(S3)3 flavor symmetry and p-->K0e+

Abstract

We show how to incorporate the lepton sector in a supersymmetric theory of flavor based on the discrete flavor group ${({S}_{3})}^{3}$. Assuming that all possible nonrenormalizable operators are generated at the Planck scale, we show that the transformation properties of the leptons and of the flavor-symmetry-breaking fields are uniquely determined. We then demonstrate that the model has a viable phenomenology and makes one very striking prediction: the nucleon decays predominantly to $\mathrm{Kl}$ where $l$ is a first generation lepton. We show that the modes $n\ensuremath{\rightarrow}{K}^{0}{\overline{\ensuremath{\nu}}}_{e}$, $p\ensuremath{\rightarrow}{K}^{+}{\overline{\ensuremath{\nu}}}_{e}$, and $p\ensuremath{\rightarrow}{K}^{0}{e}^{+}$ occur at comparable rates, and could well be discovered simultaneously at the SuperKamiokande experiment.