Tadpole-Improved Perturbation Theory for Heavy-Light Lattice Operators

Lattice calculations of matrix elements involving heavy-light quark bilinears are of interest in calculating a variety of properties of B and D mesons, including decay constants and mixing parameters. A large source of uncertainty in the determination of these properties has been uncertainty in the normalization of the lattice-regularized operators that appear in the matrix elements. Tadpole-improved perturbation theory, as formulated by Lepage and Mackenzie, promises to reduce these uncertainties below the ten per cent level at one-loop. In this paper we study this proposal as it applies to lattice-regularized heavy-light operators. We consider both the commonly used zero-distance bilinear and the distance-one point-split operator. A self-contained section on the application of these results is included. The calculation reduces the value of $f_B$ obtained from lattice calculations using the heavy quark effective theory.