The CKM Phase and $\bar\theta$ in Nelson-Barr Models

TL;DR

This paper investigates the Nelson-Barr models addressing the Strong CP Problem, deriving conditions for CKM phase reproduction, quantifying loop corrections to the QCD angle, and analyzing experimental bounds on model parameters.

Contribution

It provides a detailed analysis of the conditions needed for Nelson-Barr models to reproduce observed CP violation and quark masses, including loop correction estimates and experimental constraints.

Findings

Loop corrections to the QCD angle are below current bounds.

Most parameter space above TeV scale is allowed for down-type mediators.

Neutron electric dipole moment constrains models with multiple mediator families.

Abstract

We analyze the Nelson-Barr approach to the Strong CP Problem. We derive the necessary conditions in order to simultaneously reproduce the CKM phase and the quark masses. Then we quantify the irreducible contributions to the QCD topological angle, namely the corrections arising from loops of the colored fermion mediators that characterize these models. Corrections analytic in the couplings first arise at 3-loop order and are safely below current bounds; non-analytic effects are 2-loop order and decouple as the mediators exceed a few TeV. We discuss collider, electroweak, and flavor bounds and argue that most of the parameter space above the TeV scale is still allowed in models with down-type mediators, whereas other scenarios are more severely constrained. With two or more families of mediators the dominant experimental bound is due to the neutron electric dipole moment.