Challenges for the Nelson-Barr Mechanism

TL;DR

This paper critically examines the challenges faced by the Nelson-Barr mechanism as a solution to the strong CP problem, analyzing theoretical issues and assessing its plausibility.

Contribution

It provides a comprehensive analysis of the theoretical challenges and evaluates the viability of the Nelson-Barr mechanism for solving the strong CP problem.

Findings

Identifies hierarchy and fine-tuning issues

Highlights compatibility problems with electroweak solutions

Assesses the plausibility of Nelson-Barr scenarios

Abstract

Solutions to strong CP based on chiral structure have been subject to the most careful scrutiny and critique. Basic theoretical issues include hierarchy and fine-tuning problems, quality and genericity of symmetries, and compatibility with solutions to the electroweak hierarchy problem. We study the similar set of challenges for solutions to strong CP based on spontaneous CP violation and the Nelson-Barr mechanism. Some of our observations have appeared in the literature previously, and others are new; our purpose is to collect and analyze the issues as a whole and provide an assessment of the most plausible settings for the Nelson-Barr solution.