Theoretical study on $\mathrm{\Lambda }\alpha$ and $\mathrm{\Xi }\alpha$ correlation functions

We examine the $\mathrm{\Lambda }$-${}^4\mathrm{H}\mathrm{e}$ ($\alpha$) and $\mathrm{\Xi }\alpha$ momentum correlation in high-energy collisions to further elucidate the properties of the hyperon-nucleon interactions. For the $\mathrm{\Lambda }\alpha$ system, we compare $\mathrm{\Lambda }\alpha$ 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 $\mathrm{\Lambda }\alpha$ momentum correlation can constrain the property of the $\mathrm{\Lambda }N$ interaction at short range, which plays an essential role in dense nuclear matter. For the $\mathrm{\Xi }\alpha$ system, we employ the folding $\mathrm{\Xi }\alpha$ potential based on the lattice QCD $\mathrm{\Xi }N$ interactions. The $\mathrm{\Xi }\alpha$ potential supports a Coulomb assisted bound state of ${}_{\mathrm{\Xi }}^5\mathrm{H}$ in the ${\mathrm{\Xi }}^{-}\alpha$ channel, while the ${\mathrm{\Xi }}^0\alpha$ channel is unbound. To examine the sensitivity of the correlation function to the nature of the $\mathrm{\Xi }\alpha$ 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 ${\mathrm{\Xi }}^{-}\alpha$ correlation.