Conserved Charge Fluctuations from Lattice QCD and the Beam Energy Scan

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, $S_B{\sigma }_B={\chi }_3^B\mathrm{/}{\chi }_1^B$, and the kurtosis ratio, ${\kappa }_B{\sigma }_B^2={\chi }_4^B\mathrm{/}{\chi }_2^B$. 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 ${\kappa }_B{\sigma }_B^2$ however is approximately three times larger than that for $S_B{\sigma }_B$. 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.