Hydrodynamic Attractors, Initial State Energy, and Particle Production in Relativistic Nuclear Collisions

We exploit the concept of hydrodynamic attractors to establish a macroscopic description of the early time out-of-equilibrium dynamics of high energy heavy-ion collisions. One direct consequence is a general relation between the initial state energy and the produced particle multiplicities measured in experiments. When combined with an ab initio model of energy deposition, the entropy production during the preequilibrium phase naturally explains the universal centrality dependence of the measured charged particle yields in nucleus-nucleus collisions. Further, we estimate the energy density of the far-from-equilibrium initial state and discuss how our results can be used to constrain nonequilibrium properties of the quark-gluon plasma.

Figure 1

Hydrodynamic attractor for preequilibrium evolution of the energy density obtained from QCD and Yang Mills (YM) kinetic theory [26, 27, 28, 29], AdS/CFT [13, 14, 15], and Boltzmann RTA [16, 17, 18, 19, 20]. Solid lines show the asymptotic behavior of the attractor curves given by Eq. (4).

Figure 2

The effect of preequilibrium dynamics on the centrality dependence of the charged-particle multiplicity, $d{N}_{\mathrm{ch}}/d\eta$, can be appreciated by comparing the theoretical estimate on the gluon number (blue dashed line), given by Eq. (11), to that on the charged-particle multiplicity after equilibration (red solid line), given by Eq. (12). The green dotted-dashed line includes, as well, fluctuations in the initial state energy within a Glauber Monte Carlo approach. Experimental data points are shown for different collision systems: Xe-Xe [52], Pb-Pb [53], U-U [54], Au-Au [55], and Cu-Cu [55] collisions. All curves are normalized to present the same value of multiplicity as ALICE Pb-Pb data in the 10%–20% centrality bin. The bottom panel shows the ratio between 2.76 TeV Pb-Pb data and the theory curves.

Figure 3

Estimate of the initial energy per unit space time rapidity $d{E}_0/d{\eta }_s$ (shaded area) determined from the measured particle multiplicity in $\sqrt{s_{\mathrm{NN}}}=200\mathrm{GeV}$ Au-Au (left) and $\sqrt{s_{\mathrm{NN}}}=2.76\mathrm{TeV}$ Pb-Pb collisions (right). Bands correspond to variations of $\eta /s=0.08–0.24$ and $C_{\infty }=0.80–1.15$ while keeping all other parameters fixed as in Eq. (14), and similarly, the dashed lines correspond to specific values of $\eta /s=0.08$, 0.16. For comparison, we show data points for the experimentally measured final state energy $d{E}_{\text{final}}/dy$ [33, 54], which is smaller due to the work performed against the longitudinal expansion.