Some Comments and a Prediction Concerning the DecayK20→γγ

It is shown how only pseudoscalar (${\pi }^0,\eta$) and vector ($K^{*\mathrm{}\left(6\right)\mathrm{}}$) poles need be considered in a pole-model analysis of the decay ${K_2}^0\to \gamma \gamma$. The calculation of the decay amplitude is presented in detail, both in an $\mathrm{SU}\left(3\right)\mathrm{}$-symmetric model of $\mathrm{VVP}$ couplings with $\phi \omega$ mixing, and in a model (due to Arnowitt et al.) of PCAC breakdown with partial $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry, which fits the decay rates of ${\pi }^0\to \gamma \gamma$ and $\eta \to \gamma \gamma$ reasonably well. It is found that the pseudoscalar and vector contributions add, instead of partially canceling as claimed by earlier workers, so that theory and experiment are no longer in reasonable agreement. Moreover, a separate calculation of the important vector pole contribution to the decay amplitude in the free-field quark model yields no significant diminution of its $\mathrm{SU}\left(3\right)\mathrm{}$ magnitude.