The possible bound state of the $\varphi N\text{−}\alpha$ system is explored within the framework of the three-body cluster model. The calculations are done by employing the state-of-the-art $\varphi N$ interactions obtained from the analysis of the pure elastic scattering and the coupled-channel in the $\varphi p$ correlation functions. The $\varphi \alpha$ potentials are constructed by two methods: the single-folding potential (SFP) method for the given spin-averaged $\varphi N$ potentials in coordinate space, and the optical-model potential (OMP) approximation within the multiple-scattering framework for the given scattering length of the $\varphi N$ interaction. It is found that, when only the single-channel $\varphi N$ interactions are employed, the $\varphi N\text{−}\alpha$ system could be bound with a binding energy in the interval [3–26] MeV. However, the coupled-channel $\varphi p$ interaction, which is most consistent with experimental measurements, does not yield any bound state, even when the spin-averaged $\varphi N$ potential is employed, and this potential is found to be more attractive than the corresponding coupled-channel counterpart. It is essential to consider the contributions from the dynamics of the vector-baryon coupled channels $\varphi p$ interaction. This effect is capable of playing a decisive role in the existence of mesic nuclei.

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• Few-body systems
• Hypernuclei & mesic nuclei
• Nucleon-nucleon interactions
• Particle interactions