Bjorken Initial Energy Density and Viscous Longitudinal Hydrodynamic Evolution in Xe-Xe Collisions

TL;DR

This study uses the Bjorken framework to quantify the initial energy density ε_B in Xe–Xe collisions at √s_NN=5.44 TeV, employing a generalized elliptic overlap geometry and two formation-time scenarios (fixed and centrality-dependent). It then propagates ε_B through boost-invariant longitudinal hydrodynamics, comparing ideal and first-order viscous evolution to assess energy-density dilution, entropy production, and QGP lifetime. The results show that viscous effects slow longitudinal expansion and enhance early-time entropy production, with larger impacts in peripheral collisions, while a centrality-dependent τ0 reduces these viscous effects by delaying hydrodynamic onset. A cross-system comparison with Pb–Pb at 5.02 TeV reveals that the longitudinal evolution is primarily governed by the initial energy density scale; central collisions yield similar evolutions, while peripheral collisions diverge due to system-size and geometry. Overall, the work highlights the critical role of initial-state geometry and formation time in shaping QGP dynamics in small- and large-system heavy-ion collisions, providing benchmarks for future viscous hydrodynamic modeling.

Abstract

We present a systematic study of the Bjorken initial energy density in Xe-Xe collisions at $\sqrt{s_{NN}} = 5.44$ TeV, estimated using charged-particle multiplicity data and a generalized transverse overlap geometry applicable beyond the most central collisions. The dependence of the extracted energy density is examined by adopting both a constant formation time and a centrality-dependent formation time derived from Pb-Pb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. Corresponding Bjorken energy density estimates for Pb-Pb collisions are also presented for comparison. Taking the Bjorken energy density and formation time as initial conditions, the subsequent longitudinal evolution of the quark-gluon plasma (QGP) formed in these collisions is studied. Both ideal and first-order viscous boost-invariant hydrodynamics are employed to assess the influence of dissipation. We observe that viscous effects slow the longitudinal expansion and lead to entropy production dominated by early-time dynamics. The lifetime of the QGP is observed to increase with centrality and is substantially enhanced by viscous effects. These effects are highly sensitive to the choice of formation time, particularly in peripheral collisions. A comparative analysis of Xe-Xe and Pb-Pb collisions demonstrates that the longitudinal evolution is primarily controlled by the initial energy density scale set by the Bjorken prescription. Consequently, when this scale is comparable, both systems exhibit nearly identical evolution patterns, while appreciable distinctions emerge in peripheral collisions due to system-size and geometric effects.

Figures (12)

• Figure 1: Elliptic transverse overlap geometry formed in a non-central collision between two nuclei of radii $R$ and $r$ at impact parameter $b$.
• Figure 2: Generalized elliptic overlap area A$_{\text{overlap}}$ as a function of the number of participating nucleons N$_{\rm part}$ for Xe-Xe collisions at $\sqrt{s_{_{NN}}}$ = 5.44 TeV and Pb-Pb collisions at $\sqrt{s_{_{NN}}}$ = 5.02 TeV.
• Figure 3: Bjorken initial energy density $\varepsilon_B$ as a function of N$_{\text{part}}$ for Xe-Xe and Pb-Pb collisions under (a) fixed formation time $\tau_0$ and (b) centrality dependent $\tau_0$ scenarios.
• Figure 4: Time evolution of energy density $\varepsilon(\tau)$ for different centrality classes in Xe-Xe collisions at $\sqrt{s_{_{NN}}}$ = 5.44 TeV for ideal and viscous hydrodynamics under fixed and varying $\tau_0$ scenarios.
• Figure 5: Time evolution of shear viscosity $\eta(\tau)$ for different centrality classes in Xe-Xe collisions for (a) fixed $\tau_0$ and (b) centrality dependent $\tau_0$ scenarios.