Renormalization group scaling in nonrelativistic QCD

TL;DR

This paper develops a new renormalization group approach in velocity space for nonrelativistic QCD, enabling better summation of velocity logarithms and accurate reproduction of two-loop anomalous dimensions.

Contribution

It introduces a velocity-based subtraction scheme and derives a novel RG equation in velocity space for nonrelativistic QCD.

Findings

Successfully reproduces the two-loop anomalous dimension of the heavy quark production current.

Provides a new method for summing velocity logarithms in nonrelativistic QCD.

Demonstrates the effectiveness of the approach through multiple examples.

Abstract

We discuss the matching conditions and renormalization group evolution of non-relativistic QCD. A variant of the conventional MS-bar scheme is proposed in which a subtraction velocity nu is used rather than a subtraction scale 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.