Solving the Strong CP Problem with Discrete Symmetries and the Right Unitarity Triangle

TL;DR

This paper proposes a novel solution to the strong CP problem using spontaneous CP violation and discrete symmetries, naturally predicting an almost right-angled unitarity triangle by controlling quark mass matrix entries.

Contribution

It introduces a new model that employs discrete symmetries and specific mass matrix structures to eliminate the strong CP phase while predicting the unitarity triangle angle.

Findings

Model successfully predicts near 90° unitarity triangle angle

Mass matrices are constructed with real or imaginary entries to nullify the strong CP phase

Toy model demonstrates the viability of the proposed approach

Abstract

We present a solution to the strong CP problem based on spontaneous CP violation and discrete family symmetries. The model predicts in a natural way the almost right-angled quark unitarity triangle angle ($\alpha \simeq 90^\circ$) by making the entries of the quark mass matrices either real or imaginary. By this choice the determinants of the mass matrices are rendered real and hence the strong CP phase vanishes. We present a toy model for the quark sector that demonstrates the viability of our approach.