Correlation function and bound state from the $K D_{s0}^*(2317)$ interaction

TL;DR

This paper investigates the interaction between kaons and the $D_{s0}^*(2317)$ resonance, predicting a three-body bound state and analyzing its experimental observability in upcoming ALICE experiments.

Contribution

It introduces a novel theoretical approach using the fixed center approximation to predict a three-body bound state involving kaons and the $D_{s0}^*(2317)$ resonance.

Findings

Correlation function shows a strong attractive interaction.

A narrow resonant peak indicates a three-body bound state.

Predicted states are promising targets for future experiments.

Abstract

In anticipation of the new wave of ALICE experiments on particle-resonance correlation functions, we study the interaction of a kaon with the $D_{s0}^*(2317)$ resonance. Assuming the $D_{s0}^*(2317)$ 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 $K D_{s0}^*(2317)$ 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 $K D_{s0}^*(2317)$ threshold, signaling a three-body bound state. We discuss the experimental feasibility of observing this state through the invariant mass distribution of $K D_s^+ \pi^0$, 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.