Three-loop anomalous dimension of the heavy quark pair production current in nonrelativistic QCD

The three-loop nonmixing contributions to the anomalous dimension of the leading order quark pair production current in nonrelativistic QCD are computed. It is demonstrated that the renormalization procedure can only be carried out consistently if the dynamics of both soft and ultrasoft degrees of freedom is present for all scales below the heavy quark mass and if the soft and ultrasoft renormalization scales are always correlated.