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, which 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, which is allowed by the experimental limit of LUX and PICO-60. Also the constraints from the lepton flavor violating rare decay mode are commented. However, this model has some limitations to address the exact quark mixing and is consistent with the block diagonal structure of quark mixing matrix and nearly massless first-generation quarks. This can be resolved by the extension of the quark or Higgs sector of the present model, which is not explored in the current analysis.