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 $\text{sqrts\_\_NN ge 19.6}$ 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.