Bound states of ⁹φBe and ⁶φφHe with φ+α+α and φ+φ+α cluster models

We investigate the ⁹φBe and ⁶φφHe hypernuclei within the framework of the three-body cluster model %specifically as the φ+α+α and φ+φ+α systems, using the Faddeev formalism in configuration space. The φ-α potential is determined through a folding procedure of the HAL QCD φ-N interaction in the ⁴S3/2 channel with the matter distribution of ⁴He. The phenomenological α-α and φ-φ potentials are taken from the literature. Additionally, we construct a Wood-Saxon (WS) type interaction to simulate the φ-α potential, also taken from the literature, based on an effective Lagrangian approach that includes KK̄ meson loops in the φ-meson self-energy. A comparison of binding energies obtained for both types of the φ-α interactions reveals qualitative agreement. %between the obtained approaches. We predict the binding energy for the ⁹φBe and ⁶φφHe hypernuclei as the mirror φ+α+α and φ+φ+α systems in the range of 1-11 MeV and 3-10 MeV, respectively. The range of values of the binding energies relies on the choice of the WS φ-α interaction parameters.