Discrete R symmetries for the MSSM and its singlet extensions

Understand

We determine the anomaly free discrete R symmetries, consistent with the MSSM, that commute with SU(5) and suppress the $\mu$ parameter and nucleon decay.

• We show that the order M of such $Z_M^R$ symmetries has to divide 24 and identify 5 viable symmetries.
• The simplest possibility is a $Z_4^R$ symmetry which 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.