Discrete Symmetries in the MSSM

TL;DR

This paper explores the role of discrete abelian symmetries in the MSSM, develops a method for their spontaneous breaking, and identifies a unique Z_4^R symmetry that addresses key issues like the -problem and proton decay, with implications for grand unification and string theory.

Contribution

It introduces a novel approach to derive abelian discrete symmetries via spontaneous breaking and identifies a unique Z_4^R symmetry that solves multiple problems in the MSSM.

Findings

Discovered a unique Z_4^R symmetry compatible with grand unification.

Demonstrated anomaly cancellation via the Green-Schwarz mechanism.

Presented a string theory model exhibiting the Z_4^R symmetry.

Abstract

The use of discrete symmetries, especially abelian ones, in physics beyond the standard model of particle physics is discussed. A method is developed how a general, abelian, discrete symmetry can be obtained via spontaneous symmetry breaking. In addition, anomalies are treated in the path integral approach with special attention to anomaly cancellation via the Green-Schwarz mechanism. All this is applied to the minimal supersymmetric standard model. A unique Z_4^R symmetry is discovered which solves the \mu-problem as well as problems with proton decay and allows to embed the standard model gauge group into a simple group, i.e. the Z_4^R is compatible with grand unification. Also the flavor problem in the context of minimal flavor violation is addressed. Finally, a string theory model is presented which exhibits the mentioned Z_4^R symmetry and other desirable features.