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

الأصل · EN

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 Zₙ or Zₙʳ 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 Z₆ʳ. In the case of renormalizable lepton number violation the smallest symmetries are two hexalities, one Z₆ and one Z₆ʳ.