Discrete R symmetries for the MSSM and its singlet extensions

Abstract

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. We extend the discussion 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 problem in the NMSSM. We also show that a singlet extension of the MSSM based on a Z(4)(R) symmetry can provide a simultaneous solution to the mu and strong CP problem with the axion coupling in the favoured window. (C) 2011 Elsevier B.V. All rights reserved.