Heavy quark diffusion in strong magnetic fields at weak coupling and implications for elliptic flow

We compute the momentum diffusion coefficients of heavy quarks, kappa(parallel to) and kappa(perpendicular to), in a strong magnetic field B along the directions parallel and perpendicular to B, respectively, at the leading order in QCD coupling constant alpha(s). We consider a regime relevant for the relativistic heavy ion collisions, alpha(s)eB << T-2 << eB, so that thermal excitations of light quarks are restricted to the lowest Landau level (LLL) states. In the vanishing light-quark mass limit, we find kappa(LO)(perpendicular to) proportional to alpha(sTeB)-Te-2 in the leading order that arises from screened Coulomb scatterings with (1 + 1)-dimensional LLL quarks, while kappa(parallel to) gets no contribution from the scatterings with LLL quarks due to kinematic restrictions. We show that the first nonzero leading order contributions to kappa(LO)(parallel to) come from the two separate effects: (1) the screened Coulomb scatterings with thermal gluons, and (2) a finite light-quark mass m(q). The former leads to kappa(LO,gluon)(parallel to) proportional to alpha T-2(s)3 and the latter to kappa(LO,massive)(parallel to) proportional to alpha(s)(alpha(s)eB)(1/2)m(q)(2). Based on our results, we propose a new scenario for the large value of heavy-quark elliptic flow observed in RHIC and LHC. Namely, when kappa(perpendicular to) >> kappa(parallel to), an anisotropy in drag forces gives rise to a sizable amount of the heavy-quark elliptic flow even if heavy quarks do not fully belong to an ellipsoidally expanding background fluid.