Global fit ofππandπKelastic scattering in chiral perturbation theory with dispersion relations

Abstract

We apply the one-loop results of the $\mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_L\times \mathrm{SU}{\mathrm{}\left(3\right)\mathrm{}}_R$ chiral perturbation theory supplemented with the inverse-amplitude method to fit the available experimental data on $\pi \pi$ and $\pi K$ scattering. With essentially only three parameters we describe accurately data corresponding to six different channels: namely, $(I, J)=(0, 0), (2, 0), (1, 1), (\frac{1}{2}, 0), (\frac{3}{2}, 0), \mathrm{and} (\frac{1}{2}, 1)$. In addition we reproduce the first resonances of the (1,1) and (½,1) channel with the right mass corresponding to the $\rho$ and the $K^{*} \mathrm{}\left(892\right)\mathrm{}$ particles.