Power counting and β function in NRQCD Original Research Article

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 homogeneity of dimensional regularisation. They also apply to threshold expansion and are used to prove that ultrasoft quarks with energy and momentum of order Mv2 decouple from the theory.