Discrete R symmetries for the MSSM and its singlet extensions Original Research Article

We determine the anomaly free discrete R symmetries, consistent with the MSSM, that commute with image and suppress the μ parameter and nucleon decay. We show that the order M of such image symmetries has to divide 24 and identify 5 viable symmetries. The simplest possibility is a image symmetry which commutes with image. We present a string-derived model with this image symmetry and the exact MSSM spectrum below the GUT scale; in this model image originates from the Lorentz symmetry of compactified dimensions. We extend the discussion to include the singlet extensions of the MSSM and find image and image are the only possible symmetries capable of solving the μ problem in the NMSSM. We also show that a singlet extension of the MSSM based on a image symmetry can provide a simultaneous solution to the μ and strong CP problem with the axion coupling in the favoured window.