Discrete R symmetries for the MSSM and its singlet extensions

TL;DR

This paper identifies anomaly-free discrete R symmetries compatible with the MSSM, explores their origins from string theory, and demonstrates their potential to solve the $5$ problem, nucleon decay, and the strong CP problem.

Contribution

It classifies viable discrete R symmetries for the MSSM, derives a string-based model with a $Z_4^R$ symmetry, and shows how these symmetries can address key supersymmetric and axion-related issues.

Findings

Identifies 5 anomaly-free $Z_M^R$ symmetries with M dividing 24.

Constructs a string-derived model with a $Z_4^R$ symmetry consistent with MSSM.

Shows $Z_4^R$ and $Z_8^R$ can solve the $5$ problem in 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 $Z_{24}^R$ symmetry can provide a simultaneous solution to the $\mu$ and strong CP problem with the axion coupling in the favoured window.