Solving the four-dimensional $NN-\pi NN$ equations for scalars below meson-production threshold

Abstract

The four-dimensional $NN-\pi NN$ equations are adapted to the case of scalar particles with a ${\varphi }^2\sigma$ interaction Lagrangian, and solved for energies below the $\sigma$-production threshold. This is achieved in the approximation where $\varphi \sigma$ scattering is dominated by the $s$-channel $\varphi$-pole term. The importance of the removal of double-counting is investigated, and a detailed comparison of the results of a covariant coupled-channels formulation and the Bethe-Salpeter equation in the ladder and ladder plus crossed-box approximations is presented. A brief discussion of the extension of the method to energies above the $\sigma$-production threshold is given.

23 pages, RevTeX, 17 encapsulated postscript files included, manuscript uses BoxedEPS.tex

References in corpus (6)

• Chiral Dynamics in Nucleons and Nuclei
• Chiral perturbation theory
• Chiral Perturbation Theory
• Covariant three-body equations in phi^3 field theory
• The classification of diagrams in perturbation theory
• Covariant four-dimensional scattering equations for the $NN-\pi NN$ system

Cited by in corpus (4)

• Two-fermion relativistic bound states in Light-Front Dynamics
• Ground states of the Wick-Cutkosky model using light-front dynamics
• Remarks on non-perturbative three--body dynamics and its application to the $KK\bar{K}$ system
• Unitarity and the Bethe-Salpeter Equation