Reliable estimation of the radius of convergence in finite density QCD

Abstract

We study different estimators of the radius of convergence of the Taylor series of the pressure in finite density QCD. We adopt the approach in which the radius of convergence is estimated first in a finite volume, and the infinite-volume limit is taken later. This requires an estimator for the radius of convergence that is reliable in a finite volume. Based on general arguments about the analytic structure of the partition function in a finite volume, we demonstrate that the ratio estimator cannot work in this approach, and propose three new estimators, capable of extracting reliably the radius of convergence, which coincides with the distance from the origin of the closest Lee-Yang zero. We also provide an estimator for the phase of the closest Lee-Yang zero, necessary to assess whether the leading singularity is a true critical point. We demonstrate the usage of these estimators on a toy model, namely 4 flavors of unimproved staggered fermions on a small $6^3\times 4$ lattice, where both the radius of convergence and the Taylor coefficients to any order can be obtained by a direct determination of the Lee-Yang zeros. Interestingly, while the relative statistical error of the Taylor expansion coefficients steadily grows with order, that of our estimators stabilizes, allowing for an accurate estimate of the radius of convergence. In particular, we show that despite the more than 100\% error bars on high-order Taylor coefficients, the given ensemble contains enough information about the radius of convergence.

14 pages, 11 figures

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• Lattice QCD Equation of State for Nonvanishing Chemical Potential by Resumming Taylor Expansion
• Lattice Constraints on the QCD Chiral Phase Transition at Finite Temperature and Baryon Density
• Apparent convergence of Padé approximants for the crossover line in finite density QCD
• Equation of state of a hot-and-dense quark gluon plasma: lattice simulations at real ${\mu }_B$ vs. extrapolations
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential
• Continuum extrapolated high order baryon fluctuations
• Constraining the QCD phase diagram at finite temperature and density
• Eye of the Tyger: early-time resonances and singularities in the inviscid Burgers equation
• Overview of the QCD phase diagram -- Recent progress from the lattice
• Locating Critical Points Using Ratios of Lee-Yang Zeros
• Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD
• Estimates of Lee-Yang zeros and a possible critical point on the pion condensate boundary in the QCD isospin phase diagram using an unbiased exponential resummation on the lattice
• Corrections to the hadron resonance gas from lattice QCD and their effect on fluctuation-ratios at finite density
• Universality, Lee-Yang singularities and series expansions
• A new way of determining the Lattice QCD equation of state at a finite chemical potential
• Resummed lattice QCD equation of state at finite baryon density: strangeness neutrality and beyond