Quark masses, the Dashen phase, and gauge field topology

TL;DR

This paper explores the behavior of quark masses, gauge field topology, and the CP-violating Dashen phase in QCD, highlighting how topological susceptibility signals the vanishing up-quark mass and discussing related ambiguities.

Contribution

It analyzes the relationship between quark mass differences, the Dashen phase, and gauge field topology, providing insights into the topological susceptibility as an indicator of the up-quark mass vanishing point.

Findings

Topological susceptibility diverges negatively near the Dashen phase.

A zero in susceptibility may indicate the up-quark mass vanishes.

Ambiguities exist in using susceptibility zero as a definitive signal.

Abstract

The CP violating Dashen phase in QCD is predicted by chiral perturbation theory to occur when the up-down quark mass difference becomes sufficiently large at fixed down-quark mass. Before reaching this phase, all physical hadronic masses and scattering amplitudes are expected to behave smoothly with the up-quark mass, even as this mass passes through zero. In Euclidean space, the topological susceptibility of the gauge fields is positive at positive quark masses but diverges to negative infinity as the Dashen phase is approached. A zero in this susceptibility provides a tentative signal for the point where the mass of the up quark vanishes. I discuss potential ambiguities with this determination.