We discuss the matching conditions and renormalization group evolution of non-relativistic QCD. A variant of the conventional MS̄ scheme is proposed in which a subtraction velocity ν is used rather than a subtraction scale μ. 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.
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Luke et al. (2000) studied this question.
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