Investigating three-body resonances in $\alpha\alpha\Omega/\Omega_{ccc}$ clusters within the $^{9}_{\Omega/\Omega_{ccc}}{\mathrm{Be}}$ nucleus

Abstract

We investigate the bound and resonant states of the $\alpha+\alpha+\Omega$ and $\alpha+\alpha+\Omega_{ccc}$ three-body systems, corresponding to $^{9}_{\Omega}{\mathrm{Be}}$ and $^{9}_{\Omega_{ccc}}{\mathrm{Be}}$, within the Gaussian expansion method combined with the complex scaling method. The $\alpha\Omega$ and $\alpha\Omega_{ccc}$ interactions are constructed by folding the $N\Omega$ and $N\Omega_{ccc}$ potentials obtained from lattice QCD calculations by the HAL QCD Collaboration with the nucleon density distribution of the $\alpha$ particle. The uncertainty associated with the $\alpha$-particle matter radius is also examined. For the $\Omega$ sector, the strong $N\Omega$ attraction generates deeply bound $0_1^+$, $2_1^+$, and $4_1^+$ states in $^{9}_{\Omega}{\mathrm{Be}}$, accompanied by a pronounced contraction of the $\alpha\alpha$ core, demonstrating a strong gluelike effect of the $\Omega$ baryon. An unconventional inversion between the $0_1^+$ and $4_1^+$ levels is also predicted. In contrast, the $\Omega_{ccc}$ baryon produces considerably weaker attraction: the $0_1^+$ state of $^{9}_{\Omega_{ccc}}{\mathrm{Be}}$ is weakly bound, whereas the $2_1^+$ and $4_1^+$ states remain resonances. Their resonance energies and widths exhibit a clear dependence on the strength of the $\alpha\Omega_{ccc}$ interaction. These results reveal qualitatively different gluelike behaviors of the $\Omega$ and $\Omega_{ccc}$ baryons and provide predictions for the spectroscopy of exotic multistrange and triply charmed hypernuclei.