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We determine the anomaly free discrete R symmetries, consistent with theMSSM, that commute with SU(5) and suppress the $\mu$ parameter and nucleondecay. We show that the order M of such $Z_M^R$ symmetries has to divide 24 andidentify 5 viable symmetries. The simplest possibility is a $Z_4^R$ symmetrywhich commutes with SO(10). We present a string-derived model with this $Z_4^R$symmetry and the exact MSSM spectrum below the GUT scale; in this model $Z_4^R$originates from the Lorentz symmetry of compactified dimensions. We extend thediscussion to include the singlet extensions of the MSSM and find $Z_4^R$ and$Z_8^R$ are the only possible symmetries capable of solving the $\mu$ problemin the NMSSM. We also show that a singlet extension of the MSSM based on a$Z_{24}^R$ symmetry can provide a simultaneous solution to the $\mu$ and strongCP problem with the axion coupling in the favoured window.

Discrete R symmetries for the MSSM and its singlet extensions