Conserved Charge Fluctuations from Lattice QCD and the Beam Energy Scan

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, $S_B\ddot{I}{ƒ}_B=\ddot{I}{‡}_3^B/\ddot{I}{‡}_1^B$, and the kurtosis ratio, $\hat{I}{º}_B\ddot{I}{ƒ}_B^2=\ddot{I}{‡}_4^B/\ddot{I}{‡}_2^B$. 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 $\hat{I}{º}_B\ddot{I}{ƒ}_B^2$ however is approximately three times larger than that for $S_B\ddot{I}{ƒ}_B$. 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.

4 pages, 4 figures, contribution to the Quark Matter 2015 proceedings