  Heavy-light decays such as $B \to \pi \ell \nu$, $B \to K^{*} \gamma$ and $B
\to K^{(*)} \ell \ell$ can be used to constrain the parameters of the Standard
Model and in indirect searches for new physics. While the precision of
experimental results has improved over the last years this has still to be
matched by equally precise theoretical predictions. The calculation of
heavy-light form factors is currently carried out in lattice QCD. Due to its
small Compton wavelength we discretize the heavy quark in an effective
non-relativistic theory. By formulating the theory in a moving frame of
reference discretization errors in the final state are reduced at large recoil.
Over the last years the formalism has been improved and tested extensively.
Systematic uncertainties are reduced by renormalizing the m(oving)NRQCD action
and heavy-light decay operators. The theory differs from QCD only for large
loop momenta at the order of the lattice cutoff and the calculation can be
carried out in perturbation theory as an expansion in the strong coupling
constant. In this paper we calculate the one loop corrections to the
heavy-light vector and tensor operator. Due to the complexity of the action the
generation of lattice Feynman rules is automated and loop integrals are solved
by the adaptive Monte Carlo integrator VEGAS. We discuss the infrared and
ultraviolet divergences in the loop integrals both in the continuum and on the
lattice. The light quarks are discretized in the ASQTad and highly improved
staggered quark (HISQ) action; the formalism is easily extended to other quark
actions.
