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

Canonical partition functions and Lee-Yang zeros of QCD at finite density and high temperature are studied. Recent lattice simulations confirm that the free energy of QCD is a quartic function of quark chemical potential at temperature slightly above pseudocritical temperature Tc, 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.

Note:

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

11.15.Ha
12.38.Gc
12.38.Mh
temperature: high
fermion: determinant
density: finite
potential: chemical
partition function
critical phenomena
saddle-point approximation

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