Majorana dark matter and neutrino mass with $S_3$ symmetry

Abstract: This model includes a minimal extension of the standard model with $S_3$ and $Z_2$ symmetries to explain neutrino masses and mixing along with the dark matter phenomenology. Neutrino phenomenology is explored, consistent with the $3 \sigma$ observation of oscillation parameters and a nonzero reactor mixing angle ($\theta_{13}$) is obtained. The $S_3$ singlet Majorana neutrino couples to the third generation of leptons, gives a correct relic density compatible with the Planck data. This model does not allow tree level direct detection, therefore we discuss the loop level effective interaction with the nucleus mediated by gauge boson. Also the constraints from the lepton flavor violating rare decay mode is commented.