Dynamics of heavy flavour in a weakly magnetized hot QCD medium

TL;DR

This paper calculates how a weak magnetic field affects the diffusion and energy loss of heavy quarks in a hot QCD medium, revealing anisotropic effects and mass-dependent differences.

Contribution

It provides the first detailed analysis of heavy quark transport coefficients in a weak magnetic field, considering both parallel and perpendicular orientations.

Findings

Charm quarks experience larger diffusion and energy loss than bottom quarks.

Magnetic field effects are more pronounced for charm than bottom quarks.

Momentum transfer is anisotropic, favoring the direction of heavy quark velocity.

Abstract

We obtain the spatial and momentum diffusion coefficients ($D_s$ and $\kappa$), and the collisional energy loss ($dE/dx$) of a heavy quark (HQ) traversing through a thermal medium of quarks and gluons in a weak magnetic field ($B$), for the two cases of the HQ moving either parallel or perpendicular to $\bm{B}$. For that purpose, we consider Coulomb scatterings ($t$-channel) of the HQ with the light quarks, obtained from the imaginary part of the HQ self-energy via the cutting rules. Both the normalised (by $T^3$) %\textit{momentum} diffusion coefficients, $\kappa$, as well as $dE/dx$, for charm quarks are larger than that for bottom quarks due to the larger mass of the latter. Also, the effect of $B$ is more feeble on the bottom quark, compared to the charm quark. Comparatively, the magnitudes of both $\kappa$ and $dE/dx$ are significantly smaller for the case of $\bm{v}\perp\bm{B}$. For both the cases, our results show that the momentum transfer between the HQ and the medium takes place preferentially along the direction of HQ velocity, thus leading to a significant increase in the momentum diffusion anisotropy, compared to $B=0$. We also calculate the (scaled) spatial diffusion coefficient, which we find to be independent of the heavy flavor mass and is almost unaffected by changes in $B$.