High-precision baryon number cumulants from lattice QCD in a finite box: cumulant ratios, Lee-Yang zeros and critical endpoint predictions

TL;DR

This study uses high-precision lattice QCD simulations to analyze baryon number fluctuations, estimate the critical endpoint's location, and explore the properties of Lee-Yang zeros, providing insights into QCD phase transitions.

Contribution

The paper introduces a novel rational function approach satisfying QCD symmetries to estimate Lee-Yang zeros and the critical endpoint from lattice data.

Findings

Critical endpoint likely below 103 MeV or absent

High-statistics data improves zero estimation accuracy

Systematic errors remain significant despite high statistics

Abstract

We have performed high-statistics lattice simulations using 4HEX improved staggered fermions on $16^3 \times 8$ lattices. We calculated the Taylor expansion coefficients of the pressure with respect to the baryochemical potential to the tenth order at zero, and fourth order at purely imaginary chemical potentials. We used this data to construct rational function approximations of the free energy. We use a rational ansatz that explicitly satisfies the charge conjugation symmetry and the Roberge-Weiss periodicity, which are exact properties of the QCD free energy. We use this ansatz to estimate the position of Lee-Yang zeros in the complex chemical potential plane. The temperature dependence of the imaginary part of the Lee-Yang zeros is then fitted with ans\"atze motivated by the universal behavior of the free energy near a 3D Ising critical point. In principle, this allows one to estimate the temperature of the critical endpoint. We consider several sources of systematic errors. On this single lattice spacing we find that with $84\%$ probability, the chiral critical endpoint is either below $103$~MeV temperature or it does not exist. We also identify some caveats of the method, which do not disappear even with the extremely high statistics of this present study. We discuss to what extent these can be eliminated by future high statistics lattice analyses.