Does proton stability imply the existence of an extra Z0?

Abstract

It is well known that the minimal supersymmetric standard model admits in general Yukawa couplings violating baryon and lepton number. We argue that a generic four-dimensional SU (3) × SU (2) × U (1) string does have in general this type of dangerous couplings. We propose as the most natural solution to the proton stability problem the existence of extra low-energy gauge symmetries (U(1)'s) forbidding these terms. We construct in a systematic way the minimal extensions of the supersymmetric standard model in which gauge symmetries forbid all baryon- and/or lepton-number-violating couplings but allow Yukawa couplings for quarks and charged leptons. These models contain an extra U(1) which is not of the E6-type.