Net-baryon multiplicity distribution consistent with lattice QCD

We determine a net-baryon multiplicity distribution which reproduces all cumulants measured so far by lattice QCD. We present the dependence on the volume and temperature of this distribution. We find that for temperatures and volumes encountered in heavy-ion reactions, the multiplicity distribution is very close to the Skellam distribution, making the experimental determination of it rather challenging. We further provide estimates for the statistics required to measure cumulants of the net-baryon and net-proton distributions.

Figure 1

LQCD-based net-baryon multiplicty distribution at $T=155$ MeV compared with the Skellam distrubution at the same width for (a) $V=5280{\mathrm{fm}}^3$ and (b) $V=2100{\mathrm{fm}}^3$. For clarity, we only show a limited number of points for the Skellam distribution. The results are based on the cluster expansion model of Ref. [38] and are consistent with all net-baryon cumulants presently known from lattice QCD.

Figure 2

The ratios (model over Skellam) of the distributions presented in Fig. 1 for (a) broad range of $\mathcal{N}$ and (b) close to $\mathcal{N}\sim 0$.

Figure 3

LQCD-based net-baryon multiplicty distribution at $T=180$ MeV compared with the Skellam distrubution at the same width for (a) $V=5280{\mathrm{fm}}^3$ and (b) $V=2100{\mathrm{fm}}^3$. For clarity, we only show a limited number of points for the Skellam distribution. The results are based on the cluster expansion model of Ref. [38] and are consistent with all net-baryon cumulants presently known from lattice QCD.

Figure 4

The ratios (model over Skellam) of the distributions presented in Fig. 3 for (a) broad range of $\mathcal{N}$ and (b) close to $\mathcal{N}\sim 0$.

Figure 5

The ratios of the distributions presented in Figs. 1 and 3 with $\mathcal{N}$ rescaled by the respective widths, $\sigma$ [see Eq. (12)].

Figure 6

The ratios (model over Skellam) for the virial expansion model of Ref. [40].