Application of heavy-quark effective theory to lattice QCD. III. Radiative corrections to heavy-heavy currents

We apply heavy-quark effective theory (HQET) to separate long- and short-distance effects of heavy quarks in lattice gauge theory. In this paper we focus on flavor-changing currents that mediate transitions from one heavy flavor to another. We stress differences in the formalism for heavy-light currents, which are discussed in a companion paper, showing how HQET provides a systematic matching procedure. We obtain one-loop results for the matching factors of lattice currents, needed for heavy-quark phenomenology, such as the calculation of zero-recoil form factors for the semileptonic decays $\overrightarrow{B}{D}^{\left(*\right)}l\nu .$ Results for the Brodsky-Lepage-Mackenzie scale $q^{*}$ are also given.