$(S_3)^3$ flavor symmetry and $p\to K^0 e^+$

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 $K l$ where $l$ is a {\em first} generation lepton. We show that the modes $n \rightarrow K^0 \bar{\nu}_e$, $p\rightarrow K^+ \bar{\nu}_e$, and $p\rightarrow K^0 e^+$ occur at comparable rates, and could well be discovered simultaneously at the SuperKamiokande experiment.