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

Alexander Adam1, Szabolcs Borsányi1, Zoltán Fodor2,1,3,4, Jana N. Guenther1, Piyush Kumar1, Paolo Parotto5, Attila Pásztor3,6,*, and Chik Him Wong1

  • *Contact author: attila.pasztor@ttk.elte.hu
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Phys. Rev. D 113, 074525 – Published 30 April, 2026

DOI: https://doi.org/10.1103/pcjv-74sj

Abstract

We have performed high-statistics lattice simulations using 4HEX improved staggered fermions on 163×8 lattices. We calculated the Taylor expansion coefficients of the pressure with respect to the baryochemical potential to the tenth order at zero and the 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 quantum chromodynamics 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 ansätze 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.

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Outline

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Phys. Rev. D 113, 074525– Published 30 April, 2026
  • Received 22 September 2025
  • Accepted 12 November 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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