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Sommerfeld enhancement: general results from field theory diagrams · Around

2009

Sommerfeld enhancement: general results from field theory diagrams

Iengo, R.

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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.

Built on

L.D.Landau,E.M.Lifshitz, ”Quantum Mechanics” Pergamon Press 1958
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C.Itzykson,J-B.Zuber, ”Quantum Field Theory” McGraw-Hill 1985
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M.E.Peskin,D.V.Schroeder, ”An Introduction to Quantum Field Theory” Perseus Books 1995
Original
1995
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