Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition

TL;DR

This paper analytically and numerically investigates the distribution of Lee-Yang zeros in high-temperature QCD, revealing their connection to the Roberge-Weiss phase transition and confirming Gaussian behavior of canonical partition functions.

Contribution

It provides an analytic derivation of Lee-Yang zeros for high-temperature QCD and validates these results with lattice simulations, linking zeros to phase transition phenomena.

Findings

Canonical partition functions follow a Gaussian distribution.

Lee-Yang zeros accumulate indicating a first-order Roberge-Weiss transition.

Analytic and numerical results are consistent within the studied range.

Abstract

Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. Recent lattice simulations have confirmed that the free energy of QCD is a quartic function of quark chemical potential at temperature slightly above pseudo-critical temperature $T_c$, as in the case with a gas of free massless fermions. We present analytic derivation of the canonical partition functions and Lee-Yang zeros for this type of free energy using the saddle point approximation. We also perform lattice QCD simulation in a canonical approach using the fugacity expansion of the fermion determinant, and carefully examine its reliability. By comparing the analytic and numerical results, we conclude that the canonical partition functions follow the Gaussian distribution of the baryon number, and the accumulation of Lee-Yang zeros of these canonical partition functions exhibit the first-order Roberge-Weiss phase transition. We discuss the validity and applicable range of the result and its implications both for theoretical and experimental studies.