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Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point

Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential ($μ_B$) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature $T$ and $μ_B$ to the universal properties of the second order chiral phase transition were determined by lattice QCD calculations. Motivated by these advances, first, we discuss the analytic structure of the partition function -- the so-called Yang-Lee edge singularity -- in the QCD crossover regime, solely based on universal properties. Then, utilizing the lattice calculated non-universal parameters, we map this singularity to the real $T$ and complex $μ_B$ plane, in order to find the radius of convergence for a Taylor series expansion of QCD partition function around $μ_B=0$ in the QCD crossover regime. Our most important findings are: (i) An universality-based estimate of the radius of convergence around $μ_B=0$; (ii) Universality and lattice QCD based constraints on the location of the QCD critical point in the $T-μ_B$ plane.