B meson decays from moving NRQCD on fine MILC lattices

Lattice simulations of $B\to\pi l\nu$ decays are problematic in the low $q^{2}$ region when the pion has to have large momentum in the lattice frame for a $B$ meson at rest or moving slowly. The moving-NRQCD formalism provides a way around this by giving an accurate discretization of a $b$ quark moving at arbitrary velocity $v$, and therefore a $B$ meson moving at high momentum in the lattice frame. Here we show results from simulations of the moving-NRQCD action complete through $O(1/M)$ coupled to the asqtad action on a MILC fine ensemble. We show $B$, $B^{*}$ masses as a function of $v$ and demonstrate how to determine the meson kinetic mass and the renormalization of $v$ non-perturbatively. We will also discuss the perturbative renormalization of the moving-NRQCD action from high-$\beta$ Monte Carlo simulations.