Nucleon EDM and rare decays of eta mesons

I consider rare CP-violating decay modes $\eta(\eta')\to\pi\pi$ and note that an interaction that leads to such decays would necessarily induce a nucleon electric dipole moment (EDM). The experimental limits for the corresponding branching ratios are quite soft. I relate these decay branching ratios to the value of the induced nucleon EDM and translate the experimental limits on the neutron EDM into much more stringent constraints on these decay rates: $\frac{\Gamma_{\eta\to\pi\pi}}{\Gamma_\eta}\lesssim3.5\times10^{-14}$ and $\frac{\Gamma_{\eta'\to\pi\pi}}{\Gamma_\eta'}\lesssim1.8\times10^{-17}$.