Theoretical study of the $\Xi \alpha$ correlation function

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 ${}_{\Xi }^5\mathrm{H}$ 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.

7 pages, 6 figures, published version

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