CP symmetry and the strong interactions

TL;DR

This paper explores CP symmetry breaking in strong interactions, analyzing spontaneous and explicit CP violation through effective Lagrangians, and discusses implications for lattice simulations and quark mass limits.

Contribution

It provides a detailed analysis of CP violation mechanisms in strong interactions and highlights issues with removing CP violation via quark mass limits.

Findings

CP symmetry can be spontaneously broken in certain quark mass regions.

Explicit CP violation can arise from complex quark masses.

Removing CP violation by setting the lightest quark mass to zero is ill-defined.

Abstract

I discuss several aspects of CP non-invariance in the strongly interacting theory of quarks and gluons. I use a simple effective Lagrangian technique to map out the region of quark masses where CP symmetry is spontaneously broken. I then turn to the possible explicit CP violation arising from a complex quark mass. After summarizing the definition of the renormalized theory as a limit, I argue that attempts to remove the CP violation by making the lightest quark mass vanish are not well defined. I close with some warnings for lattice simulations.