(Field) symmetrization selection rules

QCD and QED exhibit an infinite set of three-point Green’s functions that contain only Okubo-Zweig-Iizuka (OZI) rule violating contributions, and (for QCD) are subleading in the large $N_c$ expansion. The Green’s functions describe the “decay” of a $J^{\mathrm{PC}}=\{1,3,5,\dots {\}}^{-+}$ exotic hybrid meson current to two $J=0\mathrm{}$ (hybrid) meson currents with identical P and C. We prove that the QCD amplitude for a neutral hybrid $\{1,3,5,\dots {\}}^{-+}$ exotic current to create $\eta {\pi }^0$ only comes from OZI rule violating contributions under certain conditions, and is subleading in $N_c.$