Natural emergence of neutrino masses and dark matter from $R$-symmetry

Abstract: We propose a supersymmetric extension of the Standard Model (SM) with a continuous global $U(1)R$ symmetry. The $R$-charges of the SM fields are identified with that of their lepton numbers. As a result, both bilinear and trilinear `$R$-parity violating' (RPV) terms could be present at the superpotential. However, $R$-symmetry is not an exact symmetry as it is broken by supergravity effects. Hence, sneutrinos acquire a small vacuum expectation value in this framework. However, a suitable choice of basis ensures that the bilinear RPV terms can be completely rotated away from the superpotential and the scalar potential. On the other hand, the trilinear terms play a very crucial role in generating neutrino masses and mixing at the tree level. This is noticeably different from the typical $R$-parity violating Minimal Supersymmetric Standard Model. Also, gravitino mass turns out to be the order parameter of $R$-breaking and is directly related to the neutrino mass. We show that such a gravitino, within the mass range $200~\text{keV}\lesssim m{3/2}\lesssim 0.1~\text{GeV}$ can be an excellent dark matter candidate. Finally, we looked into the collider implications of our framework.