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.

23 pages, one figure (added), title changed, discussion added on sneutrino vev basis, accepted for publication in JHEP

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