A unique Z_4^R symmetry for the MSSM

TL;DR

The authors identify a unique $\mathbb{Z}_4^R$ discrete $R$-symmetry that commutes with $SO(10)$ and anomaly-cancels via the Green-Schwarz mechanism, which forbids the perturbative $\mu$-term and dangerous baryon/lepton-number violating operators in the MSSM. Non-perturbative effects break $\mathbb{Z}_4^R$ to $\mathbb{Z}_2$ matter parity, allowing a mu-term at the electroweak scale and inducing only highly suppressed dimension-five baryon/lepton-number operators, thereby satisfying nucleon decay constraints. The framework naturally links the mu-problem to SUSY-breaking dynamics (with $\mu$ of order the gravitino mass) and can arise from string-theory compactifications as remnants of the Lorentz symmetry of the extra dimensions. Cosmological concerns such as domain walls are addressed via inflationary constraints and a Green-Schwarz–guided anomaly cancellation, with explicit string-model realizations illustrated as proof-of-principle UV completions. Overall, the work provides a UV-consistent route to MSSM viability with controlled proton decay and a solved mu-problem via a unique discrete $R$-symmetry.

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.