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Unitarity and the Bethe-Salpeter Equation

A. D. Lahiff·I. R. Afnan
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Abstract

We investigate the relation between different three-dimensional reductions of the Bethe-Salpeter equation and the analytic structure of the resultant amplitudes in the energy plane. This correlation is studied for both the $ϕ^2σ$ interaction Lagrangian and the $πN$ system with $s$-, $u$-, and $t$-channel pole diagrams as driving terms. We observe that the equal-time equation, which includes some of the three-body unitarity cuts, gives the best agreement with the Bethe-Salpeter result. This is followed by other 3-D approximations that have less of the analytic structure.

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A. D. Lahiff, I. R. Afnan. 2002-08-22. Unitarity and the Bethe-Salpeter Equation. https://doi.org/10.1103/physrevc.66.044001

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