The $kappa$ resonance in s wave $pi K$ scatterings

A new unitarization approach incorporated with chiral symmetry is established and applied to study the $pi K$ elastic scatterings. We demonstrate that the $kappa$ resonance exists, if the scattering length parameter in the I=1/2, J=0 channel does not deviate much from its value predicted by chiral perturbation theory. The mass and width of the $kappa$ resonance is found to be $M_kappa=594pm 79MeV$, $Gamma_kappa=724pm 332MeV$, obtained by fitting the LASS data up to 1430MeV. Better determination to the pole parameters is possible if the chiral predictions on scattering lengths are taken into account.