Isospin breaking and the chiral condensate

TL;DR

This paper explores how isospin breaking affects the chiral condensate, revealing a split into two phase transitions with distinct order parameters, even without near-zero eigenvalues of the Dirac operator.

Contribution

It demonstrates that non-degenerate quark masses cause the single chiral transition to split into two Ising-like transitions, providing new insights into phase structure in QCD.

Findings

The chiral condensate exhibits two separate transitions with non-degenerate quarks.

The order parameter is identified as the neutral pion field expectation value.

Transitions occur without the Dirac operator having near-zero eigenvalues.

Abstract

With two degenerate quarks, the chiral condensate exhibits a jump as the quark masses pass through zero. I discuss how this single transition splits into two Ising like transitions when the quarks are made non-degenerate. The order parameter is the expectation of the neutral pion field. The transitions represent long distance coherent phenomena occuring without the Dirac operator having vanishingly small eigenvalues.