(3+1)D event-by-event pre-equilibrium dynamics in heavy-ion collisions

TL;DR

This work introduces KøMPøST-3D, a comprehensive framework for (3+1)D pre-equilibrium dynamics in heavy-ion collisions that extends non-equilibrium Green's function-based propagation from the transverse plane to full three-dimensional space. It combines a kinetic-theory-based pre-equilibrium stage with a 3D hydrodynamic evolution (CLVisc) and a hadronic afterburner (SMASH), using a McDipper-derived initial state and a Gaussian-averaged background around each space-time point to propagate perturbations via 3D response functions. The study demonstrates a smooth transition from pre-equilibrium to hydrodynamics, with hydrodynamization occurring across much of the fireball and only weak sensitivity of final observables to the hydro starting time, thereby reducing theoretical uncertainties in early-time modeling. The framework paves the way for more accurate extraction of QCD transport coefficients by exploiting longitudinal structure in observables and motivates future enhancements to include full perturbations and QCD kinetic theory inputs across a wider range of collision systems and energies.

Abstract

So far a major source of uncertainty in the study of heavy-ion collisions arises from the early time dynamics which includes initial state and pre-equilibrium dynamics. The state-of-the-art framework, KoMPoST, employs non-equilibrium Green's functions to propagate the initial energy-momentum tensor to the hydrodynamic phase, yet currently only treats transverse plane dynamics under boost-invariant conditions. In this work, we extend KoMPoST to include non-boost-invariant responses to initial conditions, essential for accurately capturing the longitudinal structures observed in heavy-ion collisions. Non-boost-invariant fluctuations on top of a homogeneous background are evolved using (3+1)D response functions calculated in kinetic theory. To assess kinetic theory's transition towards hydrodynamic evolution, we systematically compare the out-of-equilibrium shear-stress tensor from KoMPoST-3D with estimates based on Navier-Stokes hydrodynamics. Subsequently, a comprehensive (3+1)D framework, McDIPPER+KoMPoST-3D+CLVisc+SMASH, is utilized to simulate the complete spacetime evolution of heavy-ion collisions. The sensitivity of key observables, including longitudinal structure of anisotropic flow, to variations in the hydrodynamic initialization time is thoroughly investigated.

Figures (17)

• Figure 1: Evolution of the energy response ($G_s^s(|\mathbf{k_T}|\Delta\tau, k_\eta)$) and longitudinal momentum response ($G_s^{s,\eta}(|\mathbf{k_T}|\Delta\tau, k_\eta)$) to an initial energy perturbation as a function of $|\mathbf{k_T}|\Delta\tau$ and $k_\eta$. Different panels correspond to different points in time. The color indicates the magnitude of respective response functions.
• Figure 2: Evolution of the energy response ($G_s^s(|\mathbf{r}|/\Delta\tau, \eta)$) and longitudinal momentum response ($G_s^{s,\eta}(|\mathbf{r}|/\Delta\tau, \eta)$) to an initial energy perturbation as a function of $|\mathbf{r}|/\Delta\tau$ and $\eta$. Different panels correspond to different points in time. The color indicates the magnitude of respective response functions.
• Figure 3: Examination of the constitutive relations, Eqs.(\ref{['eq:const1']}) and (\ref{['eq:const2']}), at scaled times $\tilde{w}\approx 2$ and $5$. The response functions $\tilde{G}_s^{t,\delta}$ (upper panels) and $\tilde{G}_s^{v,\eta}$ (lower panels) from RTA dynamics (denoted as RTA) are compared with those reconstructed from $\tilde{G}_s^s$, $\tilde{G}_s^v$ and $\tilde{G}_s^{s,\eta}$, $\tilde{G}_s^v$ according to the constitutive relations at various $|\mathbf{k_T}|\Delta\tau$ or $k_\eta$.
• Figure 4: Comparison of the energy response functions in QCD and in RTA for $k_\eta=0$ (left) and $k_T=0$ (right) at three selected times.
• Figure 5: Three-dimensional energy density distribution $\tau T^{\tau\tau}(x,y,\eta_s)$ for the McDipper initial condition, shown before the kinetic-theory pre-equilibrium evolution at $\tau_{\mathrm{EKT}} = 0.01~\mathrm{fm}$ (upper) and at the hydrodynamic initialization time $\tau_{\mathrm{hydro}} = 1.0~\mathrm{fm}$ (lower). Arrows in the lower panel indicate the direction of the energy-flow components $(T^{\tau x}, T^{\tau y}, \tau T^{\tau\eta})$.