$\mathrm{\Xi }$-deuteron low-energy $s$-wave phase shifts and momentum correlation functions in Faddeev formulation

The low-energy $\mathrm{\Xi }$-deuteron scattering is investigated through the solution of Faddeev equations, employing three sets of the currently available parametrization of the $\mathrm{\Xi }$-nucleon interactions. One of these is the chiral NLO interaction parametrized by the Jülich group, and the other two are based on the calculations by the HAL-QCD method. The $s$-wave phase shifts in the $J=3\mathrm{/}2$ and $J=1\mathrm{/}2$ states are presented. Three-body wave functions in coordinate space are constructed from the Faddeev amplitudes in momentum space. These functions are used in the calculation of $\mathrm{\Xi }d$ momentum correlation functions. The effects of the deuteron breakup are significant in the $J=3\mathrm{/}2$ channel. The differences in the magnitude of the calculated correlation function show the quantitative difference of the $\mathrm{\Xi }N$ interactions in the spin-isospin channels. The prospective experimental data on the $\mathrm{\Xi }d$ momentum correlation function could contribute to a better description of the $\mathrm{\Xi }N$ interactions.