$\phi NN$ bound states within the spin-averaged HAL QCD potential model

The interaction between the $\phi$ meson and the nucleon has recently been derived from (2+1)-flavor lattice QCD simulations with nearly physical quark masses. The HAL QCD potentials are defined for the $\phi N(^2S_{1/2})$ and $\phi N(^4S_{3/2})$ channels. These interactions lead to three-body bound states, $\phi NN(0(0^-))$ and $\phi NN(0(1^-))$. In the full model, the $(0(1^-))$ state involves coupling between the two $\phi N$ channels. A unitary transformation of the spin--isospin basis in the $YNN$ system allows for the construction of an averaged effective potential model. A similar reduction applied to the $\phi NN(0(1^-))$ configuration leads to a simplified bosonic-like model. Faddeev calculations are performed within this averaged model and compared with results obtained from the full coupled-channel treatment. The two approaches are shown to produce identical binding energies for the $\phi NN(0(1^-))$ state. The relation between the binding energies of the $\phi NN(0(0^-))$ and $\phi NN(0(1^-))$ systems is also discussed.