The inverse amplitude method in Chiral Perturbation Theory

Based on a dispersive approach, we apply the inverse amplitude method to unitarize the one-loop $SU(2)$ and $SU(3)$ Chiral Perturbation Theory. We find that this unitarization technique yields the correct complex analytical structure in terms of cuts and poles. As a matter of fact, we obtain the poles associated to the $\rho(770)$ and $K^*(982)$ resonances. We obtain their masses and widths within a 15\% error, when using the present chiral parameter estimates obtained from low energy experiments. However, by fixing the actual mass values of both resonances we obtain a parametrization of the $\pi\pi$ and $\pi K$ phase shifts up to the first inelastic threshold, which yields the correct values of their widths. With this fit we have also calculated several phenomenological parameters, including the scattering lengths, which can be of interest for future experiments.