Energy Loss of a Heavy Quark in a Collisional Quark-Gluon Plasma

TL;DR

The paper develops a complete QCD calculation of heavy-quark collisional energy loss in a collisional Quark-Gluon Plasma by employing a hard-thermal-loop (HTL) resummed gluon propagator to treat arbitrary momentum transfer and encoding medium collisions through a BGK kernel. It establishes gauge independence and the cancellation of unphysical gluon polarizations within HTL, now including both quark–quark and quark–gluon scatterings, with quark–gluon scattering found to significantly contribute to the total energy loss. Numerically, collisions increase -dE/dx by about 8% for α_s ≈ 0.3 at large incident velocities, and the energy loss is partitioned with quark–gluon scattering generally dominating over quark–quark scattering; results converge with known hard/soft limits (RS) in those regimes. The methodology, which avoids artificial momentum-cutoff dependence and self-consistently includes collision effects, provides a more robust baseline for jet quenching studies and can be extended to account for additional medium effects or background fields near Tc.

Abstract

We extend our previous work on the energy loss of a heavy fermion in a QED plasma to the Quark-Gluon plasma, using the same Bhatnagar-Gross-Krook collisional kernel. The calculation is carried out with a theoretical method where the hard-thermal-loop resummed gluon propagator is used for arbitrary momentum transfer in the scattering processes. Encoding the collision effect in a self-consistent manner, the resummed gluon propagator regulates the infrared divergence in the scattering amplitude without introducing an artificial cutoff for the transferred momenta and makes the analysis on the hard and soft processes in a unified framework. To place our computation on a more solid foundation, we also explicitly demonstrate the gauge independence of the interaction rate as well as the elimination of unphysical gluon polarizations by the ghost field under the use of the resummed gluon propagator. In addition, with our complete QCD calculation by including both quark-quark and quark-gluon scatterings, we provide a quantitatively reliable result on the collisional energy loss of a heavy quark where the new contribution from quark-gluon scatterings accounts for a larger portion of the total energy loss. In general, collisions between the thermal partons result in an increased energy loss which becomes more pronounced with increasing gauge coupling. Considering a typical coupling constant in QCD, $α_s = 0.3$, the energy loss increases $\sim 8$% at large incident velocities as compared to the collisionless limit. Such a collision-induced correction is still moderate although it is sightly suppressed as compared to our previous estimate based on a QED calculation using couplings consistent with those expected to be generated in the Quark-Gluon plasma.

Figures (6)

• Figure 1: The tree-level Feynman diagrams for the elastic scatterings $Q q \rightarrow Q q$ and $Q g\rightarrow Q g$.
• Figure 2: Hard and soft contributions to the collisional energy loss as a function of $q^*/T$. Results obtained from three different theoretical methods are presented for comparison.
• Figure 3: Collisional energy loss of a heavy quark as a function of $v$ at different coupling constants. Results obtained from three theoretical methods are presented for comparison.
• Figure 4: The heavy-quark energy loss as a function of the incident velocity at different coupling constants. Besides the total energy loss, contributions from quark-quark and quark-gluon scatterings are also presented separately.
• Figure 5: The energy loss ratio as a function of the heavy-quark velocity at different coupling constants or collision rates. The bands correspond to varying the parameter $c$ in Eq. (\ref{['nu']}) from $1$ to $2$.