Conserved Charge Fluctuations from Lattice QCD and the Beam Energy Scan

TL;DR

This paper analyzes higher-order cumulant ratios of net-baryon fluctuations from lattice QCD, revealing their energy dependence and consistency with experimental data, which enhances understanding of QCD matter under extreme conditions.

Contribution

It provides a next-to-leading order analysis of cumulant ratios, highlighting their differences and energy dependence, and compares these theoretical predictions with experimental measurements.

Findings

Differences between skewness and kurtosis ratios are small at low chemical potential.

Next-to-leading order correction to kurtosis ratio is significantly larger than that for skewness.

Predicted patterns align with net-proton fluctuation data from STAR at high energies.

Abstract

We discuss the next-to-leading order Taylor expansion of ratios of cumulants of net-baryon number fluctuations. We focus on the relation between the skewness ratio, $S_B\sigma_B = \chi_3^B/\chi_1^B$, and the kurtosis ratio, $\kappa_B\sigma_B^2 =\chi_4^B/\chi_2^B$. We show that differences in these two cumulant ratios are small for small values of the baryon chemical potential. The next-to-leading order correction to $\kappa_B\sigma_B^2$ however is approximately three times larger than that for $S_B\sigma_B$. The former thus drops much more rapidly with increasing beam energy, $\sqrt{s_{NN}}$. We argue that these generic patterns are consistent with current data on cumulants of net-proton number fluctuations measured by the STAR Collaboration at $\sqrt{s_{NN}}\ge 19.6$~GeV.