K20→π0+2γDecay

Abstract

It is pointed out that if the experimentally reported large branching ratio of ${\eta }^0\to {\pi }^0+2\mathrm{}\gamma$ decay is indeed correct, it may also suggest a large branching ratio for the ${K_2}^0\to {\pi }^0+2\mathrm{}\gamma$ decay. The closeness of the masses of the $K^0$ meson and the ${\eta }^0$ meson, together with this unexpectedly large coupling constant of the ${\eta }^0\to {\pi }^0+2\mathrm{}\gamma$ decay implies that the diagram ${K_2}^0\to {\eta }^0\to {\pi }^0+2\mathrm{}\gamma$ may lead to a relatively large branching ratio of the ${K_2}^0\to {\pi }^0+2\mathrm{}\gamma$ decay, contrary to our usual expectation. Simple calculation based on the pole model with the $\mathrm{SU}\left(3\right)\mathrm{}$ symmetry indicates that the frequency of this mode is at least comparable with or may even be larger than that of ${K_2}^0\to 2\gamma$ decay. Furthermore, since both the ${K_2}^0\to 2{\pi }^0$ and the ${K_2}^0\to {\pi }^0+2\mathrm{}\gamma$ decays are essentially $4\gamma$ processes, the decay ${K_2}^0\to {\pi }^0+2\mathrm{}\gamma$ could constitute an important background for the ${K_2}^0\to 2{\pi }^0$ experiments if its rate is comparable with that of ${K_2}^0\to 2{\pi }^0$ decay. Some kinematical features of this decay are also discussed.