Renormalization of velocity-changing dimension-five operators in the heavy-quark effective theory

We study the renormalization of operators of the type hv′ΓGμνhv in the heavy-quark effective theory (HQET). We construct the combinations of such operators that are renormalized multiplicatively, and calculate their velocity-dependent anomalous dimensions at the one-loop order. We then show that the virial theorem of the HQET is not renormalized, and that in the limit of equal velocities the anomalous dimension of the chromo-electric operator vanishes to all orders in perturbation theory. This implies an exact relation between renormalization constants, which may help in a future calculation of the two-loop anomalous dimension of the chromo-magnetic operator.