Lattice study of a magnetic contribution to heavy quark momentum diffusion

Heavy quarks placed within a hot QCD medium undergo Brownian motion, characterized by specific transport coefficients. Their determination can be simplified by expanding them in $T/M$, where $T$ is the temperature and $M$ is a heavy quark mass. The leading term in the expansion originates from the colour-electric part of a Lorentz force, whereas the next-to-leading order involves the colour-magnetic part. We measure a colour-magnetic 2-point correlator in quenched QCD at $T \sim 1.2 ... 2.0 T_{\rm c}^{ }$. Employing multilevel techniques and non-perturbative renormalization, a good signal is obtained, and its continuum extrapolation can be estimated. Modelling the shape of the corresponding spectral function, we subsequently extract the momentum diffusion coefficient, $\kappa$. For charm (bottom) quarks, the magnetic contribution adds $\sim 30\%$ ($10\%$) to the electric one. The same increases apply also to the drag coefficient, $\eta$. As an aside, the colour-magnetic spectral function is computed at NLO.