Skewness and kurtosis of net baryon-number distributions at small values of the baryon chemical potential

TL;DR

This study uses lattice QCD to analyze net baryon-number fluctuations, revealing qualitative agreement with experimental data at certain energies and elucidating the relationships among various fluctuation ratios at small baryon chemical potential.

Contribution

It provides the first lattice QCD calculations of net baryon-number fluctuation ratios at small chemical potential, connecting theoretical predictions with experimental measurements.

Findings

Ratios of net baryon-number fluctuations resemble experimental net proton data at energies ≥ 19.6 GeV.

Differences in cumulant ratios are explained by QCD thermodynamics.

Close relations between skewness and kurtosis ratios are established at small chemical potential.

Abstract

We present results for the ratios of mean ($M_B$), variance ($\sigma_B^2$), skewness ($S_B)$ and kurtosis ($\kappa_B$) of net baryon-number fluctuations obtained in lattice QCD calculations with a physical light to strange quark mass ratio. Using next-to-leading order Taylor expansions in baryon chemical potential we find that qualitative features of these ratios closely resemble the corresponding experimentally measured cumulants ratios of net proton-number fluctuations for beam energies down to $\sqrt{s_{_{NN}}} \ge 19.6$ GeV. We show that the difference in cumulant ratios for the mean net baryon-number, $M_B/\sigma_B^2=\chi_1^B(T,\mu_B)/\chi_2^B(T,\mu_B)$ and the normalized skewness, $S_B\sigma_B=\chi_3^B(T,\mu_B)/\chi_2^B(T,\mu_B)$, naturally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, $S_B\sigma_B^3/M_B=\chi_3^B(T,\mu_B)/\chi_1^B(T,\mu_B)$ and $\kappa_B\sigma_B^2=\chi_4^B(T,\mu_B)/\chi_2^B(T,\mu_B)$, valid at small values of the baryon chemical potential.