Possible Existence of ${}_{\varphi }^3$H, ${}_{\varphi }^4$H, ${}_{\varphi }^4$He, and ${}_{\varphi }^5$He Nuclei

Abstract

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

6 pages, 1 figure

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