Three-body resonances of $\alpha \alpha M$ clusters ($M=\varphi$, $J/\psi$, ${\eta }_c$) in ${}_M^8\mathrm{Be}$ nuclei

Abstract

Motivated by the recently obtained HAL QCD potentials for the $N$-$\varphi$, $N$-$J/\psi$, and $N$-${\eta }_c$ interactions, we investigate the structure of the exotic nuclei ${}_{\varphi }^8\text{Be}$, ${}_{J/\psi }^8\text{Be}$, and ${}_{{\eta }_c}^8\text{Be}$ as $\alpha +\alpha +M$ three-body systems ($M$ denotes the meson). The bound and resonant states are calculated consistently using the Gaussian expansion method, with resonances identified via the complex scaling method. For the $\alpha \varphi$ and $\alpha$-charmonium interactions, a folding potential is constructed based on the HAL QCD potentials and fitted to a Woods-Saxon form. We find that the $\varphi$ meson exhibits a strong ``glue-like" effect, binding the $0_1^{+}$, $2_1^{+}$, and $4_1^{+}$ resonant states of ${}^8$Be into stable states and significantly reducing the $\alpha$-$\alpha$ distance. In contrast, the interactions of $J/\psi$ and ${\eta }_c$ with the nucleus are weaker, forming only shallow bound states with the $0_1^{+}$ state of ${}^8$Be and even increasing the $\alpha$-$\alpha$ separation. Notably, our analysis predicts weakly bound $\alpha$-$J/\psi$ states in the ${}^4{S}_{3/2}$ and ${}^2{S}_{1/2}$ channels, a result not reported in prior studies, which suggests that ${}_{J/\psi }^8\text{Be}$ may not be a Borromean nucleus. The sensitivity of the ${}_M^8\mathrm{Be}(4_1^{+})$ state-transitioning from bound to resonant depending on the $\alpha$-particle radius-highlights the subtle dynamics at play. These results provide a systematic theoretical comparison of how different vector mesons modify nuclear clustering, offering critical predictions for future experimental searches of such exotic hadron-nucleus systems.

Comments: 11 pages, 6 figures and 4 tables