ΛΛN−ΞNN S wave resonance

We use an existing model of theΛΛN−ΞNN three-body system based on two-body separable interactions to study the(I,JP)=(1/2,1/2+)three-body channel.For theΛΛ,ΞN,andΛΛ−ΞN amplitudes,we have constructed separable potentials based on the most recent results of the HAL QCD Collaboration.They are characterized by the existence of a resonance just below or above theΞN threshold in the H-dibaryon channel,(i,jp)=(0,0+).A three-body resonance appears 2.3 MeV above theΞd threshold.We show that if theΛΛ−ΞN H-dibaryon channel is not considered,theΛΛN−ΞNN S wave resonance disappears.Thus,the possible existence of aΛΛN−ΞNN resonance would be sensitive to theΛΛ−ΞN interaction.The existence or nonexistence of this resonance could be evidenced by measuring,for example,theΞd cross section.