Universality driven analytic structure of the QCD crossover: Radius of convergence in the baryon chemical potential
Swagato Mukherjee, Vladimir V. Skokov
Abstract
Recent lattice QCD calculations strongly indicate that the chiral crossover of QCD at zero baryon chemical potential (${\ensuremath{\mu}}_{B}$) 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 ${\ensuremath{\mu}}_{B}$ using nonuniversal 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 nonuniversal parameters we map this singularity to the real $T$ and complex ${\ensuremath{\mu}}_{B}$ plane, leading to the determination of the radius of convergence in ${\ensuremath{\mu}}_{B}$ 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 ${\ensuremath{\mu}}_{B}>0$. Implication of this result on the location of the conjectured QCD critical point is discussed.