A bottom-up approach to the strong CP problem

TL;DR

This paper proposes a bottom-up approach within the Standard Model framework to address the strong CP problem by analyzing Yukawa matrices, suggesting minimal assumptions can prevent CP violation in strong interactions without new physics.

Contribution

It demonstrates that under minimal assumptions, Yukawa matrices do not contribute to the strong CP problem, offering a novel bottom-up perspective without extending the Standard Model.

Findings

Yukawa matrices can be structured to avoid strong CP violation

Minimal assumptions on mass matrices suffice to solve the strong CP problem

Flavor models based on SU(3) are favored for addressing flavor puzzles

Abstract

The strong CP problem is one of many puzzles in the theoretical description of elementary particle physics that still lacks an explanation. While top-down solutions to that problem usually comprise new symmetries or fields or both, we want to present a rather bottom-up perspective. The main problem seems to be how to achieve small CP violation in the strong interactions despite large CP violation in weak interactions. Observation of CP violation is exclusively through the Higgs--Yukawa interactions. In this paper, we show that with minimal assumptions on the structure of mass (Yukawa) matrices they do not contribute to the strong CP problem and thus we can provide a pathway to a solution of the strong CP problem within the structures of the Standard Model and no extension at the electroweak scale is needed. However, to address the flavor puzzle, models based on minimal SU(3) flavor groups leading to the proposed flavor matrices are favored. Though we refrain from an explicit a UV completion of the Standard Model, we provide a simple requirement those models should have to intrinsically not show a strong CP problem.