Matching the HQET to Coulomb Type Bound States

We show that the infinite imaginary anomalous dimensions of certain heavy quark-antiquark currents in the HQET arise due to an inappropriate commutation of two limits, namely coinciding velocities and infinite cut-off. This commutation is not apparent when dimensional regularization is used, but it can be made manifest in a cut-off regularization. We argue that operators containing heavy quark and antiquark fields with the same velocity in the HQET must not be matched to perturbative QCD but to Coulomb-type bound state contributions. We show how to do so at one loop level.