Minijet thermalization and jet transport coefficients in QCD kinetic theory

TL;DR

This work uses leading-order QCD kinetic theory with isotropic HTL screening to study minijet thermalization in a gluonic Quark-Gluon Plasma and to relate full kinetic evolution to conventional jet transport coefficients. By linearizing the Boltzmann equation and employing a single-hit (opacity) expansion, the authors define transport observables such as $\hat q_\perp$, $\hat q_\parallel$, $\hat q_L$, $\eta_D$, and $\hat\Gamma_{i_0}$, and compare them to full kinetic-theory simulations. They show that medium recoil and radiative processes contribute non-negligibly to several coefficients, reconcile these with the kinetic evolution, and reveal that the minijet thermalization time scales with $\hat q_\perp$ through parametric relations such as $t_{\mathrm{th}} \sim \frac{1}{\alpha_s}\sqrt{E/\hat q_\perp}$ (or equivalently $t_{\mathrm{th}}^E \sim \frac{1}{T}\frac{\sqrt{E/E_0}}{\hat q_\perp/T^3}$). The results provide a practical link between jet quenching observables and the microscopic dynamics, yielding a phenomenological estimate for heavy-ion collisions and highlighting universal scaling when time is rescaled by $\hat q_\perp$. Overall, the study clarifies the limitations of conventional transport coefficients and demonstrates how they emerge from the full kinetic evolution, with implications for interpreting jet quenching and the onset of thermalization in QGP.

Abstract

We apply weakly coupled QCD kinetic theory to investigate the thermalization of high-momentum on-shell partons (minijets) in a Quark-Gluon Plasma (QGP). Our approach incorporates isotropic hard thermal loop screening to model soft quark and gluon exchanges, allowing us to verify consistency with established analytic results of jet transport coefficients. We perform kinetic simulations of minijets propagating through a thermal gluon plasma, incorporating both collinear radiation and elastic scatterings. The resulting evolution is compared to predictions from jet transport coefficients, including the longitudinal and transverse jet-quenching parameters $\hat{q}$, energy loss, and the drag coefficient. We find that standard definitions of jet transport coefficients neglect the contributions from recoiling medium particles. Including these contributions restores consistency with the kinetic evolution. Finally, we show that the minijet thermalization time scales remarkably well with $\hat{q}$ and we produce a phenomenological estimate of the minijet quenching time in heavy-ion collisions.

Figures (11)

• Figure 1: Transverse momentum broadening coefficient $\hat{q}_{\perp}$ for initial minijet energy $E=50T$ and different couplings $\lambda$ as a function of lower momentum cutoff $p>\Lambda_\text{min}$. Bands indicate statistical uncertainty of a single-step evolution of a gaussian perturbation in EKT, while points show the direct Monte-Carlo evaluation of a single-hit transport integrals, see \ref{['eq:LB_qhat', 'eq:qhat_cutoff']}. Dashed lines show the traditional cutoff independent definition of $\hat{q}_\perp$, \ref{['eq:qhat_stand']}.
• Figure 2: Longitudinal momentum broadening coefficient $\hat{q}_\parallel$ for initial minijet energy $E=50T$ and different couplings $\lambda$ as a function of lower momentum cutoff $p>\Lambda_\text{min}$. Bands indicate statistical uncertainty of a single-step evolution of a gaussian perturbation in EKT, while points show the direct Monte-Carlo evaluation of a single-hit transport integrals, see \ref{['eq:LB_qhat_parallel']}. The lower panel shows the relative contribution of inelastic processes.
• Figure 3: Longitudinal momentum broadening coefficient $\hat{q}_L$ for initial minijet energy $E=50T$ and different couplings $\lambda$ as a function of lower momentum cutoff $p>\Lambda_\text{min}$. Bands indicate statistical uncertainty of a single-step evolution of a gaussian perturbation in EKT, while points show the direct Monte-Carlo evaluation of a single-hit transport integrals, see \ref{['eq:LB_qhat_L']}. The lower panel shows the relative contribution of inelastic processes.
• Figure 4: Longitudinal momentum drag coefficient $\eta_D$ for initial minijet energy $E=50T$ and different couplings $\lambda$ as a function of lower momentum cutoff $p>\Lambda_\text{min}$. Bands indicate statistical uncertainty of a single-step evolution of a gaussian perturbation in EKT, while points show the direct Monte-Carlo evaluation of a single-hit transport integrals, see \ref{['eq:LB_drag']}. The lower panel shows the relative contribution of inelastic processes.
• Figure 5: Momentum broadening $\langle \bm{p}_{\perp}^2 \rangle$ and $\langle \bm{p}_{\parallel}^2 \rangle$ as a function of time for different couplings $\lambda$, at fixed jet energy $E=50T$. We scale the time with transverse and longitudinal broadening coefficients $\hat{q}_{\perp}$ and $\hat{q}_{L}$, respectively. The gray lines show the linear slope. The inset shows the unscaled evolution as a function of $tT$. The vertical black line indicates the time where the minijet is within $10\%$ deviation from the equilibrium value.