High quality Nelson-Barr solution to the strong CP problem with $\theta=\pi$

TL;DR

This paper proposes a composite UV completion of the Nelson-Barr solution to the strong CP problem, utilizing spontaneous CP violation in a hidden QCD sector and a scalar portal to the visible sector, resolving previous quality issues.

Contribution

It introduces a minimal, calculable scheme for Nelson-Barr models with composite UV completion that avoids the quality problem by mediating CP violation through a scalar portal.

Findings

A simple, calculable scheme for Nelson-Barr models with composite UV completion.

Resolution of the quality problem in minimal Nelson-Barr theories.

Successful realization of the Nelson-Barr construction with dynamical CP violation.

Abstract

We discuss composite UV completions of the Nelson-Barr(NB) solution to the strong CP problem. In our construction, the CP symmetry is broken spontaneously by the dynamics of a hidden QCD at $\theta=\pi$. We focus on the minimal implementation of the NB construction where the visible sector contains one extra pair of vector-like up/down quarks. We show that the minimal NB theory suffers from a quality problem, and discuss how composite UV completions may resolve it. We present a simple calculable scheme, free of a quality problem, where dynamical CP violation in the hidden sector is mediated through a scalar portal to the visible sector, which successfully realizes the NB construction.