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 $T_{\rm pc}$ at vanishing baryon chemical potential $μ<em>B$. By reconstructing the finite-density baryon number susceptibility $χ_2<sup>B$, we define two thermal-derivative observables whose peak positions yield $T</em>{\rm pc}<sup>T=160.2(4)(3)$ MeV and $T_{\rm pc}<sup>C=158.1(5)(3)$ MeV. We also show that the pseudocritical temperature, $T_{\rm pc}<sup>χ$ obtained from the peak of the fourth-order baryon number susceptibility $χ_4<sup>B$ 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 $χ_4<sup>B$ and the thermal derivatives of $χ_2<sup>B$ yield mutually consistent estimates of the leading second order curvature coefficient $κ_2<sup>B$ at the corresponding pseudocritical temperatures. A direct analysis of the $μ_B$ 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.