Unitarity and the Bethe-Salpeter Equation

Details Unitarity and the Bethe-Salpeter Equation Unitarity and the Bethe-Salpeter Equation

2002-05-29

arxiv.org/abs/nucl-th/0205076v2

Phys.Rev. C66 (2002) 044001

Physics

Nuclear Physics

Nuclear Theory

17 pages, 8 figures; RevTeX. Version accepted for publication in Phys. Rev. C

Scientific paper

10.1103/PhysRevC.66.044001

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 $\phi^2\sigma$ interaction Lagrangian and the $\pi N$ 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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