Bethe-Salpeter Approach for Meson-Meson Scattering in Chiral Perturbation Theory
arXiv:nucl-th/9807035 · doi:10.1016/S0370-2693(99)00461-X
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 $ÏÏ$ scattering amplitudes both for s- and p-waves at lowest order in the proposed expansion where a successful description of the low-lying resonances ($Ï$ and $Ï$) and threshold parameters is obtained. We also extract the SU(2) low energy parameters ${\bar l}_{1,2,3,4}$ from our amplitudes.
11 pages, final version submitted to PLB