What is the discrete gauge symmetry of the R-parity violating MSSM?

TL;DR

This paper investigates the possible discrete gauge symmetries in the R-parity violating MSSM that can stabilize the proton, allow neutrino masses, and solve the mu problem, identifying minimal symmetries like Z_6 and Z_6^R.

Contribution

It systematically classifies discrete gauge symmetries compatible with R-parity violation, anomaly cancellation, and neutrino mass generation in the MSSM.

Findings

Identifies Z_6^R as the minimal symmetry for baryon number violation.

Finds Z_6 and Z_6^R as minimal symmetries for lepton number violation.

Ensures symmetries are anomaly-free and solve the mu problem.

Abstract

The lack of experimental evidence for supersymmetry motivates R-parity violating realizations of the MSSM. Dropping R-parity, alternative symmetries have to be imposed in order to stabilize the proton. We determine the possible discrete R and non-R symmetries, which allow for renormalizable R-parity violating terms in the superpotential and which, at the effective level, are consistent with the constraints from nucleon decay. Assuming a gauge origin, we require the symmetry to be discrete gauge anomaly-free, allowing also for cancellation via the Green Schwarz mechanism. Furthermore, we demand lepton number violating neutrino mass terms either at the renormalizable or non-renormalizable level. In order to solve the mu problem, the discrete Z_N or Z_N^R symmetries have to forbid any bilinear superpotential operator at tree level. In the case of renormalizable baryon number violation the smallest possible symmetry satisfying all conditions is a unique hexality Z_6^R. In the case of renormalizable lepton number violation the smallest symmetries are two hexalities, one Z_6 and one Z_6^R.