Chiral dynamics in the low-temperature phase of QCD

TL;DR

This paper explores the low-temperature phase of QCD with two light quark flavors, identifying a sharp pion-like excitation, deriving a sum rule for spectral functions, and validating chiral expansion predictions through lattice QCD and Maximum Entropy Method analyses.

Contribution

It introduces a detailed analysis of chiral dynamics near the QCD crossover, deriving a sum rule and determining pion dispersion parameters from lattice data, testing chiral expansion validity.

Findings

Identification of a sharp pion-like excitation in the spectral function.

Derivation of an exact sum rule for the axial charge spectral function.

Consistent lattice QCD results supporting chiral expansion predictions.

Abstract

We investigate the low-temperature phase of QCD and the crossover region with two light flavors of quarks. The chiral expansion around the point $(T,m=0)$ in the temperature vs. quark-mass plane indicates that a sharp real-time excitation exists with the quantum numbers of the pion. An exact sum rule is derived for the thermal modification of the spectral function associated with the axial charge density; the (dominant) pion pole contribution obeys the sum rule. We determine the two parameters of the pion dispersion relation using lattice QCD simulations and test the applicability of the chiral expansion. The time-dependent correlators are also analyzed using the Maximum Entropy Method, yielding consistent results. Finally, we test the predictions of the chiral expansion around the point $(T=0,m=0)$ for the temperature dependence of static observables.