Modification of Kawai model about the mixing of the pseudoscalar mesons

The Kawai model describing the glueball-quarkonia mixing is modified. The mixing of $\eta$, $\eta^\prime$ and $\eta(1410)$ is re-investigated based on the modified Kawai model. The glueball-quarkonia content of the three states is determined from a fit to the data of the electromagnetic decays involving $\eta$, $\eta^\prime$. Some predictions about the electromagnetic decays involving $\eta(1410)$ are presented.