Impact of momentum-dependent drag coefficient on energy loss of charm and bottom quarks in QGP

TL;DR

This work addresses how heavy-quark momentum in a QGP shapes energy loss and the resulting $R_{AA}$ by introducing a momentum-dependent drag coefficient derived from a linear expansion of collisional and radiative energy-loss terms. The authors implement a Fokker–Planck transport in a Bjorken-expanding QGP, with a temperature-dependent coupling and HTL/DGLV energy-loss inputs, to evolve heavy-quark distributions and compare to ALICE and ATLAS data at $\sqrt{S_{NN}}=5.02$ TeV. They find that including linear momentum terms increases the drag at high $p_T$, improving agreement with data, and they quantify that radiative losses are more relevant for charm while collisional losses dominate bottom in the accessible momentum range. The study provides a transparent baseline for momentum-dependent transport and motivates future work with explicit hadronization and fully dynamic 3+1D hydrodynamics.

Abstract

This paper investigates how the momentum of heavy particles affects their interaction rate, and the resulting drag coefficient in a quark-gluon plasma. To account for this momentum dependence, the drag coefficient is derived by expressing the energy loss coefficients as polynomial expansions of momentum ($p$). This approach allows for a more precise investigation of momentum dependence of drag coefficient by incorporating the linear terms of these expansions. Additionally, the influence of particle's momentum on radiative and collisional energy loss is more clearly determined. The study focuses on calculation of the nuclear modification factor ($R_{AA}$) of charm and bottom quarks in Pb-Pb collisions at $\sqrt{S_{NN}} = 5.02 \: TeV$. The initial distribution functions have been evolved numerically based on the Fokker-Planck equation. The results are compared with the latest data from ALICE and ATLAS experiments, conducted in 2021 and 2022.

Figures (5)

• Figure 1: Drag coefficient as a function of $P_T$, calculated by constant rate (solid line) and momentum-dependent rate (dashed line) at T=250 MeV.
• Figure 2: Nuclear modification factor of charm quark in the (20–40%) centrality Pb-Pb collisions at $\sqrt{S_{NN}}=5.02$ TeV compared with ALICE 2021 data at forward rapidity ($2.5<y< 4$) ALICE:2020sjb. The solid line represents the results obtained from the momentum-dependent coefficients, and dashed line corresponds to the drag coefficient with constant coefficients.
• Figure 3: Nuclear modification factor of charm quark in the (30–50%) centrality Pb-Pb collisions at $\sqrt{S_{NN}}=5.02$ TeV compared with ALICE 2022 data at mid-rapidity ($|y|<0.5$) ALICE:2021rxa. The solid line represents the results obtained from the momentum-dependent coefficients, while the dashed line corresponds to the drag coefficient with constant coefficients.
• Figure 4: Nuclear modification factor of bottom quark in the (40–60%) centrality Pb-Pb collisions at $\sqrt{S_{NN}}=5.02$ TeV (solid line) is compared with ATLAS collaboration data ATLAS:2021xtw and theoretical predictions from Shu-Qing Li et al. Li:2024wqq (dashed line).
• Figure 5: Nuclear modification factor of bottom quark in the (40–60%) centrality Pb-Pb collisions at $\sqrt{S_{NN}}=5.02$ TeV compared with ATLAS 2022 data ATLAS:2021xtw.