Can the Mechanism for ${\pi }_1\to \eta \pi ,{\eta }^{\mathrm{\prime }}\pi$ Hybrid Decays be Detected?

Two mechanisms for the ${\pi }_1$ ($J^{PC}=1^{-+}$) hybrid meson decay processes ${\pi }_1\to \eta \pi ,{\eta }^{\mathrm{\prime }}\pi$ are investigated. These mechanisms are applied to $\varphi \to \eta \gamma ,{\eta }^{\mathrm{\prime }}\gamma$ and $J\mathrm{/}\psi \to \eta \gamma ,{\eta }^{\mathrm{\prime }}\gamma$ decays to illustrate the validity of the decay mechanisms and to obtain independent information on the coupling of $\eta ,{\eta }^{\mathrm{\prime }}$ to quark and gluonic operators. From this information, we find that $\mathrm{\Gamma }({\pi }_1\to \eta \pi )\mathrm{/}\mathrm{\Gamma }({\pi }_1\to {\eta }^{\mathrm{\prime }}\pi )$ is substantially different in the two decay mechanisms, and hence future experimental measurements of this ratio will provide valuable information for substantiating the hybrid nature of these states and for determining the mechanism for these hybrid decays.