A unique Z_4^R symmetry for the MSSM

TL;DR

This paper identifies a unique Z_4^R symmetry in the MSSM that forbids the mu-term perturbatively, is anomaly-free, and naturally addresses the mu-problem while suppressing dangerous baryon- and lepton-number violating operators.

Contribution

The paper proves the uniqueness of the Z_4^R symmetry in the MSSM that commutes with SO(10) and demonstrates its role in solving the mu-problem and suppressing proton decay.

Findings

Identifies a unique Z_4^R symmetry consistent with anomaly cancellation.

Shows non-perturbative effects generate a suitable mu-term.

Ensures proton stability by suppressing dangerous operators.

Abstract

We consider the possible anomaly free Abelian discrete symmetries of the MSSM that forbid the mu-term at perturbative order. Allowing for anomaly cancellation via the Green-Schwarz mechanism we identify discrete R-symmetries as the only possibility and prove that there is a unique Z_4^R symmetry that commutes with SO(10). We argue that non-perturbative effects will generate a mu-term of electroweak order thus solving the mu-problem. The non-perturbative effects break the Z_4^R symmetry leaving an exact Z_2 matter parity. As a result dimension four baryon- and lepton-number violating operators are absent while, at the non-perturbative level, dimension five baryon- and lepton-number violating operators get induced but are highly suppressed so that the nucleon decay rate is well within present bounds.