The three-body $\eta K^{*}{\overline{K}}^{*}$, $\pi K^{*}{\overline{K}}^{*}$, and $K{K}^{*}{\overline{K}}^{*}$ systems are investigated within the framework of fixed-center approximation to the Faddeev equations, where $K^{*}{\overline{K}}^{*}$ is treated as the scalar meson $f_0(1710)$. The interactions between $\pi$, $\eta$, $K$, and $K^{*}$ are taken from the chiral unitary approach. By scattering the $\eta$ meson on the clusterized $(K^{*}{\overline{K}}^{*}{)}_{f_0(1710)}$ system, we find a peak in the modulus squared of the three-body scattering amplitude and it can be associated as a bound state with quantum numbers $I^G(J^{PC})=0^{+}(0^{-+})$. Its mass and width are around 2054 and 60 MeV, respectively. This state could be associated with the $\eta (2100)$ meson. For the $\pi (K^{*}{\overline{K}}^{*}{)}_{f_0(1710)}$ scattering, we find a bump structure around 1900–2000 MeV with quantum numbers $1^{-}(0^{-+})$, while for the $K(K^{*}{\overline{K}}^{*}{)}_{f_0(1710)}$ system, there are three structures. One of them is quite stable and its mass is about 2130 MeV. It is expected that these theoretical predictions here could be tested by future experimental measurements, such as by the BESIII, BelleII, and LHCb Collaborations.

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• Multiquark bound states
• Particle interactions
• Phenomenology
• QCD phenomenology