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 ($\ddot{I}{ƒ}_B^2$), skewness ($S_B)$ and kurtosis ($\hat{I}{º}_B$) 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, $M_B/\ddot{I}{ƒ}_B^2=\ddot{I}{‡}_1^B(T,\hat{I}{¼}_B)/\ddot{I}{‡}_2^B(T,\hat{I}{¼}_B)$ and the normalized skewness, $S_B\ddot{I}{ƒ}_B=\ddot{I}{‡}_3^B(T,\hat{I}{¼}_B)/\ddot{I}{‡}_2^B(T,\hat{I}{¼}_B)$, naturally arises in QCD thermodynamics. Moreover, we establish a close relation between skewness and kurtosis ratios, $S_B\ddot{I}{ƒ}_B^3/M_B=\ddot{I}{‡}_3^B(T,\hat{I}{¼}_B)/\ddot{I}{‡}_1^B(T,\hat{I}{¼}_B)$ and $\hat{I}{º}_B\ddot{I}{ƒ}_B^2=\ddot{I}{‡}_4^B(T,\hat{I}{¼}_B)/\ddot{I}{‡}_2^B(T,\hat{I}{¼}_B)$, valid at small values of the baryon chemical potential.

14 pages, 13 figures, minor updates, final version