The limits of the strong $CP$ problem

TL;DR

This paper discusses recent theoretical developments suggesting that the strong $CP$ problem may be resolved by boundary condition considerations, which could render the $CP$ violation parameter $ heta$ unobservable in QCD.

Contribution

It introduces a novel perspective on the strong $CP$ problem by analyzing boundary conditions and the infinite volume limit, challenging the traditional view of a fine-tuned $ heta$ parameter.

Findings

$ heta$ drops out of fermion correlation functions in the infinite volume limit

Boundary conditions can eliminate observable $CP$ violation in QCD

Challenges the necessity of fine-tuning $ heta$ in the strong $CP$ problem

Abstract

While $CP$ violation has never been observed in the strong interactions, the QCD Lagrangian admits a $CP$-odd topological interaction proportional to the so called $\theta$ angle, which weighs the contributions to the partition function from different topological sectors. The observational bounds are usually interpreted as demanding a severe tuning of $\theta$ against the phases of the quark masses, which constitutes the strong $CP$ problem. Here we report on recent challenges to this view based on a careful treatment of boundary conditions in the path integral and of the limit of infinite spacetime volume, which leads to $\theta$ dropping out of fermion correlation functions and becoming unobservable, implying that $CP$ is preserved in QCD.