Quark masses in two-flavor QCD

TL;DR

This paper explores how quark masses in two-flavor QCD influence phase transitions and highlights the scheme dependence of quark mass ratios, complicating the understanding of the strong CP problem.

Contribution

It clarifies the scheme dependence of quark mass ratios and discusses the implications for the strong CP problem in two-flavor QCD.

Findings

Identification of phase transition regions in quark mass parameter space

Demonstration of scheme dependence in quark mass ratios

Implication that a vanishing up quark mass does not resolve the strong CP problem

Abstract

Considered as a function of the quark mases, two-flavor QCD depends on three parameters, including one that is CP violating. As the masses vary to unphysical values, regions of both first- and second-order phase transitions are expected. For non-degenerate quarks, non-perturbative effects leave individual quark mass ratios with a renormalization scheme dependence. This complicates matching lattice results with perturbative schemes and clarifies the tautology with attacking the strong CP problem via a vanishing up quark mass.