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

TL;DR

This paper uses heavy-quark effective theory to compute one-loop radiative corrections for lattice QCD heavy-heavy currents, aiding precise calculations of semileptonic B to D decays.

Contribution

It provides the first systematic one-loop matching factors for heavy-heavy currents in lattice QCD using HQET, including scale setting for phenomenological applications.

Findings

One-loop matching factors for heavy-heavy currents derived.

Results applicable to B to D semileptonic decay form factors.

Scale $q^*$ determined for improved accuracy.

Abstract

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 $B\to D^{(*)}l\nu$. Results for the Brodsky-Lepage-Mackenzie scale $q^*$ are also given.