Lattice $B$-field correlators for heavy quarks

We analyze the color-magnetic (or "$B$") field two-point function that encodes the finite-mass correction to the heavy quark momentum diffusion coefficient. The simulations are done on fine isotropic lattices in the quenched approximation at $1.5\,T_c$, using a range of gradient flow times for noise suppression and operator renormalization. The continuum extrapolation is performed at fixed flow time followed by a second extrapolation to zero flow time. Perturbative calculations to next-to-leading order of this correlation function, matching gradient-flowed correlators to MS-bar, are used to resolve nontrivial renormalization issues. We perform a spectral reconstruction based on perturbative model fits to estimate the coefficient $\kappa_B$ of the finite-mass correction to the heavy quark momentum diffusion coefficient. The approach we present here yields high-precision data for the correlator with all renormalization issues incorporated at next-to-leading order, and is also applicable for actions with dynamical fermions.