KKN and KKN Molecular States with I=1/2, 3/2 and J^P=1/2⁺ Studied with Three-Body Faddeev Calculations

Using the Akaishi–Yamazaki (AY) and Hyodo–Weise (HW) effective KK, KN, KK and KN interactions, we study possible existence of KKN and KKN molecule states with I=1/2, 3/2 and J^P=1/2⁺ by means of three−body Faddeev equations. We find that for HW potential, KKN and KKN systems with I=1/2 both are bound hadron molecular states with about 10 MeV binding energy. The relativistic effects of kinetic energy are of the order of 4–5 MeV. AY potential would give larger binding energy because of overestimating KN interaction strength. Although there are attractive interactions in the case of I=3/2, the interaction is too weak to bind the systems.