The QCD crossover temperature and curvature coefficient from unbiased exponential resummation at physical quark masses in (2+1)-flavor lattice QCD

Abstract

We present the first application of the unbiased exponential resummation method to the determination of the QCD pseudocritical temperature $T_{\mathrm{pc}}$ at vanishing baryon chemical potential ${\mu }_B$. By reconstructing the finite-density baryon number susceptibility ${\chi }_2^B$, we define two thermal-derivative observables whose peak positions yield $T_{\mathrm{pc}}^T=160.2(4)(3)$ MeV and $T_{\mathrm{pc}}^C=158.1(5)(3)$ MeV. We also show that the pseudocritical temperature, $T_{\mathrm{pc}}^{\chi }$ obtained from the peak of the fourth-order baryon number susceptibility ${\chi }_4^B$ is consistent with these determinations and with previous lattice-QCD results based on Taylor expansions \cite{Bollweg:2022Pade}. Further, we demonstrate that scaling relations \cite{Bollweg:2022fqq} between ${\chi }_4^B$ and the thermal derivatives of ${\chi }_2^B$ yield mutually consistent estimates of the leading second order curvature coefficient ${\kappa }_2^B$ at the corresponding pseudocritical temperatures. A direct analysis of the ${\mu }_B$ dependence of the pseudocritical temperatures provides an independent but substantially less constrained determination of the curvature, which remains statistically consistent with the scaling-based estimates. These results demonstrate the consistency of unbiased exponential resummation with the expected scaling behavior and establish it as a complementary approach for probing the QCD crossover at small finite baryon density.

6 pages, 4 figures, 2 tables