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