Dynamically generated states from the $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$, and $K{K}^{\ast }{\bar{K}}^{\ast }$ systems within the fixed-center approximation

Abstract

The three-body systems $\eta K^{\ast }{\bar{K}}^{\ast }$, $\pi K^{\ast }{\bar{K}}^{\ast }$, and $K{K}^{\ast }{\bar{K}}^{\ast }$ are further investigated within the framework of fixed-center approximation, where $K^{\ast }{\bar{K}}^{\ast }$ is treated as the fixed-center, corresponding to the possible scalar meson $a_0(1780)$ or the tensor meson $f_2^{\prime }(1525)$. The interactions between $\eta$, $\pi$, $K$, and $K^{\ast }$ are taken from the chiral unitary approach. The resonance structures appear in the modulus squared of the three-body scattering amplitude and suggest that $\eta /\pi /K$-$(K^{\ast }{\bar{K}}^{\ast }{)}_{a_0(1780)/f_2^{\prime }(1525)}$ hadron state can be formed. By scattering the $\eta$ meson on the fixed-center $(K^{\ast }{\bar{K}}^{\ast }{)}_{a_0(1780)}$, it is found that there is a distinct peak around 2100 MeV, as shown in the modulus squared of the three-body scattering amplitude, which can be associated with the meson $\pi (2070)$. For the scattering of the $\eta$ meson on the $(K^{\ast }{\bar{K}}^{\ast }{)}_{f_2^{\prime }(1525)}$, a resonance structure around 1890 MeV is found and it can be associated with the ${\eta }_2(1870)$ meson. Other resonance structures are also found and can be associated with ${\pi }_2(1880)$ and $\eta (2010)$.

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