The strong decays of the $\pi (2070)$, $\eta (2010)$, $\eta (2100)$, $\eta (2190)$, and $\eta (2225)$ as the $4{}^{1}S_0$ quark-antiquark states are investigated in the framework of the ${}^{3}P_0$ meson decay model. It is found that the $\pi (2070)$, $\eta (2100)$, and $\eta (2225)$ appear to be the convincing $4{}^{1}S_0$ $q\overline{q}$ states, while the assignment of the $\eta (2010)$ and $\eta (2190)$ as the $4{}^{1}S_0$ isoscalar states is not favored by their widths. In the presence of the $\pi (2070)$, $\eta (2100)$, and $\eta (2225)$ being the members of the $4{}^{1}S_0$ meson nonet, the mass of the $4{}^{1}S_0$ kaon is phenomenologically determined to be about 2153 MeV. The width of this unobserved kaon is expected to be about 197 MeV in the ${}^{3}P_0$ decay model.

• Received 20 May 2008

DOI:https://doi.org/10.1103/PhysRevD.78.054013