Pion-Pole Mechanism and the Application of the Veneziano Model toK20→π+π−γDecay

The $\mathrm{CP}$-conserving decay mode ${\pi }^{+}{\pi }^{-}\gamma$ of the ${K_2}^0$ is calculated in the pion-pole model (with $\eta -{\pi }^0$ mixing) with the strong-interaction part of the decay amplitude described by the Veneziano model. Because of sign ambiguities introduced by a model of physical $\mathrm{PVV}$ couplings (which fits both ${\pi }^0\to 2\gamma$ and $\eta \to 2\gamma$ rates) and the unknown sign of $\eta -{\pi }^0$ mixing relative to the weak $K-\pi$ mixing, values of the branching ratio $r\left(\frac{({K_2}^0\to {\pi }^{+}{\pi }^{-}\gamma )}{({K_2}^0\to \mathrm{all}\mathrm{modes})}\right)$ are obtained ranging from 7.6×${10}^{-5\mathrm{}}$ to 3.1×${10}^{-4\mathrm{}}$, but all are consistent with the present experimental upper limit of 4×${10}^{-4\mathrm{}}$.