Radiative Energy Loss in a Temperature-Evolving QGP with Dynamical Constituents

TL;DR

This paper develops a temperature-evolving, first-order-in-opacity radiative energy-loss kernel for a finite-size QGP with dynamical constituents, enabling precise evaluations of parton and jet quenching under arbitrary $T(\tau)$ profiles. By employing local thermal equilibrium and HTL propagators, it derives a comprehensive spectrum dependent on $\chi(T)$, $\xi(T)$, and $\zeta(T)$, with a jet-cone constraint that unifies parton ($R=0$) and jet ($R>0$) energy loss. The formalism is extended to include magnetic screening and running coupling, yielding a generalized kernel suitable for QGP tomography within the DREENA framework. Qualitative results illustrate distinct path-length dependences for partons and jets, predicting stronger $L$-scaling for hadron energy loss than for jets, and offering concrete, testable implications for high-$p_T$ observables at RHIC and LHC energies.

Abstract

We present a theoretical formalism for calculating first-order-in-opacity radiative energy loss that incorporates the spatial and temporal temperature evolution of the quark-gluon plasma (QGP) in a finite-size QCD medium with dynamical (i.e., moving) constituents. The derived expressions allow for arbitrary temperature profiles, enabling detailed evaluations of radiative energy loss across different medium-evolution scenarios. Importantly, the resulting kernel applies to both single partons (R = 0) and jets (R > 0) via an out-of-cone selection, providing a unified starting point for precision QGP tomography.

Figures (12)

• Figure 1: Illustrative observables from the analytic energy--loss kernel. (a) Medium--induced gluon radiation spectrum $dN_g/dx$ for an initial parton energy $E_0 = 100~\mathrm{GeV}$, shown for a parton ($R = 0$, total radiative loss) and for jets with several radii $R$ (see legend). Angles are selected via $\theta \simeq k_\perp/(xE)$ so that the factor $\Theta(|\bm{k}|/(xE) - R)$ implements the out-of-cone loss. (b) Fractional energy loss $\Delta E/E$ as a function of path length $L$ at fixed $E_0 = 100~\mathrm{GeV}$; slopes shown correspond to log--log fits (see text). (c) Fractional energy loss $\Delta E/E$ as a function of initial energy $E$ at fixed $L = 4~\mathrm{fm}$. All panels are computed from Eq. (17) in a Bjorken 1D background Zigic:2018ovr, with initialization at $\tau_0 = 0.6~\mathrm{fm}$ and $T_0 \approx 500~\mathrm{MeV}$; $\Lambda_{\mathrm{QCD}} = 0.2~\mathrm{GeV}$, $n_f = 3$; $M = \mu_E/\sqrt{6}$, $m_g = \mu_E/\sqrt{2}$DG_TM; $\mu_E$ defined by Eq. (14) and $\mu_M/\mu_E = 0.6$Borsanyi:2015yka.
• Figure 2: Feynman diagram $M_{1,0,1, C}$, contributing to radiative energy loss at first order in opacity. The left (right) gray ellipse represents the source $J$, which produces a high-$p_\perp$ parton with momentum $p_2$ ($p_5$) at time $x_0$ ($x_5$). Large dashed circles denote effective HTL gluon propagators DG_TM. The cut gluon propagators with momenta $k$ and $q$ correspond to the radiated gluon and a collisional interaction with a parton in the medium, respectively. Specific time points are denoted by $x_i$. Calculations are performed in the light cone coordinate system, with conditions $x_1^+-x_0^+ < 2L$ and $x_5^+-x_4^+ < 2L$, ensuring that the collisional interaction occurs before the high-$p_\perp$ parton exits the QGP. The total path-length $L$ traversed by the high-$p_\perp$ parton represents the distance traveled from its creation point $(x_0, y_0)$ at $\tau_0 = 0$ until the condition $T(x_0 + \tau \cos\phi, y_0 + \tau \sin\phi) < T_c$ is satisfied.
• Figure 3: Feynman diagrams $M_{1,0,2,C}$, $M_{1,0,2,L}$, and $M_{1,0,2,R}$, labeled equivalently to Fig. \ref{['fig_M101C']}. The left, middle, and right panels depict three possible cuts (central, left, and right, respectively) of the same 2-HTL Feynman diagram, all contributing to the first-order in opacity radiative energy loss.
• Figure 4: Feynman diagrams $M_{1,0,3, C}$ and $M_{1,0,4, C}$, labeled in the same way as Fig. \ref{['fig_M101C']}.
• Figure 5: Feynman diagrams $M_{1,0,3, R}$ and $M_{1,0,4, L}$, labeled in the same way as Fig. \ref{['fig_M101C']}.