Higher order cumulants of net baryon-number distributions at non-zero ${\mu }_B$

Abstract

Using recent results on higher order cumulants of conserved charge fluctuations from lattice QCD, we construct mean, variance, skewness, kurtosis, hyper-skewness and hyper-kurtosis of net-baryon number distributions for small baryon chemical potentials ${\mu }_B$. For the strangeness neutral case (${\mu }_S=0$) at fixed ratio of electric charge to baryon number density ($\frac{n_Q}{n_B}=0.4$), which is appropriate for a comparison with heavy ion collisions, we present results for ${\kappa }_B{\sigma }_B^2$, $S_B{\sigma }_B^3/M_B$, ${\kappa }_B^H{\sigma }_B^4$ and $S_B^H{\sigma }_B^5/M_B$ on the crossover line for the chiral transition, $T_{pc}({\mu }_B)$. Continuum extrapolations for this pseudo-critical transition line have recently been reported by HotQCD up to baryon chemical potentials ${\mu }_B\simeq 300$ MeV [arXiv:1812.08235]. These cumulant ratios are of direct relevance for comparisons with corresponding ratios measured by STAR in the BES-I and II runs at beam energies $\sqrt{s_{NN}}\ge 20$ GeV. In particular, we point out that recent high statistics results on skewness and kurtosis of net-baryon number distributions obtained by STAR at $\sqrt{s_{NN}}=54.4$ GeV put strong constraints on freeze-out parameters and are consistent with predictions from thermal QCD.

Comments: 4 pages, 6 figures, Contribution to the Quark Matter 2019 Conference Proceedings