Within the framework of the Faddeev formalism in configuration space, we investigate bound states in the $\varphi NN$ system with total isospin $T=0$ and $T=1$. The recently proposed lattice HAL QCD $\varphi N$ potential in the ${{}^{4}S}_{3/2}$ channel does not support either $\varphi N$ or $\varphi NN$ bound states. The HAL QCD $\varphi N$ potential in the ${{}^{2}S}_{1/2}$ channel suggests the bound states for $\varphi N$ and $\varphi NN(S=0)$ systems. However, the binding energies are highly sensitive to variations of the enhancement factor $\beta$, and the $\varphi NN$ system is extremely strongly bound in the state $S=0$. Considering a spin-averaged potential for the state $S=1$ yields a bound state for the ${}_{\varphi }{}^3\mathrm{H}$ ($S=1$) hypernucleus with the binding energy (BE) 14.9 MeV when $\beta =6.9$. The evaluation of the BE for the $S=1$, $T=1$ three-body state results in 5.47 MeV. Additionally, calculations using our approach confirm the bound states for the $\varphi NN$ ($S=2$, $T=0$ and $S=1$, $T=1$) system previously predicted with the Yukawa-type potential motivated by the QCD van der Waals attractive force, mediated by multigluon exchanges.

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• Mesons
• Few-body systems
• Lattice QCD