Collision-energy dependence of $p_t$ correlations in Au + Au collisions at energies available at the BNL Relativistic Heavy Ion Collider

We present two-particle $p_t$ correlations as a function of event centrality for Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=7.7$, 11.5, 14.5, 19.6, 27, 39, 62.4, and 200 GeV at the Relativistic Heavy Ion Collider using the STAR detector. These results are compared to previous measurements from CERES at the Super Proton Synchrotron and from ALICE at the Large Hadron Collider. The data are compared with UrQMD model calculations and with a model based on a Boltzmann-Langevin approach incorporating effects from thermalization. The relative dynamical correlations for Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=200$ GeV show a power-law dependence on the number of participant nucleons and agree with the results for Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76\mathrm{TeV}$ from ALICE. As the collision energy is lowered from $\sqrt{s_{\mathrm{NN}}}=200$ to 7.7 GeV, the centrality dependence of the relative dynamical correlations departs from the power-law behavior observed at the higher collision energies. In central collisions, the relative dynamical correlations increase with collision energy up to $\sqrt{s_{\mathrm{NN}}}=200$ GeV in contrast to previous measurements that showed little dependence on the collision energy.

Figure 1

The relative dynamical correlation $\sqrt{〈\mathrm{\Delta }{p}_{t,i},\mathrm{\Delta }{p}_{t,j}〉}/〈〈p_t〉〉$ as a function of $N_{\mathrm{part}}$ for eight collision energies and UrQMD calculations. Statistical and systematic errors are shown. The solid straight lines represent a power law given by $22.3\%/\sqrt{N_{\mathrm{part}}}$. Also shown are the ratios of the measured data to the power law and to UrQMD calculations.

Figure 2

UrQMD calculations for the relative dynamical correlation $\sqrt{〈\mathrm{\Delta }{p}_{t,i},\mathrm{\Delta }{p}_{t,j}〉}/〈〈p_t〉〉$ as a function of $N_{\mathrm{part}}$ for eight collision energies. Three cases are shown; UrQMD uncorrected, which has no efficiency corrections, UrQMD 80% eff., which uses a fixed efficiency of 80%, and UrQMD, which uses a tracking efficiency that depends on particle type, $p_t$, centrality, and collision energy.

Figure 3

Comparison of a model [23] incorporating a Boltzmann-Langevin approach to the calculation of thermalization effects for the relative dynamical correlation from Au+Au collisions at $\sqrt{s_{\mathrm{NN}}}=19.6$ and 200 GeV. Also shown are model comparisons to results from Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [36].

Figure 4

The relative dynamical correlation $\sqrt{〈\mathrm{\Delta }{p}_{t,i},\mathrm{\Delta }{p}_{t,j}〉}/〈〈p_t〉〉$ for $\sqrt{s_{\mathrm{NN}}}=7.7$ GeV and $200\mathrm{GeV}$ Au+Au collisions compared with similar results from Pb+Pb collisions at $\sqrt{s_{\mathrm{NN}}}=2.76$ TeV [36]. The dashed line represents a fit the to data at $\sqrt{s_{\mathrm{NN}}}=200$ GeV given by $22.3\%/\sqrt{N_{\mathrm{part}}}$. Statistical and systematic errors are shown.

Figure 5

The relative dynamical correlation $\sqrt{〈\mathrm{\Delta }{p}_{t,i},\mathrm{\Delta }{p}_{t,j}〉}/〈〈p_t〉〉$ for Au+Au collisions as a function of collision energy for the 0–5% centrality bin along with results for Pb+Pb from CERES [35] and results for Pb+Pb from ALICE [36] along with UrQMD calculations and results from Boltzmann-Langevin model calculations [23]. The solid line is drawn to guide the eye. Statistical and systematic errors are shown for the data points.