Non-perturbative heavy quark diffusion coefficients in a weakly magnetized thermal QCD medium

In this work, the perturbative and non-perturbative contributions to the heavy quark (HQ) momentum ($\kappa$) as well as spatial ($D_s$) diffusion coefficients are computed in a weak background magnetic field. The formalism adopted here involves calculation of the in-medium potential of the HQ in a weak magnetic field, which then serves as a proxy for the resummed gluon propagator in the calculation of HQ self-energy ($\Sigma$). The self-energy determines the scattering rate of HQs with light thermal partons, which is subsequently used to evaluate $\kappa$ and $D_s$. It is observed that non-perturbative effects play a dominant role at low temperature. The spatial diffusion coefficient $2\pi T D_s$, exhibits good agreement with recent LQCD results. These findings can be applied to calculate the heavy quark directed flow at RHIC and LHC energies. An extension of this formalism to the case of finite HQ momentum has also been attempted.