Threshold expansion and dimensionally regularized NRQCD

A Lagrangian and a set of Feynman rules are presented for non-relativistic QFT’s with manifest power counting in the heavy particle velocity $v.\mathrm{}$ A regime is identified in which energies and momenta are of order $\mathrm{Mv}.\mathrm{}$ It is neither identical to the ultrasoft regime corresponding to radiative processes with energies and momenta of order ${\mathrm{Mv}}^2,$ nor to the potential regime with on shell heavy particles and Coulomb binding. In this soft regime, massless particles are on shell, and heavy particle propagators become static. Examples show that it contributes to one- and two-loop corrections of scattering and production amplitudes near threshold. Hence, NRQFT agrees with the results of threshold expansion. A simple example also demonstrates the power of dimensional regularization in NRQFT.