Non-invertible Symmetry as a Solution to the Strong CP Problem in a GUT-inspired Standard Model

Abstract

We propose a three-zero texture for the down-quark mass matrix within a $SU(5)$ GUT-inspired Standard Model, enforced by a non-invertible selection rule originating from ${\mathbb{Z}}_2$ gauging of ${\mathbb{Z}}_N$ symmetries. Assuming CP invariance at the high-energy scale, our framework solves the strong CP problem while reproducing a realistic quark mass matrix. The CP symmetry is spontaneously broken down at an intermediate scale via complex vacuum expectation values of new scalar fields ${\eta }_i$, which generate the CP phase in the CKM matrix without inducing the QCD $\bar{\theta }$ term. The present model incorporates three generations of matter, Higgs, and additional scalars with a common structure under the non-invertible symmetry, which may be naturally embedded into $SO(10)$ GUTs at high energies.

Comments: 12 pages