A Realistic Approach to the $\Xi NN$ Bound-State Problem based on Faddeev Equation

Abstract

The Faddeev equations for the $\Xi NN$ bound-state problem are solved where the three $S$=$-2$ baryon-baryon interactions of J\"ulich-Bonn-M\"unchen chiral EFT, HAL QCD and Nijmegen ESC08c are used. The $T$-matrix $T_{\Xi N, \Xi N}$ obtained within the original $\Lambda\Lambda$-$\Xi N$-$\Sigma\Sigma$ $/$ $\Xi N$-$\Lambda \Sigma$-$\Sigma\Sigma$ coupled-channel framework is employed as an input to the equations. We found no bound state for J\"ulich-Bonn-M\"unchen chiral EFT and HAL QCD but ESC08c generates a bound state with the total isospin and spin-parity $(T,J^{\pi})=(1/2, 3/2^+)$ where the decays into $\Lambda\Lambda N$ are suppressed.