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

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.

11 pages, 7 figures. Accepted to Phys. Rev. D

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• Reliable estimation of the radius of convergence in finite density QCD
• Anomaly matching in QCD thermal phase transition
• High-temperature domain walls of QCD with imaginary chemical potentials
• Path optimization for $U(1)$ gauge theory with complexified parameters
• From Hagedorn to Lee-Yang: Partition functions of $\mathcal{N}=4$ SYM theory at finite $N$
• Finite-Density Massless Two-Color QCD at Isospin Roberge-Weiss Point and 't Hooft Anomaly