Power counting and beta function in NRQCD

A computation of the NRQCD beta function both in the Lorentz gauge family a nd in the Coulomb gauge to one loop order endorses a velocity power countin g scheme for dimensionally regularised NRQCD. In addition to the ultrasoft scale represented by bremsstrahlung gluons and the potential scale with Cou lomb gluons and on-shell quarks, a soft regime is identified in which energ ies and momenta are of order M nu, gluons are on shell and the quark propag ator becomes static. The instantaneous gluon propagator has a non-zero vacu um polarisation only because of contributions from this regime, irrespectiv e of the gauge chosen. Rules are derived which allow one to read up from a given graph whether it is zero because of the homogeneity of dimensional re gularisation. They also apply to threshold expansion and are used to prove that ultrasoft quarks with energy and momentum of order M nu(2) decouple fr om the theory. (C) 2000 Elsevier Science B.V. All rights reserved.