I. INTRODUCTION
The nonvanishing neutrino masses have been conﬁrmed by various n eutrino oscillation
phenomena and indicate the evidence of new physics beyond the Sta ndard Model. The most
attractive idea to naturally explain the tiny neutrino masses is the se esaw mechanism [1], in
which the right-handed (RH) neutrinos singlet under the SM gauge g roup are introduced.
The minimal gauged U(1)B−L model based on the gauge group SU(3)C × SU(2)L × U(1)Y ×
U(1)B−L [2] is an elegant and simple extension of the SM, in which the RH neutrino s of
three generations are necessarily introduced because of the gau ge and gravitational anomaly
cancellations. In addition, the mass of RH neutrinos arises associat ed with the U(1)B−L
gauge symmetry breaking.
Although the scale of the B−Lgauge symmetry breaking is basically arbitrary as long as
phenomenological constraints are satisﬁed, one interesting optio n is to take it to be the TeV
scale [3]. It has been recently pointed out [4] that when the classica l conformal invariance
is imposed on the minimal U(1)B−L model, the symmetry breaking scale appears to be the
TeV scale naturally. If this is the case, all new particles, the Z′ gauge boson, the B − L
Higgs boson H and the RH neutrinos appear at the TeV scale unless the U(1)B−L gauge
coupling is extremely small, and they can be discovered at Large Hadr on Collider [5–8].
Then we may be able to understand the relation between the gauge s ymmetry breaking and
the origin of neutrino masses.
Although such a TeV scale model is interesting and appealing, one migh t think that the
absence of dark matter (DM) candidate is a shortcoming of this mod el. A sterile RH neutrino
with mass of the order of MeV is one possibility [9]. In this paper, we pro pose a very simple
idea to introduce the DM candidate in the minimal gauged U(1)B−L model. We introduce
the Z2 parity into the model and impose one of three RH neutrinos to be odd , while the
others even. In this way, the Z2-odd RH neutrino becomes stable and the DM candidate.
Note that two RH neutrinos are enough to reconcile with the observ ed neutrino oscillation
data, with a prediction of one massless light neutrino. Therefore, w ithout introducing any
additional new dynamical degrees of freedom, the DM particle arise s in the minimal gauged
U(1)B−L model.
The paper is organized as follows. In the next section, we brieﬂy des cribe our model. In
section III, we estimate the thermal relic density of the RH neutrin o and identify the model
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