Family Symmetries and Proton Decay

Abstract

The proton decay modes $p\to K^0 e^+$ and $p\to K^0 μ^+$ may be visible in certain supersymmetric theories, and if seen would provide evidence for new flavor physics at extremely short distances. These decay modes can arise from the dimension five operator $(Q_1Q_1Q_2L_{1,2})$, where $Q_i$ and $L_i$ are ${i^{th}}$ generation quark and lepton superfields respectively. Such an operator is not generated at observable levels due to gauge or Higgs boson exchange in a minimal GUT. However in theories that explain the fermion mass hierarchy, it may be generated at the Planck scale with a strength such that the decays $p\to K^0 \ell^+$ are both compatible with the proton lifetime and visible at Super-Kamiokande. Observable proton decay can even occur in theories without unification.