Two-loop renormalization of heavy–light currents at order 1/mQ in the heavy-quark expansion

We present exact results, at next-to-leading order in renormalization-group improved perturbation theory, for the Wilson coefficients appearing at order 1/mQ in the heavy-quark expansion of heavy–light current operators. To this end, we complete the calculation of the corresponding two-loop anomalous dimension matrix. Our results are important for determinations of |Vub| using exclusive and inclusive semileptonic B decays. They are also relevant to computations of the decay constant fB based on a heavy-quark expansion.