Sommerfeld enhancement: general results from field theory diagrams

Assuming that two incoming annihilating particles interact by exchanging a generally massive attractive vector (or scalar) boson, we find, by taking the non-relativistic limit of the field theory ladder diagrams, that the complete annihilation amplitude A is equal to: the convolution of a solution of the Schroedinger equation (including the attractive potential) with the Fourier transform of the bare (i.e. ignoring the attraction) annihilation amplitude A0. The main novelty is that A0 can be completely arbitrary. For a Coulomb potential we find analytically the enhancement for the l-partial-wave cross-section, e.g. the P wave enhancement 2π(α/v)3 (v relative velocity), for a Yukawa potential we describe a simple algorithm and give numerical results showing an important P wave enhancement with a resonant pattern.