StudyingKπS-wave scattering in theK-matrix formalism

Abstract

We generalize our previous work on $\ensuremath{\pi}\ensuremath{\pi}$ scattering to $K\ensuremath{\pi}$ scattering, and reanalyze the experiment data for $K\ensuremath{\pi}$ scattering below 1.6 GeV. Without any free parameter, we explain the $K\ensuremath{\pi}$ $I=3/2$ S-wave phase shift very well by using t-channel $\ensuremath{\rho}$ and u-channel ${K}^{*}$ meson exchange. With the t-channel and u-channel meson exchange fixed as the background term, we fit the $K\ensuremath{\pi}I=1/2$ S-wave data of the LASS experiment quite well by introducing one or two s-channel resonances. It is found that there is only one s-channel resonance between the $K\ensuremath{\pi}$ threshold and 1.6 GeV, i.e., ${K}_{0}^{*}(1430)$ with a mass around 1438--1486 MeV and a width of about 346 MeV, while the t-channel $\ensuremath{\rho}$ exchange gives a pole at $(450--480i)$ MeV for the amplitude, rather uncertain due to the limitations of the approach used.