Effects of three-body ΛNN forces in light hypernuclei

Effects of the two-pion-exchange ΛNN force on the binding energies of Λ5He and Λ3H are examined in detail. This ΛNN force W consists of two parts: W = Wp + Ws, where Wp and Ws are due to the p-wave and s-wave π-Λ interaction, respectively. For Wp, the effect of Y1∗ (1385) is also taken into account. For Ws, a suppression factor of the s-wave π-Λ interaction is introduced in analogy to the π-N case. Since we do not know the short-range part of the ΛNN force, we introduce a cutoff radius d and W is set to be zero for ΛN distances less than d. The effect of Wp in Λ5He is found to be repulsive and quite appreciable. For instance, for d = 1F, it reduces the binding energy of Λ5He by about 2 MeV. This results in a substantial reduction in the overbinding of Λ5He that was obtained when only a two-body ΛN force was used that fitted Alexander et al.'s low-energy scattering parameters. Bulk of this contribution comes from the “tensor part” of Wp which has been ignored in previous works. Ws is unimportant provided the s-wave suppression factor is 10 or more. The ΛNN force plays only a minor role in Λ3H.