The $KD$, $\eta D_s$ interaction in finite volume and the nature of the $D_{s^* 0}(2317)$ resonance

TL;DR

This paper extends a chiral unitary approach to finite volume to study the $D_{s^*0}(2317)$ resonance, demonstrating how lattice data can reveal its molecular or non-molecular nature through finite volume spectra analysis.

Contribution

It develops a finite volume formalism based on SU(4) extrapolation of chiral theory to analyze the $D_{s^*0}(2317)$ resonance and its nature using lattice-like energy levels.

Findings

Accurate $KD$ phase shifts and resonance position can be obtained with coupled channels.

Finite volume spectra differ significantly depending on the resonance's molecular nature.

Finite volume analysis can distinguish between molecular and non-molecular states.

Abstract

An SU(4) extrapolation of the chiral unitary theory in coupled channels done to study the scalar mesons in the charm sector is extended to produce results in finite volume. The theory in the infinite volume produces dynamically the $D_{s^*0}(2317)$ resonance by means of the coupled channels $KD$, $\eta D_s$. Energy levels in the finite box are evaluated and, assuming that they would correspond to lattice results, the inverse problem of determining the bound states and phase shifts in the infinite volume from the lattice data is addressed. We observe that it is possible to obtain accurate $KD$ phase shifts and the position of the $D_{s^*0}(2317)$ state, but it requires the explicit consideration of the two coupled channels in the analysis if one goes close to the $\eta D_s$ threshold. We also show that the finite volume spectra look rather different in case the $D_{s^*0}(2317)$ is a composite state of the two mesons, or if it corresponds to a non molecular state with a small overlap with the two meson system. We then show that a careful analysis of the finite volume data can shed some light on the nature of the $D_{s^*0}(2317)$ resonance as a $KD$ molecule or otherwise.