UrQMD Simulations of Higher-order Cumulants in Au+Au Collisions at High Baryon Density

TL;DR

The paper tackles the search for the QCD critical point in the high baryon density region by examining high-order cumulants of conserved charges, particularly protons and net-protons, in Au+Au collisions. It employs the hadronic transport model UrQMD to generate a dynamical non-critical baseline across $\sqrt{s_{NN}} = 3.0$--$19.6$ GeV, analyzing cumulants up to the $4^{th}$ order and their dependence on beam energy, centrality, and rapidity acceptance while quantifying the impact of initial volume fluctuations. Key findings show that initial volume fluctuations and baryon-number conservation strongly influence $C_4/C_2$ at low energies and large acceptances, with a transition to positive values at higher energies; FXT data are reasonably described by UrQMD at the low-energy end, constraining the possible CP location to higher energies. The work provides essential dynamical baselines for BES and CBM programs, aiding in the interpretation of potential CP signatures by separating non-critical backgrounds from critical phenomena.

Abstract

High moments of conserved quantities such as net-baryon, net-electric charge, and net-strangeness in heavy-ion collisions are sensitive to fluctuations caused by the QCD critical point (CP). The event-by-event analysis of high moments of the conserved charges has been widely used in experiments to search for the CP, especially in the RHIC-STAR experiment. In order to establish a {\it dynamical non-critical base line}, especially at the high baryon density region, we have performed a systematic analysis of the proton multiplicity distributions from Au+Au collisions at 3 $\leq$ $\sqrt{s_{NN}}$ $\leq$ 9.2 GeV collisions. The results on beam energy, centrality and rapidity width dependence of proton (factorial) cumulants, up to the $4^{th}$ order, are extracted from the calculations of the hadronic transport model UrQMD. In addition, the effects of initial volume fluctuation is also discussed. These results will be important when we do physics analysis the RHIC beam energy scan (BES) data, especially for the fixed-target data and experimental data from future CBM experiment at FAIR.

Figures (6)

• Figure 1: Reference multiplicity distribution in Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0, 3.2, 3.5, 3.9, 4.5, 4.9, 7.7 and 9.2 GeV calculated by the UrQMD model. The regions with black and blue shading indicate the most central 0--5% collision.
• Figure 2: Transverse momentum ($p_{\rm T }$) versus proton rapidity (y) in Au+Au minimum bias collisions at $\sqrt{s_{NN}}$ = 3.0 and 4.9 GeV calculated by the UrQMD model. Protons from rapidity window $|y| < 0.5$ (red-dashed box) and $-0.5 < y < 0.0$ (black box) are used in the analysis for the collider and FXT mode, respectively.
• Figure 3: Centrality dependence of the proton cumulant ratio, $C_{4}/C_{2}$, in Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0 -- 9.2 GeV calculated by the UrQMD model. Solid black circles and red open squares represent results for proton in the rapidity acceptance -0.5 $<$ y $<$ 0 and $\left|y\right|$$<$ 0.5, respectively. Blue solid crosses and open crosses are calculations with a cut on impact parameter $b\leq$ 3 fm, for -0.5 $<$ y $<$ 0 and $\left|y\right|$$<$ 0.5, respectively. For these calculations, the $p_{\rm T}$ acceptance of protons and anti-protons is $0.4 < p_{T} < 2.0$ GeV/$c$.
• Figure 4: Left panel: Correlation distribution of reference multiplicity vs. $N_{part}$ in Au+Au collisions at $\sqrt{s_{NN}}$ = 3.0 GeV calculated by the UrQMD model. The vertical black dashed line indicate the 0--5% central collisions selected by reference multiplicity. Right panel: Correlation distribution of b vs. $N_{part}$. The vertical red dashed line indicate a cut on b $\leq$ 3 fm.
• Figure 5: Collision energy dependence of proton cumulant ratios ($C_{2}/C_{1}$, $C_{3}/C_{2}$ and $C_{4}/C_{2}$) and factorial cumulant ratios ($\kappa_{2}/\kappa_{1}$, $\kappa_{3}/\kappa_{1}$ and $\kappa_{4}/\kappa_{1}$) in 0--5% central Au+Au collisions from the UrQMD model. Black solid circles and red open squares represent proton results in the rapidity acceptance -0.5 $<$ y $<$ 0 and $\left|y\right|$$<$ 0.5, respectively. Blue solid crosses and open crosses are calculations with a cut on b $\leq$ 3 fm, for -0.5 $<$ y $<$ 0 and $\left|y\right|$$<$ 0.5, respectively.