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A narrow $DNN$ quasi-bound state

The energies and widths of $DNN$ quasi-bound states with isospin I=1/2 are evaluated in two methods, the fixed center approximation to the Faddeev equation and the variational method approach to the effective one-channel Hamiltonian. The $DN$ interactions are constructed so that they dynamically generate the $Λ_c(2595)$ (I=0, $J^π =1/2^-$) resonance state. We find that the system is bound by about 250 MeV from the $DNN$ threshold, $\sqrt{s} \sim 3500$ MeV. Its width including both the mesonic decay and the $D$ absorption, is estimated to be about 20-40 MeV. The I=0 $DN$ pair in the $DNN$ system is found to form a cluster that is similar to the $Λ_c(2595)$.