Physics – High Energy Physics – High Energy Physics - Phenomenology
Scientific paper
1998-10-02
Nucl.Phys. B579 (2000) 313-351
Physics
High Energy Physics
High Energy Physics - Phenomenology
41 pages, LaTeX2e, uses feynmp to generate 122 drawings in 10 figures, 4 tables and 45 graphs in equations; necessary METAPOST
Scientific paper
10.1016/S0550-3213(99)00325-9
A computation of the NRQCD $\beta$ 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 r\'egime 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 r\'egime, 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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