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Bethe-Salpeter Approach for Meson-Meson Scattering in Chiral Perturbation Theory

Juan Nieves·Enrique Ruiz Arriola
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Abstract

The Bethe-Salpeter equation restores exact elastic unitarity in the s- channel by summing up an infinite set of chiral loops. We use this equation to show how a chiral expansion can be undertaken by successive approximations to the potential which should be iterated. Renormalizability of the amplitudes in a broad sense can be achieved by allowing for an infinite set of counter-terms as it is the case in ordinary Chiral Perturbation Theory. Within this framework we calculate the $ππ$ scattering amplitudes both for s- and p-waves at lowest order in the proposed expansion where a successful description of the low-lying resonances ($σ$ and $ρ$) and threshold parameters is obtained. We also extract the SU(2) low energy parameters ${\bar l}_{1,2,3,4}$ from our amplitudes.

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Juan Nieves, Enrique Ruiz Arriola. 1999-04-05. Bethe-Salpeter Approach for Meson-Meson Scattering in Chiral Perturbation Theory. https://doi.org/10.1016/s0370-2693(99)00461-x

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