Constructing new pseudoscalar meson nonets with the observed $X(2100)$, $X(2500)$, and $\eta(2225)$

Stimulated by the BESIII observation of $X(2100)$, $X(2500)$, and $\eta(2225)$, we try to pin down new pseudoscalar meson nonets including these states. The analysis of mass spectra and the study of strong decays indicate that $X(2120)$ and $\eta(2225)$ associated with $\pi(2070)$ and the predicted kaon $K(2150)$ may form a new pseudoscalar meson nonet. In addition, more experimental data for $X(2100)$ are necessary to determine its structure of nonets. Then, $X(2500)$, $X(2370)$, $\pi(2360)$, and the predicted kaon $K(2414)$ can be grouped into another new nonet. These assignments to the discussed pseudoscalar states can be further tested in experiment.