The mixing of scalar mesons and the baryon-baryon interaction

Abstract

By introducing the mixing of scalar mesons in the chiral SU(3) quark model, we dynamically investigate the baryon-baryon interaction. The hyperon-nucleon and nucleon-nucleon interactions are studied by solving the resonating group method (RGM) equation in a coupled-channel calculation. In our present work, the experimental lightest pseudoscalar $ \pi$ , K, $ \eta$ , $ \eta^{{\prime}}_{}$ mesons correspond exactly to the chiral nonet pseudoscalar fields $ \pi$ , K, $ \eta$ , $ \eta^{{\prime}}_{}$ in the chiral SU(3) quark model. The $ \eta$ , $ \eta^{{\prime}}_{}$ mesons are considered as the mixing of singlet and octet mesons, and the mixing angle $ \theta_{{ps}}^{}$ is taken to be -23° . For scalar nonet mesons, we suppose that there exists a correspondence between the experimental lightest scalar f 0(600) , $ \kappa$ , a 0(980) , f 0(980) mesons and the theoretical scalar nonet $ \sigma$ , $ \kappa$ , $ \sigma^{{\prime}}_{}$ , $ \epsilon$ fields in the chiral SU(3) quark model. For scalar mesons, we consider two different mixing cases: one is the ideal mixing and another is the $ \theta_{s}^{}$ = 19° mixing. The masses of the $ \sigma^{{\prime}}_{}$ and $ \epsilon$ mesons are taken to be 980MeV, which are just the masses of the experimental a 0(980) , f 0(980) mesons. The mass of the $ \sigma$ meson is an adjustable parameter and is decided by fitting the binding energy of the deuteron, the masses of 560MeV and 644MeV are obtained for the ideal mixing and the $ \theta_{s}^{}$ = 19° mixing, respectively. We find that, in order to reasonably describe the YN interactions, the mass of the $ \kappa$ meson is near 780MeV for the ideal mixing. However, we must enhance the mass of the $ \kappa$ meson for the $ \theta_{s}^{}$ = 19° mixing, the 1050MeV is favorably used in the present work. The experimental $ \sigma$ and $ \kappa$ scalar mesons are very strange, both have larger widths. Hence, no matter what kind of mixing is considered, all the masses of scalar mesons we used in the present work seem to be consistent with the present PDG information.