CP conservation in the strong interactions

TL;DR

This paper argues that CP symmetry is preserved in strong interactions due to the order of limits in topological quantization and volume considerations, aligning with path integral and effective field theory approaches.

Contribution

It clarifies the conditions under which CP is conserved in the strong interactions, addressing objections related to theta-parameter effects and instanton sampling.

Findings

CP is conserved when infinite volume limits are taken before summing over topological sectors.

The path integral construction with steepest-descent contours supports CP conservation.

Volume dependence does not imply CP violation in the strong interactions.

Abstract

We discuss matters related to the point that topological quantization in the strong interaction is a consequence of an infinite spacetime volume. Because of the ensuing order of limits, i.e. infinite volume prior to summing over topological sectors, CP is conserved. Here, we show that this reasoning is consistent with the construction of the path integral from steepest-descent contours. We reply to some objections that aim to support the case for CP violation in the strong interactions that are based on the role of the CP-odd theta-parameter in three-form effective theories, the correct sampling of all configurations in the dilute instanton gas approximation and the volume dependence of the partition function. We also show that the chiral effective field theory derived from taking the volume to infinity first is in no contradiction with analyses based on partially conserved axial currents.