Qualities of axion and LSP in Pati-Salam unification with $Z^R_{4}\times Z_{N}$ symmetry

TL;DR

This paper constructs supersymmetric Pati-Salam models with discrete symmetries that preserve the Peccei-Quinn symmetry, addressing the strong CP problem and exploring implications for axion and LSP properties, including R-parity violation effects.

Contribution

It introduces explicit supersymmetric Pati-Salam models with discrete symmetries that maintain the PQ symmetry and analyze R-parity violation impacts on axion and LSP phenomenology.

Findings

Minimal model with highly suppressed R-parity violation

Non-minimal model with significant R-parity violation

Neutralino becomes unstable as LSP in the non-minimal model

Abstract

In this paper we construct supersymmetric Pati-Salam (PS) models containing the minimal supersymmetric standard model and an invisible axion. The models include two discrete symmetries, $\mathbb{Z}_4^R \times \mathbb{Z}_N$, which maintain the $quality$ of the accidental Peccei-Quinn (PQ) symmetry and thus the solution to the strong CP problem. We require that the discrete anomaly conditions are satisfied for both $\mathbb{Z}_4^R \times G_{\rm PS}^2$ and $ \mathbb{Z}_N \times G_{\rm PS}^2$. The vacuum expectation value of the PQ field spontaneously breaks all the discrete symmetries. R-parity is violated if any of the PQ field(s) has an odd charge under $\mathbb{Z}_4^R$. We present two explicit models which we refer to as a minimal model where R-parity violation is extremely suppressed, and a non-minimal model where R-parity violation is significant. In the latter model, the neutralino becomes unstable even if it is the Lightest Supersymmetric Particle (LSP), and, in addition, there are new low-energy vector-like states. In both examples, R-parity violation is sufficiently suppressed such that the proton is stable.