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

## TL;DR

This paper introduces a supersymmetric model with a continuous $U(1)_R$ symmetry that naturally explains neutrino masses and proposes a light gravitino as a dark matter candidate, with implications for collider experiments.

## Contribution

It presents a novel supersymmetric extension with $U(1)_R$ symmetry where neutrino masses arise from trilinear RPV terms and links the gravitino mass to neutrino mass, proposing a dark matter candidate.

## Key findings

- Neutrino masses generated at tree level via trilinear RPV terms.
- Gravitino with mass 200 keV to 0.1 GeV can serve as dark matter.
- Collider signatures consistent with the model's predictions.

## 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.