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

TL;DR

This paper introduces a GUT-inspired Standard Model with a non-invertible symmetry that naturally solves the strong CP problem and reproduces realistic quark masses by employing a three-zero down-quark mass matrix and spontaneous CP breaking.

Contribution

It presents a novel non-invertible symmetry mechanism derived from $ ext{Z}_N$ gauging to enforce texture zeros, addressing the strong CP problem within a GUT framework.

Findings

Successfully reproduces realistic quark mass matrices.

Provides a mechanism for spontaneous CP violation without a QCD $ar{ heta}$ term.

Integrates non-invertible symmetry into a GUT-inspired model with three generations.

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.