When CP requires $\bar\theta=0$, not $\bar\theta=\pi$

TL;DR

This paper discusses how the combination of CP symmetry and gauge group embedding naturally selects a zero topological angle in QCD, offering insights into the Strong CP problem.

Contribution

It demonstrates that CP symmetry alone cannot solve the Strong CP problem, but when combined with gauge group embedding, it naturally favors ar=0.

Findings

ar=0 is naturally selected with combined assumptions

CP symmetry alone is insufficient for solving the Strong CP problem

Gauge group embedding influences topological angle selection

Abstract

Imposing CP or P forces the QCD topological angle to be either $\bar\theta=0$ or $\bar\theta=\pi$. However, only the former is phenomenologically viable. This implies that the assumption of CP or P alone cannot provide a framework for unambiguously solving the Strong CP problem. We show that $\bar\theta=0$ is naturally selected when the assumption of CP is combined with the hypothesis that the Standard Model is embedded in a suitable gauge group.