Strange dibaryon resonance in the K ¯ NN - π Y N system

Three-body resonances in the $\overline{K}\mathit{NN}$ system have been studied within a framework of the $\overline{K}\mathit{NN}$-$\ensuremath{\pi}YN$ coupled-channel Faddeev equation. By solving the three-body equation, the energy dependence of the resonant $\overline{K}N$ amplitude is fully taken into account. The $S$-matrix pole has been investigated from the eigenvalue of the kernel with the analytic continuation of the scattering amplitude on the unphysical Riemann sheet. The $\overline{K}N$ interaction is constructed from the leading order term of the chiral Lagrangian using relativistic kinematics. The $\ensuremath{\Lambda}(1405)$ resonance is dynamically generated in this model, where the $\overline{K}N$ interaction parameters are fitted to the data of scattering length. As a result we find a three-body resonance of the strange dibaryon system with binding energy $B~79$ MeV and width $\ensuremath{\Gamma}~74$ MeV. The energy of the three-body resonance is found to be sensitive to the model of the $I=0$ $\overline{K}N$ interaction.