Correlation function for the $n \bar{D}_{s0}^*(2317)$ interaction and the issue of elastic unitarity

TL;DR

This paper investigates the neutron interaction with the $D_{s0}^*(2317)$ resonance, modeled as a $DK$ molecule, using an improved Fixed Center Approximation to Faddeev equations that enforces elastic unitarity, revealing a potential new resonant state.

Contribution

It introduces an improved Fixed Center Approximation method that incorporates elastic unitarity around threshold for studying the $n ar D_{s0}^*(2317)$ interaction, providing new insights into possible resonant states.

Findings

Identification of a resonant state below threshold with 130 MeV binding and 80 MeV width.

Prediction of a correlation function peak that can be observed in $ar D o ext{invariant mass}$ measurements.

Encouragement for experimental searches in reactions like $ ext{p}f_1(1285)$ to explore the resonance's nature.

Abstract

We study the interaction of a neutron with the $\bar D_{s0}^*(2317)$ resonance and look at the amplitude below threshold and close above threshold. The study is done from the perspective that the $D_{s0}^*(2317)$ resonance is a molecular state of $DK$ in $I=0$. To study this interaction, we use the Fixed Center Approximation to Faddeev equations that considers the $DK$ molecule as the cluster and the neutron as the external particle. We improve the Fixed Center approach to implement elastic unitarity around threshold, which is needed to obtain scattering parameters and to evaluate the $n \bar D_{s0}^*(2317)$ correlation function that we determine here. One interesting result of the study is the appearance of a resonant state below threshold with a binding of about 130 MeV and a width of about 80 MeV, which we suggest to look at in reactions measuring the invariant mass of $\pi \Sigma \bar D$. The ALICE collaboration has initiated studies of this type, by looking at the $p f_1(1285)$ correlation function, and we can only encourage work in this direction which should provide much valuable information on the nature of many resonant states.