Higher order cumulants of net baryon-number distributions at non-zero $μ_B$

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 $μ_B$. For the strangeness neutral case ($μ_S=0$) 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 $κ_B σ_B^2$, $S_B σ_B^3/M_B$, $κ^{H}_{B}σ_{B}^4$ and $S^{H}_{B}σ^5_{B}/M_{B}$ on the crossover line for the chiral transition, $T_{pc}(μ_B)$. Continuum extrapolations for this pseudo-critical transition line have recently been reported by HotQCD up to baryon chemical potentials $μ_B\simeq 300$ 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.

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