A Theoretical Framework for R-parity Violation

TL;DR

This paper introduces a string theory-based framework that naturally suppresses dangerous R-parity violating operators, addressing proton decay and neutrino mass constraints within supersymmetric models.

Contribution

It presents a novel Calabi--Yau compactification approach that enforces a selection rule to control R-parity violation, providing solutions to proton decay and neutrino mass issues.

Findings

Trilinear R-parity violation is suppressed or negligible.

Bilinear R-parity violation remains small enough to satisfy experimental bounds.

Dimension-5 R-parity violating operators can be generated, leading to nucleon decay.

Abstract

We propose a theoretical framework for R-parity violation. It is realized by a class of Calabi--Yau compactification of Heterotic string theory. Trilinear R-parity violation in superpotential is either absent or negligibly small without an unbroken symmetry, due to a selection rule based on charge counting of a spontaneously broken U(1) symmetry. Although such a selection rule cannot be applied in general to non-renormalizable operators in the low-energy effective superpotential, it is valid for terms trilinear in low-energy degrees of freedom, and hence can be used as a solution to the dimension-4 proton decay problem in the minimal supersymmetric standard model. Bilinear R-parity violation is generated, but there are good reasons why they are small enough to satisfy its upper bounds from neutrino mass and washout of baryon/lepton asymmetry. All R-parity violating dimension-5 operators can be generated. In this theoretical framework, nucleons can decay through squark-exchange diagrams combining dimension-5 and bilinear R-parity violating operators. B-L breaking neutron decay is predicted.