Abstract
Recent lattice QCD calculations strongly indicate that the chiral crossover of QCD at zero baryon chemical potential \mu_B is a remnant of the second-order chiral phase transition. Universal properties of this second-order phase transition can be mapped to QCD temperature T and \mu_B using non-universal parameters determined by lattice QCD recently. Motivated by these results, first, we discuss the analytic structure of the partition function in the QCD crossover regime - the so-called Yang-Lee edge singularity - solely based on universal properties. Next, utilizing the lattice QCD results for non-universal parameters we map this singularity to the real T and complex \mu_B plane, leading to the determination of the radius of convergence is in \mu_B in the QCD crossover regime. These universality- and QCD-based results provide tight constraints on the range of validity of the lattice QCD calculations at \mu_B. Implication of this result on the location of the conjectured QCD critical point is discussed.
Highlights
The chiral symmetry of quantum chromodynamics (QCD) is spontaneously broken in the vacuum
Firstprinciple lattice QCD calculations have conclusively shown that the approximate chiral symmetry with physical values of quark masses gets nearly restored at a pseudocritical temperature Tpc 1⁄4 156.5 Æ 1.5 MeV [1] via a smooth crossover [2,3]
It has been conjectured that at some sufficiently large values of μB the chiral restoration in QCD takes place through a first order transition; the point in the T − μB phase diagram at which the chiral crossover line turns into a first order phase transition line is known as the QCD critical endpoint (CEP), for a review, see Ref. [4]
Summary
The chiral symmetry of quantum chromodynamics (QCD) is spontaneously broken in the vacuum. The present lattice calculations providing information on the QCD thermodynamics— either by carrying out Taylor expansions around μB 1⁄4 0 [5] or through analytic continuation from purely imaginary values of μB [6,7,8]—crucially rely on the assumption that the QCD partition function is an analytic function of complex μB within a radius of convergence. A true second order (chiral) phase transition takes place at t 1⁄4 h 1⁄4 0, while for any fixed h ≠ 0 the system undergoes a smooth crossover transition as a function of the parameter t. This is manifest in the dependence of the equation of state on ðt; hÞ in the real domain Recent theoretical advances in lattice QCD and Ref. [13] provide both required ingredients and allow us to extract the radius of convergence of the Taylor series of the pressure near zero baryon chemical potential
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