On a possible ³φH hypernucleus with HAL QCD interaction

Within the framework of the Faddeev formalism in configuration space, we investigate bound states in the φ NN system with total isospin $T=0$ and $T=1$. The recently proposed lattice HAL QCD φ N potential in the ⁴S3/2 channel does not support either φ N or φ NN bound states. The HAL QCD φ N potential in the ²S1/2 channel suggests the bound states for φ N and φ NN (S=0) systems. However, the binding energies are highly sensitive to variations of the enhancement factor β, and the φ NN system is extremely strongly bound in the state $S=0$. Considering a spin-averaged potential %(1/3Vφ N1/2+2/3Vφ N3/2) for the state $S=1$ yields a bound state for ³_φH $(S=1)$ hypernucleus with the binding energy (BE) 14.9 MeV when β = 6.9. The evaluation of the BE for the $S=1$, $T=1$ three-body state results in 5.47 MeV. %Also, We evaluated the BE for the $S=1$, $T=1$ three-body state as 5.47 MeV. Additionally, calculations using our approach confirm the bound states for the φ NN ($S=2,T=0$ and $S=1, T=1$) system previously predicted with the Yukawa-type potential motivated by the QCD van der Waals attractive force, mediated by multi-gluon exchanges.