2009/02/28 by Roberto Iengo, R. Iengo · 3 citations
Mathematics · Physics and Astronomy · #Amplitude #Annihilation #Convolution (computer science) #Cosmology and Gravitation Theories #Dark Matter and Cosmic Phenomena #Field (mathematics) #Field theory (psychology) #Fourier transform #Limit (mathematics) #Massless particle #Mathematical analysis #Mathematical physics #Mathematics #Particle physics theoretical and experimental studies #Physics #Pure mathematics #Quantum electrodynamics #Quantum mechanics #Vector field #Wave vector #astro-ph.HE #hep-ph #hep-th
paper · pdf · doi:10.1088/1126-6708/2009/05/024
published as JHEP 0905:024,2009 · published version, it contains also the material of 0903.0317
openalex publication_date 2009/05/06 · arxiv created 2009/05/13 · arxiv updated 2010/04/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.