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

TL;DR

The paper investigates the interaction of a neutron with the molecular $\bar{D}_{s0}^*(2317)$, treated as a $DK$ bound state in $I=0$, using an improved Fixed Center Approximation to enforce elastic unitarity near threshold and to compute the $n\,\bar{D}_{s0}^*(2317)$ scattering parameters and correlation function. A coherent, unitarized three-body treatment yields a notable resonance below threshold with binding around $130\,\mathrm{MeV}$ and width about $80\,\mathrm{MeV}$, arising from $\bar{K}N\to\pi\Sigma$ dynamics rather than a narrow elementary decay. The near-threshold amplitude provides a scattering length $a = 0.60 - i 0.29\ \mathrm{fm}$ and effective range $r_0 = 1.14 - i 0.11\ \mathrm{fm}$, and the calculated correlation function $C(p)$ exhibits a strong structure for a Gaussian source with $R\sim 1$ fm, consistent with a bound-state scenario. The results offer a concrete, experimentally accessible signature to test the molecular interpretation of $D_{s0}^*(2317)$ via correlation measurements and related observables in high-energy collisions.

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 $πΣ\bar D$. 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.

Figures (4)

• Figure 1: Diagrams appearing in the FCA to the $n(\bar{D}\bar{K})_{\text{cluster}}$ interaction.
• Figure 2: Terms entering the coherent propagator of the $n\bar{D}_{s0}^{*}$.
• Figure 3: The scattering amplitude $\tilde{T}^\prime_{\text{sum}}$ for the $n \bar{D}_{s0}^*(2317)$ interaction as a function of $\sqrt{s}$. The red dashed line shows the real part of the amplitude $\tilde{T}^\prime_\text{sum}$, the blue dotted line the imaginary part of $\tilde{T}^\prime_\text{sum}$, and the black solid line the modulus squared of $\tilde{T}^\prime_\text{sum}$. The vertical lines indicate the $n \bar{D}_{s0}^*(2317)$ threshold and the appearance of the $\pi \Sigma$ channel in $\bar{K} n \to \pi \Sigma$, corresponding to $s_2$ of Eq. \ref{['eq:s1s2']}.
• Figure 4: The correlation function of $n \bar{D}_{s0}^*(2317)$ for the different value of $R$.