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.

arXiv comment14 pages, 11 figures

References in corpus (46)

• Critical point of QCD at finite T and μ, lattice results for physical quark masses
• The QCD phase diagram for small densities from imaginary chemical potential
• Lattice determination of the critical point of QCD at finite T and μ
• The QCD thermal phase transition in the presence of a small chemical potential
• QCD Equation of State and Hadron Resonance Gas
• Finite density QCD via imaginary chemical potential
• Thermodynamics of Two Flavor QCD to Sixth Order in Quark Chemical Potential
• A new method to study lattice QCD at finite temperature and chemical potential
• The QCD Equation of State to $\mathcal{O}({\mu }_B^6)$ from Lattice QCD
• Fluctuations of conserved charges at finite temperature from lattice QCD
• QCD equation of state at nonzero chemical potential: continuum results with physical quark masses at order mu^2
• QCD at finite chemical potential with six time slices
• Canonical partition function and finite density phase transition in lattice QCD
• Higher order fluctuations and correlations of conserved charges from lattice QCD
• Results on Finite Density QCD
• Curvature of the chiral pseudo-critical line in QCD: continuum extrapolated results
• Finite density QCD with a canonical approach
• The QCD equation of state at finite density from analytical continuation
• Curvature of the pseudocritical line in QCD: Taylor expansion matches analytic continuation
• Constraining the hadronic spectrum through QCD thermodynamics on the lattice
• Diagonal and off-diagonal quark number susceptibilities at high temperatures
• Trajectory phase transitions, Lee-Yang zeros, and high-order cumulants in full counting statistics
• Thermodynamics of two flavor QCD from imaginary chemical potentials
• Repulsive baryonic interactions and lattice QCD observables at imaginary chemical potential
• The chiral phase transition in two-flavor QCD from imaginary chemical potential
• Higher order quark number fluctuations via imaginary chemical potentials in $N_f=2+1$ QCD
• Experimental Determination of Dynamical Lee-Yang Zeros
• Critical line of 2+1 flavor QCD: Toward the continuum limit
• On the critical line of 2+1 flavor QCD
• Equation of state at finite temperature and chemical potential, lattice QCD results
• Hadron Resonance Gas with Repulsive Interactions and Fluctuations of Conserved Charges
• Cluster Expansion Model for QCD Baryon Number Fluctuations: No Phase Transition at ${\mu }_B/T<\pi$
• Critical point of $N_f=3$ QCD from lattice simulations in the canonical ensemble
• Finite density phase transition of QCD with $N_f=4$ and $N_f=2$ using canonical ensemble method
• Quark number susceptibilities and equation of state at finite chemical potential in staggered QCD with Nt=8
• Lee-Yang zeros and large-deviation statistics of a molecular zipper
• Reliability of Taylor expansions in QCD
• New approach to canonical partition functions computation in $N_f=2$ lattice QCD at finite baryon density
• Lee-Yang zero distribution of high temperature QCD and Roberge-Weiss phase transition
• Sign problem in finite density lattice QCD
• Properties of canonical determinants and a test of fugacity expansion for finite density lattice QCD with Wilson fermions
• QCD phase transition at real chemical potential with canonical approach
• Lee-Yang zeros in lattice QCD for searching phase transition points
• Mapping the phase diagram of strongly interacting matter
• Canonical approach to finite density QCD with multiple precision computation
• Generalized quark number susceptibilities from fugacity expansion at finite chemical potential for $N_f$ = 2 Wilson fermions

Cited by in corpus (28)

• The QCD crossover at finite chemical potential from lattice simulations
• Lattice QCD equation of state at finite chemical potential from an alternative expansion scheme
• Finite-density lattice QCD and sign problem: current status and open problems
• Phase Transitions in Particle Physics -- Results and Perspectives from Lattice Quantum Chromo-Dynamics
• Radius of convergence in lattice QCD at finite ${\mu }_B$ with rooted staggered fermions
• New approach to lattice QCD at finite density; results for the critical end point on coarse lattices
• Equation of state and speed of sound of (2+1)-flavor QCD in strangeness-neutral matter at non-vanishing net baryon-number density
• Lattice simulations of the QCD chiral transition at real baryon density
• Lee-Yang theory, high cumulants, and large-deviation statistics of the magnetization in the Ising model
• 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
• The effect of stout smearing on the phase diagram from multiparameter reweigthing in lattice QCD
• New Way to Resum the Lattice QCD Taylor Series Equation of State at Finite Chemical Potential
• Traces of the nuclear liquid-gas phase transition in the analytic properties of hot QCD
• 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
• Contribution to understanding the phase structure of strong interaction matter: Lee-Yang edge singularities from lattice QCD
• Locating Critical Points Using Ratios of Lee-Yang Zeros
• Towards a reliable lower bound on the location of the critical endpoint
• A new way of determining the Lattice QCD equation of state at a finite chemical potential
• 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
• Resummed lattice QCD equation of state at finite baryon density: strangeness neutrality and beyond