Possible Existence of $^3_\phi$H, $^4_\phi$H, $^4_\phi$He, and $^5_\phi$He Nuclei

Motivated by recent HAL QCD simulations of the $\phi N$ 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 $^4_\phi\mathrm{H}$, $^4_\phi\mathrm{He}$, and $^5_\phi\mathrm{He}$ nuclei by performing calculations for $\phi$-mesic $\phi NNN$ and $\phi NNNN$ systems. Both spin-dependent and spin-independent $\phi N$ interactions are considered, leading to deeply and moderately bound states, respectively. The deeply bound states originate from the strong attraction in the $^2S_{1/2}$ $\phi N$ channel. Coulomb shifts of the binding energies are evaluated. Our findings provide the binding mechanism and demonstrate the importance of short-range $\phi N$ attraction.