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arXiv · hep-ph/9810235

Power Counting and βFunction in NRQCD

H. W. Griesshammer
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Abstract

A computation of the NRQCD $β$ function both in the Lorentz gauge family and in the Coulomb gauge to one loop order endorses a velocity power counting scheme for dimensionally regularised NRQCD. In addition to the ultrasoft scale represented by bremsstrahlung gluons and the potential scale with Coulomb gluons and on-shell quarks, a soft régime is identified in which energies and momenta are of order $Mv$, gluons are on shell and the quark propagator becomes static. The instantaneous gluon propagator has a non-zero vacuum polarisation only because of contributions from this régime, irrespective of the gauge chosen. Rules are derived which allow one to read up from a given graph whether it is zero because of the homogene{\ia}ty of dimensional regularisation. They also apply to threshold expansion and are used to prove that ultrasoft quarks with energy and momentum of order $Mv^2$ decouple from the theory.

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H. W. Griesshammer. 1999-04-14. Power Counting and βFunction in NRQCD. https://doi.org/10.1016/s0550-3213(99)00325-9

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