Early-Time Dynamics of Heavy-Ion Collisions through Energy Correlators: celestial blocks and the spacetime structure of out-of-equilibrium QCD matter

TL;DR

This work addresses how to access the spacetime structure of far-from-equilibrium QCD matter formed in heavy-ion collisions by analyzing azimuthally differential energy correlators inside mid-rapidity jets. It develops a celestial-block (OPE) framework for the energy-energy correlator (EEC) in the presence of vector perturbations, and introduces the clover EEC to isolate anisotropic, early-time medium effects. Using analytical models based on Glasma and effective kinetic theory, complemented by JEWEL Monte-Carlo simulations with anisotropic backgrounds, it demonstrates that directional information about the initial state can leave measurable imprints in the EEC, potentially up to the ~10% level for sizable anisotropies. The results offer a principled observable to probe the pre-hydrodynamic spacetime structure of QCD matter and point toward extensions to higher-point correlators and generalized detectors for richer tomography of the early-time medium.

Abstract

Ultrarelativistic heavy-ion collisions provide a unique window into far-from-equilibrium states of QCD matter. The initial stages of these events are characterized by highly anisotropic, nonthermal dynamics that precede hydrodynamization, yet they remain largely inaccessible through conventional soft observables. In this work, we show that the substructure of mid-rapidity jets provides direct sensitivity to the spacetime structure of this early, anisotropic phase. Using classical Yang-Mills simulations and effective kinetic theory to model the early-time evolution of the jet quenching parameter, we compute the azimuthally differential energy-energy correlator within the BDMPS-Z framework. By decomposing the result into celestial blocks, we isolate the coefficients that encode the anisotropic geometry and dynamics of the underlying medium. We identify an observable that couples directly to spatial anisotropies in the out-of-equilibrium QCD matter and also discuss the impact of medium response on its behavior. We further extend our study to mid-rapidity jets generated with the JEWEL Monte-Carlo, adjusted to incorporate an anisotropic medium background, and find qualitative agreement with the analytical expectations. Finally, we discuss how higher-point energy correlators and generalized energy-flow operators can enhance the sensitivity to the microscopic structure of far-from-equilibrium QCD matter.

Figures (5)

• Figure 1: Top: Illustration of a typical mid-rapidity jet configuration considered in this work. Elongated color tubes represent the initial Glasma configuration which dominate the first instances after the collision, and are described within classical Yang-Mills theory. In blue we show one possible particle pair contributing to the EEC observable. The elongated jet profile along the beam indicates the expected deformation in the energy distribution inside the jet. Bottom: Particle based in-jet EEC. Here we indicate the relative angle $\theta_{ij}$, between a particle pair with respective energies $E_i$, $E_j$. The azimuthal angle $\Psi$ is defined, for each pair, with respect to the beamline. The jet radius is $R$ and the orange circle denotes its axis.
• Figure 2: Scalar part of the (quark) jet quenching parameter $\hat{q} = \hat{q}_y + \hat{q}_z$ (top panel) and anisotropy ratio $\hat{q}_y/\hat{q}_z$ (bottom panel) as a function of light-cone time $\tau$. The series of curves in the transition region $\tau \in (0.04, 0.3)$ fm/c corresponds to a family of Hermite polynomials depending on the parameter $\zeta \in (0,1.5)$. For $\hat{q}$ we take the smoothest of these ($\zeta=1$).
• Figure 3: Top: Ratio between the $\Psi$ integrated medium contribution to the energy-energy correlator (EEC$_ {\rm med}$) and the vacuum EEC$_{\rm vac}$, for the $g\rightarrow c\bar{c}$ splitting . Bottom: Ratio between the clover EEC and the $\chi-$averaged absolute value of EEC$_{\rm med}$ in the range $\chi\in(0.01,0.3)$, for the $g\rightarrow c\bar{c}$ splitting . The denominator is divided by $4$ to appropriately normalize it to half an hemisphere. We plot these quantities for initial time $\tau_0 \simeq 0.004$ fm/c and for two disparately different medium sizes -- $\tau_{\rm EKT} = 0.3$ fm/c and $L = 3$ fm/c.
• Figure 4: Top: Azimuthal distribution of pairs of jet constituents for vacuum Jewel events. The three distributions correspond to different projections of the constituent momenta and of the beamline in the plane transverse to the jet axis, defining different measures of azimuthal angle $\Psi$. Bottom: Ratio between the clover energy-energy correlator (EEC$^{\Delta}$) and the $\Psi$ integrated energy-energy correlator (EEC) inside jets reconstructed from Jewel events. The denominator is divided by $4$ to appropriately normalize it to half an hemisphere. The shaded band around each histogram corresponds to the statistical uncertainty.
• Figure 5: Illustration of the E3C as a way to map the properties of non-trivial matter states. Here we depict that the three detectors can be rotated around ($\Psi=0 \to \pi/2$), while fixing the the length of the triangle side $R_L$. Then varying the position of the central point between equilateral ($\phi\to \pi/2$) and collapsed ($\phi\to 0$) configurations one can create a picture of the underlying matter state; see also Caron-Huot:2022lff. Note that the rotation in $\Psi$ is only relevant when the bulk is not isotropic.