Non-invertible symmetry as an axion-less solution to the strong CP problem

TL;DR

This paper proposes a novel solution to the strong CP problem using non-invertible symmetry, avoiding the need for axions by constructing a specific quark mass matrix texture within a CP-invariant high-energy framework.

Contribution

It introduces a non-invertible symmetry approach to resolve the strong CP problem without axions, through a three-zero texture in the down-type quark mass matrix.

Findings

Successfully constructs a three-zero texture for the down quark mass matrix.

Provides a mechanism to solve the strong CP problem without axions.

Operates within a CP-invariant high-energy theory.

Abstract

We use a non-invertible symmetry to construct a three-zero texture for the down-type quark mass matrix, which can resolve the strong CP problem without invoking the axion, in four-dimensional spacetime with three quark families in QCD. We assume CP invariance at the fundamental high-energy scale.