Probing $ ϕ$N interaction through bound states of _ϕ⁶He mesic nuclei within ϕN-α cluster model

The spin dependence of the $ ϕ$N interaction is explored through the bound states of ϕN-α mesic nuclei with $α$ being a spectator to attract the $ ϕ$N pair without changing its spin structure. The bound state of _ϕ⁶He mesic nuclei is calculated within the framework of the developed three-body cluster model by solving the Faddeev equations in the method of hyperspherical harmonics (HH) expansions. The calculations are done by employing the state-of-the-art $ ϕ$N potential obtained from lattice QCD calculations and correlation function analysis for the ⁴S3/2 and ²S1/2 channels. The $ ϕα$ potential is constructed through a folding procedure of the spin-averaged $ ϕ$N interaction with the matter distribution of ⁴He. And for N$α$ potential two common types of N$α$ interactions are taken from the literature with central and spin-orbit components. The central binding energies of the ϕN-α bound states in the spin 3/2(1/2) channel are found to be ~ 10 (25) and 11 (13) MeV at Euclidean times $ t/a=12 $ and $14$, respectively. As well as, the corresponding nuclear matter radii are estimated to be ~ 4.5 (1.7) and 4.6 (1.8) fm.