On proton stability and the gauge hierarchy problem

Abstract

We display an intimate relationship between proton stability and the gauge hierarchy (and μ) problems within minimal supersymmetric trinification based on the grand unified symmetry SU(3) c × SU(3) L × SU(3) R . A straightforward resolution of the hierarchy problem, achieved through discrete symmetries that contain matter parity, also transforms the problematic dimension-five proton decay process into a dimension six process. The proton is predicted to be essentially stable with a lifetime in excess of 10 50 years.