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

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

1998-07-10

arxiv.org/abs/nucl-th/9807035v3

Phys.Lett. B455 (1999) 30-38

Physics

Nuclear Physics

Nuclear Theory

11 pages, final version submitted to PLB

Scientific paper

10.1016/S0370-2693(99)00461-X

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 $\pi \pi$ scattering amplitudes both for s- and p-waves at lowest order in the proposed expansion where a successful description of the low-lying resonances ($\sigma$ and $\rho$) 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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