A bottom-up approach to the strong CP problem

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 the large CP violation in weak 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 UV completion of the Standard Model, we provide a simple requirement for such models not to show a strong CP problem by construction.