Power counting in dimensionally regularized nonrelativistic QCD

Abstract

We present a scheme for calculating in nonrelativistic QCD (NRQCD) with consistent power counting in the heavy quark velocity $v$. As an example, we perform the systematic matching of an external current onto NRQCD at subleading order in $v$, a calculation relevant for the process $e^{+}{e}^{-}\to \mathrm{hadrons}$ near threshold. Consistent velocity power counting in dimensional regularization is achieved by including two distinct gluon fields, one corresponding to gluon radiation and one corresponding to an instantaneous potential. In this scheme power counting is manifest in any gauge, and also holds for nongauge interactions. The matching conditions for an external vector current in NRQCD are calculated to ${O(g}^2{v}^2)$ and the cancellation of infrared divergences in the matching conditions is shown to require both gluon fields. Some subtleties arising in the matching conditions at subleading order are addressed.