Study of the $DK$ interaction with femtoscopic correlation functions

Abstract

The $DK$ interaction in isospin zero is known to be attractive to such an extent that a bound state can be generated, which can be associated with the mysterious $D_{s0}^{\ast }(2317)$. In this work, we calculate the $DK$ femtoscopic correlation function in the coupled-channel framework for different source sizes that can directly probe the strongly attractive $DK$ interaction, which is otherwise inaccessible due to the unstable nature of $D$ and $K$ mesons, and therefore can help elucidate the nature of $D_{s0}^{\ast }(2317)$. We further generalize the study of source size dependence to various interactions, ranging from repulsive, weakly attractive, moderately attractive, and strongly attractive, in a square-well model. We hope that our study can motivate future experimental measurements of the $DK$ correlation function and other interactions relevant to the understanding of the nature of the many exotic hadrons discovered so far.

8 pages, 3 figures; clarifications added and discussions refined, to appear in Physical Review D