S-wave DK interactions in the chiral SU(3) quark model

Abstract

The $DK$ interaction is relevant to the interpretation of the $D_{sJ}(2317)$. We dynamically investigate $S$-wave $DK$ interactions in the chiral SU(3) quark model by solving the resonating group method equation. The numerical results show an attraction between $D$ and $K$, which is from boson exchanges between light quarks. However, such an attraction is not strong enough to form a $DK$ molecule. Meanwhile, $S$ partial wave phase shifts of $DK$ elastic scattering are obtained. The case of $S$-wave $D^*K$ is rather similar to that of $DK$. To draw a definite conclusion whether a molecular state exists in $DK$ or $D^*K$ system, more details of dynamics should be considered in further study.