Perturbative and non-perturbative properties of heavy quark transport in a thermal QCD medium

TL;DR

The paper addresses heavy-quark transport in a thermal QCD medium across perturbative and near-critical regimes by extending the Soft-Hard Factorized Model (SHFM) with a temperature-dependent background field that encodes semi-QGP dynamics. The framework combines soft HTL-resummed calculations with hard perturbative scatterings and incorporates a Polyakov-loop–type background to modify parton occupancies while leaving the kinematics intact, enabling a unified description from $T\gg T_c$ down to $T\lesssim 2-3T_c$. Key findings include a systematic suppression of heavy-quark energy loss $-\frac{dE}{dz}$ and momentum diffusion coefficients $\kappa_T$, $\kappa_L$ near the critical region, driven by reduced color charge screening and modified distribution functions, with the suppression strongest near $T_c$ and diminishing at higher $T$. The results offer a cohesive theoretical bridge between perturbative and non-perturbative QCD dynamics for heavy-flavor probes and provide input for phenomenological Langevin transport frameworks, while noting current limitations such as the omission of fermionic contributions and radiative energy loss.

Abstract

We investigate the perturbative and non-perturbative aspects of heavy quark transport in a thermal QCD medium. Based on the Soft-Hard Factorized Model (SHFM), we extend the original perturbative framework to the near-critical temperature region, where non-perturbative effects become significant. The transition behavior of the semi-Quark-Gluon-Plasma (semi-QGP) is described via a temperature-dependent background field incorporated in the background field effective theory. By implementing this approach, we quantitatively evaluate the collisional energy loss and momentum diffusion coefficients of charm and bottom quarks as functions of the incoming energy and medium temperature. Our results show a distinct suppression of both the energy loss and the diffusion coefficients relative to conventional perturbative estimates, especially near the critical temperature. This suppression originates from the emergence of a temperature-dependent color background field, which effectively reduces the color charge screening of the medium. These findings provide important theoretical insight into the phenomenology of heavy-flavor probes in QGP, offering a unified theoretical framework applicable across both high- and low-momentum regimes.

Figures (7)

• Figure 1: Tree-level Feynman diagrams for the scattering processes $Qg\to Qg$ in $t$ (panel-a), $s$ (panel-b) and $u$ (panel-c) channels in vacuum.
• Figure 2: (Color online) Left (a): comparison of the temperature-dependence of the non-perturbative suppression of the bosonic distribution, $n_{Avg,B}^{\mathcal{Q}\ne0}/n_{B}^{\mathcal{Q}=0}$, for three fixed momentum values: $p=0.1~{\rm GeV}$ (solid black curve), $p=0.3~{\rm GeV}$ (dashed red curve) and $p=1.0~{\rm GeV}$ (long-dashed blue curve). Right (b): same as panel-a but for $n_{Avg,B}^{\mathcal{Q}\ne0}/n_{B}^{\mathcal{Q}=0}$ as a function of energy for fixed temperatures.
• Figure 3: (Color online) Left (a): comparison of the energy loss $-dE/dz$ as a function of temperature, for charm quark with $\alpha_{s}=0.3$ and $-t^{\ast}=4m_{D}^{2}$ at a given energy $E=10~{\rm GeV}$, obtained with non-vanishing [$\mathcal{Q}\ne 0$; thick curves; Eqs. (\ref{['eq:dEdz_Soft_BFET']}), (\ref{['eq:dEdz_BFET_Hard_t']}) and (\ref{['eq:dEdz_BFET_Hard_su']})] and vanishing background [$\mathcal{Q}=0$; thin curves; Eqs. (\ref{['eq:dEdz_Soft_Perturbative']}), (\ref{['eq:dEdz_Hard_t_Perturbative']}) and (\ref{['eq:dEdz_Hard_su_Perturbative']})]. The contributions from various channels are displayed separately as curves with different styles. See the legend and text for details. Right (b): further comparison of $dE/dz$ between $\mathcal{Q}\ne 0$ and $\mathcal{Q}=0$.
• Figure 4: Same as Fig. \ref{['fig:dEdz_CmpBkg_vsT']} but as a function of heavy-quark energy at fixed temperature $T=0.3~{\rm GeV}$.
• Figure 5: (Color online) The ratio $R_{TL}=\kappa_{T}/\kappa_{L}$ of the transverse to longitudinal momentum diffusion coefficients as a function of the heavy-quark velocity $v$. The result for the background-modified case ($\mathcal{Q}\ne0$) are shown as solid red curve, while that including the background-free effects ($\mathcal{Q}=0$) is shown as dashed black curve. The result from the AdS/CFT Gubser:2006bzGubser:2006nzCasalderrey-Solana:2007ahi is shown as long-dashed pink curve for comparison.