Sommerfeld enhancement: general results from field theory diagrams

Details Sommerfeld enhancement: general results from field theory diagrams Sommerfeld enhancement: general results from field theory diagrams

2009-02-04

arxiv.org/abs/0902.0688v3

JHEP 0905:024,2009

Physics

High Energy Physics

High Energy Physics - Phenomenology

published version, it contains also the material of 0903.0317

Scientific paper

10.1088/1126-6708/2009/05/024

Assuming that two incoming annihilating particles interact by a generally massive attractive vector potential,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 vector potential) with the Fourier transform of the bare (i.e. ignoring the attraction) annihilation amplitude A0. The main novelty is that A0 is completely arbitrary. In particular for a massless vector potential we find for the l-partial-wave cross-section the Sommerfeld enhancement 2pi/(l!)^2 (alpha/ v)^{2l+1} (v relative velocity), e.g. for the P wave the enhancement 2pi(alpha/ v)^3.

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