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.

Figures (1)

• Figure 1: The upper ($a$) and ($b$) panels illustrate the distinct topological decompositions of the fully interacting $\phi NNN$ and $\phi NNNN$ clusters, respectively, into their substructures. The lower panel presents the Jacobi coordinate systems associated with each of these cluster partitions. Low panels: ($a$) K-like and H-like components, as $\Phi^l_{12,3}$ and $\Phi^l_{12,34}$, respectively. Permuting the particle indices yields 12 $\mathcal{K}$-type components and 6 $\mathcal{H}$-like components; ($b$) The five independent 5-body FYE components are denoted as K, H, T, S, F. The permutation of particle indexes gives 60 K-type amplitudes and 30 for each H, T, S, and F-type amplitudes Lazauskas2018aLazauskas2018b. Ultimately, this yields a system of 180 Faddeev-Yakubovsky equations.