$(S_3{)}^3$ 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 $Kl$ where $l$ is a {\em first} generation lepton. We show that the modes $n\to K^0{\bar{\nu }}_e$, $p\to K^{+}{\bar{\nu }}_e$, and $p\to K^0{e}^{+}$ occur at comparable rates, and could well be discovered simultaneously at the SuperKamiokande experiment.

26 pp. LaTeX