Vector-meson contributions do not explain the rate and spectrum inKL→π0γγ

We analyze the recent NA48 data for the reaction $K_L\to {\pi }^0\gamma \gamma$ with and without the assumption of vector meson dominance (VMD). We find that the data are well described by a three-parameter expression inspired by $\mathcal{O}{(p}^6)$ chiral perturbation theory. We also find that it is impossible to fit the shape of the decay distribution and the overall rate simultaneously if one imposes the VMD constraints on the three parameters. We comment on the different fits and their implications for the $\mathrm{CP}$-conserving component of the decay $K_L\to {\pi }^0{e}^{+}{e}^{-}.$