Imprint of chiral symmetry restoration on the Polyakov loop and the heavy quark free energy

TL;DR

This paper investigates how chiral symmetry restoration influences the Polyakov loop and heavy quark free energy near the transition temperature, revealing their energy-like scaling behavior consistent with the 3-d O(N) universality class.

Contribution

The study demonstrates that the Polyakov loop and heavy quark free energy exhibit energy-like scaling near the chiral transition, linking deconfinement indicators to chiral symmetry restoration.

Findings

Polyakov loop scales like energy density near transition

Heavy quark free energy responds like specific heat to chemical potential

Results consistent with 3-d O(N) universality class

Abstract

The Polyakov loop expectation value $\langle P\rangle$ is an order parameter of the deconfinement transition in the heavy quark mass regime, whereas its sensitivity to the deconfinement of light, dynamical quarks is not apparent. From the perspective of an effective Lagrangian in the vicinity of the chiral transition, the Polyakov loop, $P$, is an energy-like observable, and $\langle P\rangle$ should hence scale like the energy density. Using $N_f=2+1$ HISQ configurations at finite lattice spacing, we show that near the chiral transition temperature, the scaling behavior of $\langle P\rangle$ and the heavy quark free energy $F_q$ is consistent with energy-like observables in the 3-$d$, O($N$) universality class. We extend this analysis to other Polyakov loop observables, including the response of the heavy quark free energy, $F_q$, to the baryon chemical potential, which is expected to scale like a specific heat.