We study the problem of pseudoscalar mixing in an ${\mathrm{SU}\left(4\right)\mathrm{}\times \mathrm{SU}\left(4\right)\mathrm{}\times \mathrm{U}}_A\mathrm{}\left(1\right)\mathrm{}$ breaking framework. In this connection, we derive the condition of a vanishing $c\overline{c}$ component in the η,${\mathrm{\eta }}^{\prime }$ wave functions. We also obtain new constraints obeyed by the mixed decay constants $f_{\eta ,{\eta }^{\prime }}^q\mathrm{}(q=u,s),$ which determine the octet-singlet mixing angles. In the $\eta {\eta }^{\prime }{\eta }_c$ sector we find from a fit to the radiative decay rates of mesons that the presence of a $c\overline{c}$ admixture in ${\mathrm{\eta }}^{\prime }$ is small in disagreement with the point of view that the branching ratio of $\overrightarrow{B}{\eta }^{\prime }K$ is enhanced by ${\eta }^{\prime }{\eta }_c$ mixing.

• Received 29 December 1998

DOI:https://doi.org/10.1103/PhysRevD.60.074002