The Soft R'egime in NRQCD

Abstract

A Lagrangean and a set of Feynman rules are presented for Non-Relativistic QCD with manifest power counting in the heavy quark velocity $v$. A r\'egime is identified in which energies and momenta are of order $Mv$. It is neither identical to the ultrasoft r\'egime corresponding to radiative processes with energies and momenta of order $Mv^2$, nor to the potential r\'egime with on shell quarks and gluons providing the Coulomb binding. In this soft r\'egime, gluons are on shell, and the quark propagator becomes static. Examples show that it contributes to one- and two-loop corrections of scattering and production amplitudes near threshold. The results are readily generalised to any effective field theory with more than one low energy scale.