Short-Distance Expansion of Heavy-Light Currents at Order 1/m

The short-distance expansion of the heavy-light currents $\bar q,\gamma^\mu Q$and$\bar q,\gamma^\mu\gamma_5,Q$isconstructedtoorder$1/m_Q$, and to next-to-leading order in renormalization-group improved perturbation theory. It is shown that the $10\times 10$ 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 reparameterization invariance. The next-to-leading order expressions for the Wilson coefficients at order $1\mathrm{/}{m}_Q$ depend on only five unknown two-loop anomalous dimensions, among them that of the chromo-magnetic operator.