Preliminary study of theK¯Ninteraction in a chiral constituent quark model

Abstract

A preliminary investigation of $\overline{K}N$ interaction is performed within a chiral constituent quark model by solving the resonating group method (RGM) equation. The model parameters are taken from our previous work, which gave a satisfactory description of the $S$-, $P$-, $D$-, $F$-wave $\mathit{KN}$ scattering phase shifts. The channel-coupling between $\overline{K}N,\ensuremath{\pi}\ensuremath{\Lambda}$ and $\ensuremath{\pi}\ensuremath{\Sigma}$ is considered, and the scattering phase shifts as well as the bound-state problem of $\overline{K}N$ are dynamically studied. The results show that the $S$-wave $\overline{K}N$ interaction in the isospin $I=0$ channel is attractive, and in the extended chiral SU(3) quark model such an attraction can make for a $\overline{K}N$ bound state, which appears as a $\ensuremath{\pi}\ensuremath{\Sigma}$ resonance in the coupled-channel calculation, while the chiral SU(3) quark model cannot accommodate the existence of a $\overline{K}N$ bound state. It seems that the vector meson exchanges are necessary to be introduced in the quark-quark interactions if one tries to explain the $\ensuremath{\Lambda}(1405)$ as a $\overline{K}N$ bound state or a $\ensuremath{\pi}\ensuremath{\Sigma}$-$\overline{K}N$ resonance state.