ANOMALY-FREE GAUGED U(1)' IN LOCAL SUPERSYMMETRY AND BARYON-NUMBER VIOLATION

The supersymmetric extension of the standard model suffers from a prob lem of baryon-number violation. Discrete (and global) symmetries intro duced to protect the proton are unstable under gravitational effects. We add a gauged U(1)(x) to the standard model gauge group G(SM) and re quire it to be anomaly-free. As new (chiral) superfields we only allow G(SM)-singlets in order to maintain the good unification predictions. We find the most general set of solutions for the rational singlet ch arges. We embed our models in local supersymmetry and study the breaki ng of supersymmetry and U(1)(x) to determine M(x). We determine the fu ll non-renormalizable and gauge invariant Lagrangian for the different solutions. We expect any effective theory to contain baryon- and lept on-number violating terms of dimension four suppressed by powers of M( X)/M(Pl). The power is predicted by the U(1)(x) charges. We find consi stency with the experimental bounds on the proton lifetime and on the neutrino masses. We also expect all supersymmetric models to have an u nstable but longlived lightest supersymmetric particle. Consistency wi th underground experiments on upward going muons leads to stricter con straints than the proton decay experiments. These are barely satisfied .