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Renormalization of Velocity-Changing Dimension-Five Operators in the Heavy-Quark Effective Theory

We study the renormalization of operators of the type ${\bar h_{v'}} ΓG^{μν} h_v$ 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.