Possible existence of aπ−nnbound state

We have applied the relativistic Faddeev formalism to look for a bound state of a negative pion and two neutrons, using as input the pion-nucleon $P_{33}$ channel and the nucleon-nucleon ${}_{}{}^1{}_{}{}^{}S_0^{}{}_{}{}^{}$ channel. We found that if the pion-nucleon interaction is sufficiently short ranged, the system can be bound. We represented the pion-nucleon interaction with two different models of rank-one separable potentials, while for the nucleon-nucleon interaction we used the Yamaguchi potential and three different models of rank-two separable potentials.