Crossed-Boson-Exchange Contribution and Bethe-Salpeter Equation

• Published in: Few-body systems 2001-01, Vol.30 (1-2), p.5-19
• Main Authors: Theußl, L., Desplanques, B.
• Format: Article
• Language: English
• Subjects: High Energy Physics - Theory; Physics
• ISSN: 0177-7963; 1432-5411
• DOI: 10.1007/s006010170014

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.