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The lack of experimental evidence for supersymmetry motivates R-parityviolating realizations of the MSSM. Dropping R-parity, alternative symmetrieshave to be imposed in order to stabilize the proton. We determine the possiblediscrete R and non-R symmetries, which allow for renormalizable R-parityviolating terms in the superpotential and which, at the effective level, areconsistent with the constraints from nucleon decay. Assuming a gauge origin, werequire the symmetry to be discrete gauge anomaly-free, allowing also forcancellation via the Green Schwarz mechanism. Furthermore, we demand leptonnumber violating neutrino mass terms either at the renormalizable ornon-renormalizable level. In order to solve the mu problem, the discrete Z_N orZ_N^R symmetries have to forbid any bilinear superpotential operator at treelevel. In the case of renormalizable baryon number violation the smallestpossible symmetry satisfying all conditions is a unique hexality Z_6^R. In thecase of renormalizable lepton number violation the smallest symmetries are twohexalities, one Z_6 and one Z_6^R.

What is the discrete gauge symmetry of the R-parity violating MSSM?