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

TL;DR

This study solves Faddeev equations for the $\xi NN$ bound-state problem using different baryon-baryon interaction models, finding a bound state only with the Nijmegen ESC08c potential, which could impact understanding of hyperon interactions.

Contribution

It provides a realistic calculation of the $\xi NN$ bound state using Faddeev equations and compares results across multiple interaction models, highlighting the potential for bound states with specific quantum numbers.

Findings

No bound state with Jülich-Bonn-München or HAL QCD potentials.

ESC08c potential predicts a bound state with $(T,J^{ ext{pi}})=(1/2, 3/2^+)$.

Decay into $\Lambda\Lambda N$ is suppressed for the bound state.

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.