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

The Faddeev equations for the $Xi NN$ bound-state problem are solved where the three $S$=$-2$ baryon-baryon interactions of Julich-Bonn-Munchen chiral EFT, HAL QCD and Nijmegen ESC08c are used. The $T$-matrix $T_{Xi N, Xi N}$ obtained within the original $LambdaLambda$-$Xi N$-$SigmaSigma$ $/$ $Xi N$-$Lambda Sigma$-$SigmaSigma$ coupled-channel framework is employed as an input to the equations. We found no bound state for Julich-Bonn-Munchen 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 $LambdaLambda N$ are suppressed.