Physics Letters B 754 (2016) 114–117
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Radiative mixing of the one Higgs boson and emergent self-interacting
dark matter
Ernest Ma
a,b,∗
a
Physics & Astronomy Department and Graduate Division, University of California, Riverside, CA 92521, USA
b
HKUST Jockey Club Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
12 November 2015
Accepted
18 January 2016
Available
online 19 January 2016
Editor: A.
Ringwald
In all scalar extensions of the standard model of particle interactions, the one Higgs boson responsible for
electroweak symmetry breaking always mixes with other neutral scalars at tree level unless a symmetry
prevents it. An unexplored important option is that the mixing may be radiative, and thus guaranteed
to be small. Two first such examples are discussed. One is based on the soft breaking of the discrete
symmetry Z
3
. The other starts with the non-Abelian discrete symmetry A
4
which is then softly broken to
Z
3
, and results in the emergence of an interesting dark-matter candidate together with a light mediator
for the dark matter to have its own long-range interaction.
© 2016 The Author. 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
.
The standard model (SM) of particle interactions requires only
one scalar doublet = (φ
+
, φ
0
) which breaks the electroweak
gauge symmetry SU(2)
L
×U(1)
Y
spontaneously to electromagnetic
U (1)
Q
with φ
0
= v = 174 GeV. It predicts just one physical Higgs
boson h, whose properties match well with the 125 GeV parti-
cle
discovered [1,2] at the Large Hadron Collider (LHC) in 2012. If
there are other neutral scalars at the electroweak scale, they are
expected to mix with h at tree level, so that the observed 125 GeV
particle should not be purely h. If future more precise measure-
ments fail
to see deviations, then a theoretical understanding could
be that a symmetry exists which distinguishes h from the other
scalars. For example, a Z
2
symmetry may exist under which a sec-
ond
scalar doublet (η
+
, η
0
) is odd [3] and all SM particles are
even. This is useful for having a viable dark-matter candidate [4].
It also enables the simplest one-loop (scotogenic) model [5] of ra-
diative
neutrino mass through dark matter, if three neutral singlet
fermions N
1,2,3
are also added which are odd under Z
2
, as shown
in Fig. 1. Note that this dark Z
2
symmetry may be derived from
lepton parity [6].
Another
important new development in the understanding
of dark matter is the possibility that it has long-range self-
interactions [7–12].
This may be an elegant solution to two existing
discrepancies in astrophysical observations: (1) central density pro-
*
Correspondence to: Physics & Astronomy Department and Graduate Division,
University of California, Riverside, CA 92521, USA.
E-mail
address: ma@phyun8.ucr.edu.
files of dwarf galaxies are flatter (core) than predicted (cusp);
(2) observed number of satellites in the Milky Way is much smaller
than predicted. Although (2) is less of a problem with the recent
discovery of faint satellites, there is also (3) the new related prob-
lem
of predicted massive subhalos which are not observed. From a
particle theory perspective, if the light mediator of dark matter is
a scalar boson, then it is difficult to construct a theory such that it
does not mix substantially with h. In this paper it will be shown
how a dark-matter candidate could emerge together with its medi-
ator,
such that its mixing with h is one-loop suppressed. This will
be discussed later as part of my second example.
If
an exact dark symmetry is imposed, then any mixing of h
with
other neutral scalars in the dark sector would be forbidden.
However, if this symmetry is softly broken, it will result in nonzero
mixing, many examples of which exist. In the above scotogenic
model, if the quadratic term m
2
12
†
η + H.c. is added thus break-
ing
Z
2
softly, a nonzero vacuum expectation value η
0
would
be induced [13]. This invalidates η
0
as a dark-matter candidate.
Fig. 1. One-loop Z
2
scotogenic neutrino mass.
http://dx.doi.org/10.1016/j.physletb.2016.01.033
0370-2693/
© 2016 The Author. 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
.
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