Dynamics of heavy flavour in a weakly magnetized hot QCD medium

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 $B$.