Gauged discrete symmetries and proton stability

Rabindra N Mohapatra,Michael Ratz

doi:10.1103/physrevd.76.095003

Abstract

We discuss the results of a search for anomaly-free Abelian ${\mathbb{Z}}_{N}$ discrete symmetries that lead to automatic R-parity conservation and prevent dangerous higher-dimensional proton decay operators in simple extensions of minimal supersymmetric extension of the standard model 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 minimal supersymmetric extension of the standard model 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.

Highlights

Supersymmetry (SUSY) is widely believed to be one of the key ingredients of physics beyond the standard model (SM) for various reasons:(i) stability of the Higgs mass and the weak scale;(ii) possibility of a supersymmetric dark matter;(iii) gauge-coupling unification, suggesting that there is a grand unified theory (GUT) governing the nature of all forces and matter.The fact that the seesaw mechanism for understanding small neutrino masses requires a new scale close to the GUT scale adds another powerful reason to believe in this general picture.There are many downsides to SUSY
While the standard model guarantees nucleon stability, in its supersymmetric version, there appear two new kinds of problems: (i) There are renormalizable Rparity breaking operators allowed by supersymmetry and standard model gauge invariance, e.g
In what follows we will refer to these operators as QQQL. To understand that these problems can be attributed to SUSY, recall that the R-parity breaking terms are forbidden in the case of SM by Lorentz invariance in the standard model, and the QQQL is suppressed by two powers of Planck mass and not problematic

Summary

INTRODUCTION

Supersymmetry (SUSY) is widely believed to be one of the key ingredients of physics beyond the standard model (SM) for various reasons:. In what follows we will refer to these operators as QQQL To understand that these problems can be attributed to SUSY, recall that the R-parity breaking terms are forbidden in the case of SM by Lorentz invariance in the standard model, and the QQQL is suppressed by two powers of Planck mass and not problematic. (ii) R-parity conserving dimension five proton decay operators of type QQQL are either forbidden or suppressed to the desired level; and (iii) the superpotential of the theory has enough structure for ensuring proper symmetry breaking down to the standard model and to give fermion masses. This paper is organized as follows: in Sec. II, we discuss anomaly-free gauge symmetries ensuring proton stability in left-right models; we proceed to the Pati-Salam model in.

LEFT-RIGHT MODEL AND DISCRETE

Left-right symmetric models—doublet Higgs case

PATI-SALAM MODEL

H M 2 0 3

Findings

CONCLUSION AND COMMENTS