Qualities of the axion and LSP in Pati-Salam unification with Z4R×ZN 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, ${\mathbb{Z}}_{4}^{R}\ifmmode\times\else\texttimes\fi{}{\mathbb{Z}}_{N}$, 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 ${\mathbb{Z}}_{4}^{R}\ifmmode\times\else\texttimes\fi{}{G}_{\mathrm{PS}}^{2}$ and ${\mathbb{Z}}_{N}\ifmmode\times\else\texttimes\fi{}{G}_{\mathrm{PS}}^{2}$. 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 nonminimal 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 vectorlike states. In both examples, R-parity violation is sufficiently suppressed such that the proton is stable.