Momentum broadening of heavy quark in a magnetized thermal QCD medium

TL;DR

This paper calculates anisotropic momentum diffusion coefficients for heavy quarks in a strongly magnetized quark-gluon plasma, revealing directional dependencies and contributions from gluons and light quarks in the lowest Landau level.

Contribution

It provides the first detailed estimation of five anisotropic momentum diffusion coefficients for heavy quarks in a magnetized medium beyond the static limit, considering specific temperature and magnetic field regimes.

Findings

Diffusion coefficients depend on the orientation of heavy quark motion relative to magnetic field.

Gluon contribution to diffusion scales as T^3, light quark contribution scales as T|eB|.

Transverse diffusion dominates for both parallel and perpendicular quark motion relative to magnetic field.

Abstract

Anisotropic momentum diffusion coefficients of heavy quarks have been computed in a strongly magnetized quark-gluon plasma beyond the static limit within the framework of Langevin dynamics. Depending on the orientation of the motion of the heavy quark with respect to the direction of the magnetic field, five momentum diffusion coefficients of heavy quark have been estimated in the magnetized thermal medium. Specifically, we have focussed our attention to temperature range and strength of magnetic field satisfying the condition, $\it{i.e.}$ $M\gg\sqrt{eB}\gg T$, $M$ being the mass of heavy quark. The light quarks/antiquarks follow $1+1-$dimensional lowest Landau level (LLL) kinematics, and heavy quark dynamics are not directly affected by the magnetic field in the medium. The thermal gluon contribution to the diffusion coefficient is proportions to $T^3$, whereas, the contribution of light quarks in the lowest Landau state to the same is seen to be proportional to $T|eB|$. Furthermore, it is observed that for the case of heavy quark motion parallel to the magnetic field, the component of diffusion coefficient transverse both to the field and the heavy quark velocity $(\kappa^{\parallel}_{TT})$ turns out to be dominant as compared to the component longitudinal to both the field and motion $(\kappa^{\parallel}_{LL})$, $i.e.$, $\kappa^{\parallel}_{TT}\gg \kappa^{\parallel}_{LL}$. Further, for the case of heavy quark moving perpendicular to the magnetic field, it is seen that the diffusion coefficients transverse to the magnetic field are dominant, i.e., $\kappa^{\perp}_{LT}, \kappa^{\perp}_{TT}\gg \kappa^{\perp}_{TL}$.