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Crossed-boson exchange contribution and Bethe-Salpeter equation

L. Theussl·B. Desplanques
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Abstract

The contribution to the binding energy of a two-body system due to the crossed two-boson exchange contribution is calculated, using the Bethe-Salpeter equation. This is done for distinguishable, scalar particles interacting via the exchange of scalar massive bosons. The sensitivity of the results to the off-shell behavior of the operator accounting for this contribution is discussed. Large corrections to the Bethe-Salpeter results in the ladder approximation are found. For neutral scalar bosons, the mass obtained for the two-body system is close to what has been calculated with various forms of the instantaneous approximation, including the standard non-relativistic approach. The specific character of this result is demonstrated by a calculation involving charged bosons, which evidences a quite different pattern. Our results explain for some part those obtained by Nieuwenhuis and Tjon on a different basis. Some discrepancy appears with increasing coupling constants, suggesting the existence of sizeable contributions involving more than two-boson exchanges.

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L. Theussl, B. Desplanques. 1999-08-03. Crossed-boson exchange contribution and Bethe-Salpeter equation. https://doi.org/10.1016/s0146-6410(00)00065-x

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