Axial-Vector-Meson Dominance and a New Estimate for the DecayK+→π+γγ

The radiative decay mode $K^{+}\to {\pi }^{+}\gamma \gamma$ is studied within the framework of an axial-vector dominance model (AVDM) with the exchange of the ${A_1}^{+}\mathrm{}\left(1070\right)\mathrm{}$, $B^{+}\mathrm{}\left(1235\right)\mathrm{}$, and ${K_A}^{+}\mathrm{}\left(1320\right)\mathrm{}$ dominating the decay. We obtain a new estimate for the branching ratio $R=\frac{\Gamma (K^{+}\to {\pi }^{+}\gamma \gamma )}{\Gamma (K^{+}\to \mathrm{all})}=1.5\mathrm{}\times {10}^{-5\mathrm{}}-2.1\mathrm{}\times {10}^{-4\mathrm{}}$ depending on the $d$-wave-to-$s$-wave ratio in axial-vector-meson decays. For a modest amount of $d$ wave, the AVDM result is comparable to the value for $R$ based on the ${\pi }^0$-pole model and is also in good agreement with experiment. The ${\pi }^{+}$ energy spectrum is also calculated using AVDM and compared with the spectrum found in the ${\pi }^0$-pole model. The significance of these results for the testing of a proposed mechanism for $K^{+}\to {\pi }^{+}{\pi }^0$ is also discussed.