Correlation function and bound state from the $K{D}_{s0}^{\ast }(2317)$ interaction

Abstract

In anticipation of the new wave of ALICE experiments on particle-resonance correlation functions, we study the interaction of a kaon with the $D_{s0}^{\ast }(2317)$ resonance. Assuming the $D_{s0}^{\ast }(2317)$ to be a $DK$ molecular state in isospin $I=0$, we employ the fixed center approximation (FCA) to describe the kaon scattering off the $DK$ cluster, and implement elastic unitarity in the $K{D}_{s0}^{\ast }(2317)$ amplitude via an optical potential and the Lippmann-Schwinger equation. We evaluate the scattering length, effective range, and correlation function, which exhibits a shape characteristic of a strongly attractive interaction. Notably, the amplitude develops a narrow resonant peak about 40~MeV below the $K{D}_{s0}^{\ast }(2317)$ threshold, signaling a three-body bound state. We discuss the experimental feasibility of observing this state through the invariant mass distribution of $K{D}_s^{+}\ddot{I}{€}^0$, and argue that such three-body states, predicted by various theoretical approaches, offer promising targets for future experimental searches, providing valuable insights into the nature of exotic hadronic resonances.

8 pages, 3 figures