Short-distance expansion of heavy-light currents at order 1/mQ.

Abstract

The short-distance expansion of the heavy-light currents $\overline{q}{\ensuremath{\gamma}}^{\ensuremath{\mu}}Q$ and $\overline{q}{\ensuremath{\gamma}}^{\ensuremath{\mu}}{\ensuremath{\gamma}}_{5}Q$ is constructed to order $\frac{1}{{m}_{Q}}$, and to next-to-leading order in renormalization-group-improved perturbation theory. It is shown that the 10 \ifmmode\times\else\texttimes\fi{} 10 anomalous dimension matrix, which describes the scale dependence of the dimension-four effective current operators in the heavy quark effective theory, is to a large extent determined by the equations of motion, heavy quark symmetry, and reparametrization invariance. The next-to-leading order expressions for the Wilson coefficients at order $\frac{1}{{m}_{Q}}$ depend on only five unknown two-loop anomalous dimensions, among them that of the chromomagnetic operator.