Qualities of axion and LSP in Pati-Salam unification with $Z_4^R\times Z_N$ symmetry

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 ${\mathbb{Z}}_4^R\times G_{\mathrm{PS}}^2$ and ${\mathbb{Z}}_N\times G_{\mathrm{PS}}^2$. 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.

Comments: 32 pages, 9 tables