Threshold Expansion and Dimensionally Regularised NRQCD

Abstract

A Lagrangean and a set of Feynman rules are presented for non-relativistic QFT's with manifest power counting in the heavy particle velocity $v$. A régime is identified in which energies and momenta are of order $Mv$. It is neither identical to the ultrasoft régime corresponding to radiative processes with energies and momenta of order $Mv^2$, nor to the potential régime with on shell heavy particles and Coulomb binding. In this soft régime, 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 regularisation in NRQFT.