R parity violation from discrete R symmetries

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We consider supersymmetric extensions of the standard model in which the usual R or matter parity gets replaced by another R or non-R discrete symmetry that explains the observed longevity of the nucleon and solves the μ problem of MSSM. In order to identify suitable symmetries, we develop a novel method of deriving the maximal Zₙ⁽ʳ⁾ symmetry that satisfies a given set of constraints. We identify R parity violating (RPV) and conserving models that are consistent with precision gauge unification and also comment on their compatibility with a unified gauge symmetry such as the Pati-Salam group. Finally, we provide a counter-example to the statement found in the recent literature that the lepton number violating RPV scenarios must have μ term and the bilinear κ L Hᵤ operator of comparable magnitude.