Chiral nonet mixing inπKscattering

Abstract

The underlying mixing of quark components of scalar mesons is probed in $\ensuremath{\pi}K$ scattering within a generalized linear sigma model that contains two scalar meson nonets and two pseudoscalar meson nonets (a quark-antiquark and a four-quark). In the leading order of this model, all free parameters have been previously fixed using the mass spectra and several low-energy parameters known from experiment and consistent predictions have been made. As in other predictions of the model, in the present work the isospins $I=1/2$, $3/2$ and $J=0$ projection of the $\ensuremath{\pi}K$ scattering amplitude (as well as phase shifts) are computed and compared with experiment. In the $I=1/2$ channel, it is shown that within the uncertainties of the model parameters a good agreement with experimental data up to an energy of about 1 GeV is obtained, whereas in the $I=3/2$ channel there is a better agreement with experiment which extends to about 1.4 GeV. The effect of final state interactions of $\ensuremath{\pi}K$ in the $I=1/2$ channel is approximated by the K-matrix method and the poles of the unitarized scattering amplitude are found. It is shown that the model predicts a light and broad kappa resonance with a mass and decay width of 670--770 MeV and 640--750 MeV consistent with other prior works. Moreover, the scattering lengths in the $I=1/2$, $3/2$ are also computed and shown to qualitatively agree with experiment. The overall predictions presented here further support previous findings that the scalar mesons below and above 1 GeV have substantial underlying mixings and that those below 1 GeV have dominant four-quark substructures while those above 1 GeV are closer to conventional $P$-wave quark-antiquark states.