Physics Letters B 790 (2019) 218–224
Contents lists available at ScienceDirect
Physics Letters B
www.elsevier.com/locate/physletb
Revisiting the number-theory dark matter scenario and the weak
gravity conjecture
Kazunori Nakayama
a,b,∗
, Fuminobu Takahashi
c,b
, Tsutomu T. Yanagida
b,d
a
Department of Physics, Faculty of Science, The University of Tokyo, Bunkyo-ku, Tokyo 113-0033, Japan
b
Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, Kashiwa, Chiba 277-8583, Japan
c
Department of Physics, Tohoku University, Sendai, Miyagi 980-8578, Japan
d
T.D.Lee Institute and School of Physics and Astronomy, Shanghai Jiao Tong University, Shanghai 200240, China
a r t i c l e i n f o a b s t r a c t
Article history:
Received
16 November 2018
Received
in revised form 9 January 2019
Accepted
9 January 2019
Available
online 17 January 2019
Editor: J.
Hisano
We revisit the number-theory dark matter scenario where one of the light chiral fermions required by
the anomaly cancellation conditions of U(1)
B-L
explains dark matter. Focusing on some of the integer
B-L charge assignments, we explore a new region of the parameter space where there appear two
light fermions and the heavier one becomes a dark matter of mass O(10) keV or O(10) MeV. The
dark matter radiatively decays into neutrino and photon, which can explain the tantalizing hint of the
3.55 keV X-ray line excess. Interestingly, the other light fermion can erase the AdS vacuum around the
neutrino mass scale in a compactification of the standard model to 3D. This will make the standard model
consistent with the AdS-WGC statement that stable non-supersymmetric AdS vacua should be absent.
© 2019 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
The seesaw mechanism is the most attractive mechanism to ex-
plain
small masses of the active neutrinos [1–3]. It is based on
a new gauge symmetry called U(1)
B-L
, which requires an exten-
sion
of the standard model (SM) to make U(1)
B-L
anomaly-free.
The U(1)
B-L
symmetry becomes anomaly-free if one introduces a
right-handed neutrino (RHN) in each generation. The spontaneous
breaking of the U(1)
B-L
generates large Majorana masses for the
RHNs, and integrating them out induces small Majorana masses
for the active neutrinos through the seesaw mechanism. Not only
does it explain the smallness of neutrino masses, but it can also
explain the present baryon asymmetry via leptogenesis in which
lepton asymmetry is generated by the decay of the RHNs in the
early Universe [4].
In
a conventional framework of the SM plus three RHNs, the
RHNs acquire a heavy mass of order the U(1)
B-L
breaking scale,
and there is no dark matter (DM) candidate. In the so-called split
seesaw mechanism [5], on the other hand, one of the RHNs be-
comes
much lighter than the others. If the lightest one has a mass
less than O(10) keV and if its Yukawa couplings are sufficiently
suppressed to satisfy the X-ray bound, it becomes a plausible can-
didate
for DM. Note that, while the lightest RHN is almost decou-
*
Corresponding author.
E-mail
address: kazunori@hep-th.phys.s.u-tokyo.ac.jp (K. Nakayama).
pled from the others in this case, the seesaw mechanism, as well
as leptogenesis, still work thanks to the remaining two heavy RHNs
[6,7]. The split seesaw mechanism provides a possible answer to
the question of why there are three generations in the SM: one
of the three RHNs becomes DM, while the other two explain the
baryon asymmetry of the Universe via leptogenesis.
Alternatively,
one could introduce a set of chiral fermions
charged under U(1)
B-L
in addition to the three RHNs. The num-
ber
of such chiral fermions and their B-L charges are subject to
the anomaly cancellation conditions, and it turned out that their
number must be greater than or equal to five, partly because of
the absence of positive integers satisfying x
3
+ y
3
= z
3
, a special
case of the Fermat’s last theorem [8]. Interestingly, the lightest ex-
tra
chiral fermion with even B-L charge is stable and therefore a
candidate for DM. Since there is an intimate connection between
the number theory and the existence of DM through the anomaly
cancellation condition, we named the above model as the number-
theory
dark matter (NTDM) [9].
1
In this Letter, we revisit the NTDM model and explore a new
region of the parameter space where there appear two light chi-
ral
fermions in the low energy. Specifically, we will focus on
two possible sets of extra fermions with integer B-L charges; one
is equivalent to the case with four RHNs and four extra chi-
1
See also Refs. [10–15]for related works on the possible extensions of the SM
with U(1)
B-L
charged chiral fermions.
https://doi.org/10.1016/j.physletb.2019.01.013
0370-2693/
© 2019 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
.