Bounds on rare decays of η and η′ mesons from the neutron EDM

We provide model-independent bounds on the rates of rare decays η(η′)→ππ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological η(η′)ππ couplings, the nEDM arises at the two-loop level. The leading-order relativistic chiral perturbation theory calculation with the minimal photon coupling to charged pions and a proton inside the loops leads to a finite, counterterm-free result. This is an improvement upon previous estimates which used approximations in evaluating the two-loop contribution and were plagued by divergences. While constraints on the η(η′)ππ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD θ term, our calculation means that whatever the origin of these couplings, the decays η(η′)→2π will remain unobservable in the near future.