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

TL;DR

This study investigates S-wave D-K interactions using the chiral SU(3) quark model, finding attraction but not enough for molecule formation, and providing phase shifts for elastic scattering.

Contribution

It applies the resonating group method within the chiral SU(3) quark model to analyze D-K interactions, offering new insights into their scattering properties.

Findings

Attraction exists between D and K due to boson exchanges

Attraction is insufficient to form a D-K molecule

Provides S-wave phase shifts for D-K elastic scattering

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.