A gauge model for right handed neutrinos as dark matter

$B-L$ is known to be a symmetry somewhat linked to the origin of neutrino masses, which turns out to be anomaly free upon the sole introduction of right handed neutrinos. We suggest a simple extension of the electroweak group, $SU(2)_L\times U(1)_Y\times U(1)_{B-L}$, where the breaking of $U(1)_{B-L}$ symmetry provides masses for right handed neutrinos at an acceptable range for them to be Dark Matter candidates. We review the cosmological constraints for this type of models, in order to find the restrictions on the parameters of the model. We study the contributions due to the $B-L$ current in the process $e^+e^- \rightarrow e^+e^-$ at low energies.