Inverse amplitude method in chiral perturbation theory

Abstract

Based on a dispersive approach, we apply the inverse amplitude method to unitarize one-loop SU(2) and SU(3) chiral perturbation theory. Numerically, we find that this unitarization technique yields the correct complex analytic structure in terms of cuts and poles. Indeed, using the chiral parameter estimates obtained from low-energy experiments we obtain the poles associated with the $\ensuremath{\rho}(770)$ and ${K}^{*}(982)$ resonances. Just by fixing their actual masses we obtain a parametrization of the $\ensuremath{\pi}\ensuremath{\pi}$ and $\ensuremath{\pi}K$ phase shifts in eight different channels. With this fit we have then calculated several low-energy phenomenological parameters estimating their errors. Among others, we have obtained the chiral parameters and scattering lengths, which can be relevant for future experiments.