Spontaneous CP violation and quark mass ambiguities

TL;DR

This paper investigates conditions under which CP symmetry can be spontaneously broken in strong interactions, highlighting how quark mass ambiguities and the chiral anomaly influence these phenomena, and questioning the notion of a single massless quark.

Contribution

It clarifies the role of the chiral anomaly in quark mass ambiguities and their impact on spontaneous CP violation in QCD.

Findings

Identifies regions of quark masses where CP is spontaneously broken.

Shows that the concept of a single massless quark is ill-defined due to anomalies.

Highlights the influence of the chiral anomaly on quark mass ambiguities.

Abstract

I explore the regions of quark masses where CP will be spontaneously broken in the strong interactions. The boundaries of these regions are controlled by the chiral anomaly, which manifests itself in ambiguities in the definition of non-degenerate quark masses. In particular, the concept of a single massless quark is ill defined.