Possible Existence of $^3_ϕ$H, $^4_ϕ$H, $^4_ϕ$He, and $^5_ϕ$He Nuclei

Abstract

Motivated by recent HAL QCD simulations of the $ϕN$ interaction in the $^4S_{3/2}$ channel and its modification in the $^2S_{1/2}$ channel, we develop a first-principles few-body framework that embeds these potentials into configuration-space Faddeev--Yakubovsky equations. We predict bound $^4_ϕ\mathrm{H}$, $^4_ϕ\mathrm{He}$, and $^5_ϕ\mathrm{He}$ nuclei by performing calculations for $ϕ$-mesic $ϕNNN$ and $ϕNNNN$ systems. Both spin-dependent and spin-independent $ϕN$ interactions are considered, leading to deeply and moderately bound states, respectively. The deeply bound states originate from the strong attraction in the $^2S_{1/2}$ $ϕN$ channel. Coulomb shifts of the binding energies are evaluated. Our findings provide the binding mechanism and demonstrate the importance of short-range $ϕN$ attraction.