A Bound on $m_{\eta }\mathrm{/}{m}_{{\eta }^{\mathrm{\prime }}}$ for Large $N_C$

If the number of colors is large, the ratio $m_{\eta }\mathrm{/}{m}_{{\eta }^{\mathrm{\prime }}}$ is bounded from above. The bound is not satisfied by the observed $\eta$ and ${\eta }^{\mathrm{\prime }}$ masses.