Sommerfeld enhancement: General results from field theory diagrams

Abstract

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 A 0. The main novelty is that A 0 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. © 2009 SISSA.