Fermionic dark matter and neutrino masses in a \(\mathcal{B-L}\) model

In this work we present a common framework for neutrino mass and dark matter. Specifically, we work with a local \(\mathcal{B-L}\) extension of the standard model which has three right-handed neutrinos, \(n_{R_{i}}\), and some extra scalars, \(\Phi\), \(\phi_{i}\) besides the standard model fields. The \(n_{R_{i}}\)'s have non-standard \(\mathcal{B-L}\) quantum numbers and thus these couple to different scalars. This model has the attractive property that an almost automatic \(Z_2\) symmetry acting only on a fermionic field, \(n_{R3}\), is present. Taking advantage of this \(Z_2\) symmetry, we study both the neutrino mass generation via a natural see-saw mechanism in low energy and the possibility of \(n_{R3}\) to be a DM candidate. For this last purpose, we study its relic abundance and its compatibility with the current direct detection experiments.