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

Abstract

Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential (${\mu }_B$) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature $T$ and ${\mu }_B$ 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 ${\mu }_B$ plane, in order to find the radius of convergence for a Taylor series expansion of QCD partition function around ${\mu }_B=0$ in the QCD crossover regime. Our most important findings are: (i) An universality-based estimate of the radius of convergence around ${\mu }_B=0$; (ii) Universality and lattice QCD based constraints on the location of the QCD critical point in the $T-{\mu }_B$ plane.

arXiv commentQuark Matter 2019 Conference Proceedings; Submitted to Nuclear Physics A

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• The chiral and deconfinement aspects of the QCD transition
• Chiral crossover in QCD at zero and non-zero chemical potentials
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• The QCD phase transition with physical-mass, chiral quarks
• Chiral phase transition temperature in (2+1)-Flavor QCD
• Curvature of the chiral pseudo-critical line in QCD: continuum extrapolated results
• QCD Critical Point and Complex Chemical Potential Singularities
• Critical behavior of the bulk viscosity in QCD
• Fluctuations in cool quark matter and the phase diagram of Quantum Chromodynamics
• Universality of the critical point mapping between Ising model and QCD at small quark mass
• Chiral phase transition of (2+1)-flavor QCD

Cited by in corpus (8)

• The nonperturbative functional renormalization group and its applications
• Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme
• Five loop renormalization of ${\varphi }^3$ theory with applications to the Lee-Yang edge singularity and percolation theory
• Apparent convergence of Padé approximants for the crossover line in finite density QCD
• Universal location of Yang-Lee edge singularity in classic O(N) universality classes
• Uniformizing Lee-Yang Singularities
• Extrapolation from hypergeometric functions, continued functions and Borel-Leroy transformation; Resummation of perturbative renormalization functions from field theories
• Universality, Lee-Yang singularities and series expansions