Probing ϕN interaction through bound states of _ϕ^6He mesic nuclei within ϕN-α cluster model

The spin dependence of the ϕN interaction is explored through the bound states of ϕN-α mesic nuclei with α being a spectator to attract the ϕN pair without changing its spin structure. The bound state of _ϕ^6He 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 ϕN 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 ϕN interaction with the matter distribution of ^4He. And for Nα potential two common types of Nα 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.