Cumulants of net-proton, net-kaon, and net-charge multiplicity distributions in Au + Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV within the UrQMD model

Fluctuations of conserved quantities are sensitive observables to probe the signature of QCD phase transition and critical point in heavy-ion collisions. With the UrQMD model, we have studied the centrality and energy dependence of various order cumulants and cumulant ratios (up to fourth order) of net-proton, net-charge, and net-kaon multiplicity distributions in Au+Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, 200 GeV. The model results show that the production mechanism of the particles and antiparticles has significant impact on the cumulants of net-particles multiplicity distributions and shows strong energy dependence. We also made comparisons between model calculations and experimental data measured in the first phase of the beam energy scan (BES) program by the STAR experiment at the BNL Relativistic Heavy Ion Collider. The comparisons indicate that the baryon conservation effect strongly suppresses the cumulants of net-proton distributions at low energies and the nonmonotonic energy dependence for the net-proton $\kappa {\sigma }^2$ at the most central Au+Au collisions measured by the STAR experiment cannot be described by the UrQMD model. Since there has been no physics of QCD phase transition and QCD critical point implemented in the UrQMD, the model results provide us baselines and qualitative estimates about the noncritical background contributions to the fluctuations observables in heavy-ion collisions.

Figure 1

The $dN/dy$ distributions of net-proton, proton, antiproton, net-kaon, $K^{+}$, $K^{-}$, and $dN/d\eta$ distributions of net-charge, positive, and negative charge multiplicity in Au+Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5,19.6, 27, 39, 62.4, and 200 GeV for most central collisions (0–5%). The vertical black dashed lines in the figure represent the beam rapidity for each energy.

Figure 2

Event-by-event distributions of net-proton, net-charge, and net-kaon multiplicity distributions for Au+Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV for three centrality bins (0–5%, 30–40 %, 70–80 %).

Figure 3

Centrality dependence of cumulants ($C_1\sim C_4$) of net-proton, net-kaon, and net-charge multiplicity distributions for Au+Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV. The dashed lines represent the Poisson expectation.

Figure 4

Energy dependence of cumulants of proton, antiproton, and net-proton multiplicity distribution for Au+Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV for most central (0–5%). The lines represent the Poisson expectations.

Figure 5

Energy dependence of cumulants of kaon, antikaon, and net-kaon multiplicity distribution for Au+Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV for most central (0–5%). The lines represent the Poisson expectations.

Figure 6

Energy dependence of various cumulants of positive charge, negative charge, and net-charge multiplicity distribution for Au+Au collisions at $\sqrt{s_{NN}}=7.7$, 11.5, 19.6, 27, 39, 62.4, and 200 GeV for most central (0–5%). The lines represent the Poisson expectations.

Figure 7

Centrality dependence of the cumulant ratios ($S\sigma$, $\kappa {\sigma }^2$) of net-proton multiplicity distributions for Au+Au collisions at $\sqrt{s_{NN}}=7.7$ to 200 GeV. The solid markers represent the results from the STAR measurement, the open markers represent results from the UrQMD calculation. The dashed lines denote the Poisson expectations for the STAR data.

Figure 8

Centrality dependence of the cumulant ratios ($S\sigma$, $\kappa {\sigma }^2$) of net-kaon multiplicity distributions for Au+Au collision at $\sqrt{s_{NN}}=7.7$ to 200 GeV. The open markers represent results from the UrQMD calculation.

Figure 9

Centrality dependence of the cumulant ratios ($S\sigma$, $\kappa {\sigma }^2$) of net-charge multiplicity distributions for Au+Au collision at $\sqrt{s_{NN}}=7.7$ to 200 GeV. The solid markers represent the results from the STAR measurement, the open markers stand for the results from the UrQMD calculation. The dashed lines denote the Poisson expectations for the STAR data.

Figure 10

Energy dependence of cumulant ratios ($S\sigma$, $\kappa {\sigma }^2$) of net-proton, net-charge, and net-kaon multiplicity distributions for the Au+Au collision at $\sqrt{s_{NN}}=7.7$ to 200 GeV. The solid markers represent the results from the STAR measurement, the open markers represent results from the UrQMD calculation. The dashed lines denote the Poisson expectations for the STAR data.