Theoretical study on $\Lambda\alpha$ and $\Xi\alpha$ correlation functions

TL;DR

This study uses momentum correlation functions in high-energy collisions to investigate hyperon-nucleon interactions, revealing how different potential models affect observable correlations and indicating the presence of bound states.

Contribution

It provides a theoretical analysis of $\Lambda ext{-} ext{He}$ and $\Xi ext{-} ext{alpha}$ correlation functions, linking potential models to measurable momentum correlations and bound state signatures.

Findings

$\Lambda ext{-} ext{He}$ correlation constrains short-range $\Lambda N$ interactions.

$\Xi ext{-} ext{alpha}$ correlation reflects the bound state in the $\Xi^- ext{-} ext{alpha}$ channel.

Potential models influence the shape of the correlation functions.

Abstract

We examine the $\Lambda$-${}^4\mathrm{He}$ ($\alpha$) and $\Xi \alpha$ momentum correlation in high-energy collisions to further elucidate the properties of the hyperon-nucleon interactions. For the $\Lambda\alpha$ system, we compare $\Lambda\alpha$ potential models with different strengths at short range. We find that the difference among the models is visible in the momentum correlation from a small-size source. This indicates that the $\Lambda\alpha$ momentum correlation can constrain the property of the $\Lambda N$ interaction at short range, which plays an essential role in dense nuclear matter. For the $\Xi\alpha$ system, we employ the folding $\Xi \alpha$ potential based on the lattice QCD $\Xi N$ interactions. The $\Xi \alpha$ potential supports a Coulomb assisted bound state of ${}^5_{\Xi}\mathrm{H}$ in the $\Xi^-\alpha$ channel, while the $\Xi^0\alpha$ channel is unbound. To examine the sensitivity of the correlation function to the nature of the $\Xi \alpha$ potential, we vary the potential strength simulating stronger and weaker interactions. The result of the correlation function clearly reflects the bound state nature in the $\Xi^-\alpha$ correlation.