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

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