Theoretical study on $\Xi\alpha$ correlation function

TL;DR

This paper investigates the $\Xi ext{-} ext{He}$ correlation functions in high-energy nuclear collisions using lattice QCD-based potentials to understand $\Xi N$ interactions and bound states.

Contribution

It provides a theoretical analysis of $\Xi ext{-} ext{He}$ correlations with potentials derived from lattice QCD, highlighting the sensitivity to bound states and interaction strength.

Findings

Correlation functions are sensitive to the existence of bound states.

The $\Xi^0 ext{-} ext{He}$ channel shows unbound behavior, while $\Xi^- ext{-} ext{He}$ supports a Coulomb-assisted bound state.

Repulsive core effects produce distinctive dips in the correlation at intermediate momenta.

Abstract

We study $\Xi$-$^4{\mathrm{He}}$ ($\alpha$) momentum correlation functions in the high-energy nuclear collisions to investigate the nature of the $\Xi N$ interactions. We employ the folding $\Xi \alpha$ potential based on the lattice QCD $\Xi N$ interactions to compute the correlation function. The $\Xi \alpha$ potential supports a Coulomb-assisted bound state ${}^5_{\Xi}\mathrm{H}$ 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 $\Xi \alpha$ interaction, we vary the potential strength simulating stronger and weaker interactions. The result of the correlation function is sensitive to the existence of the bound state in the $\Xi^0 \alpha$ channel, and the characteristic behavior of the bound state remains also in the $\Xi^-\alpha$ correlation with the Coulomb interaction. The effect of the repulsive core of the $\Xi\alpha$ potential can be found in the correlation from the small source as the distinctive dip in the intermediate momentum region.