entropy counts the
number of states of a BH. Therefore, such objects are ruled out, as
are continuous global symmetries [5].
While
there are general arguments for the breaking of contin-
uous
global symmetries at the scales of quantum gravity, those
http://dx.doi.org/10.1016/j.physletb.2016.07.076
0370-2693/
© 2016 The Author(s). 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
.