Renormalization group scaling in nonrelativistic QCD

Abstract

We discuss the matching conditions and renormalization group evolution of non-relativistic QCD. A variant of the conventional $\overline{\mathrm{MS}}$ scheme is proposed in which a subtraction velocity $\ensuremath{\nu}$ is used rather than a subtraction scale $\ensuremath{\mu}.$ We derive a novel renormalization group equation in velocity space which can be used to sum logarithms of $v$ in the effective theory. We apply our method to several examples. In particular we show that our formulation correctly reproduces the two-loop anomalous dimension of the heavy quark production current near threshold.