Towards the assignment for the $4^1{S}_0$ meson nonet

Abstract

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 $4^1{S}_0$ $q\bar{q}$ 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 $4^1{S}_0$ kaon is phenomenologically determined to has a mass of about 2153 MeV. The width of this unobserved kaon is expected to be about 197 MeV in the ${}^3{P}_0$ decay model.

Comments: 15 pages, 5 figures, version accepted for publication in Physical Review D