Making the Sneutrino a Higgs with a $U(1)_R$ Lepton Number

Abstract

We present a supersymmetric extension of the Standard Model that posseses a continuous $ U(1)_R$ symmetry, which is identified with one of three lepton numbers, and where a sneutrino vev gives mass to the down type quark and leptons. This idea allows for a smaller particle content than the minimal $R$-symmetric supersymmetry extension of the standard model (MRSSM). We explore bounds on this model coming from electroweak precision measurements, neutrino masses and gravitino decay. Bounds from electroweak precision measurements lead to a two-sided bound on $\tan \beta$ while gravitino decay forces a low reheating temperature. Finally, the generation of neutrino masses from $R$-symmetry violation put an upper bound on the SUSY breaking scale. Despite all of this, we find that the allowed parameter space is still large and would lead to a distinctive phenomenology at the LHC.