Gauged Discrete Symmetries and Proton Stability

TL;DR

This paper investigates anomaly-free discrete symmetries in supersymmetric models that automatically conserve R-parity and prevent proton decay, finding models that restrict the number of generations.

Contribution

It identifies viable anomaly-free Z_N discrete symmetries in extended MSSM models, linking symmetry constraints to the number of generations.

Findings

Viable models with anomaly-free discrete symmetries found in various extensions

Symmetry constraints restrict the number of fermion generations

Models ensure R-parity conservation and suppress proton decay operators

Abstract

We discuss the results of a search for anomaly free Abelian Z_N discrete symmetries that lead to automatic R-parity conservation and prevents dangerous higher-dimensional proton decay operators in simple extensions of the minimal supersymmetric extension of the standard model (MSSM) based on the left-right symmetric group, the Pati-Salam group and SO(10). We require that the superpotential for the models have enough structures to be able to give correct symmetry breaking to MSSM and potentially realistic fermion masses. We find viable models in each of the extensions and for all the cases, anomaly freedom of the discrete symmetry restricts the number of generations.