Probing a slepton Higgs on all frontiers

We study several aspects of supersymmetric models with a $U(1)_R$ symmetry where the Higgs doublet is identified with the superpartner of a lepton. We derive new, stronger bounds on the gaugino masses based on current measurements, and also propose ways to probe the model up to scales of $\mathcal{O}(10\, \textrm{TeV})$ at future $e^+e^-$ colliders. Since the $U(1)_R$ symmetry cannot be exact, we analyze the effects of $R$-symmetry breaking on neutrino masses and proton decay. In particular, we find that getting the neutrino mixing angles to agree with experiments in a minimal model requires a UV cutoff for the theory at around $10 \text{ TeV}$.