Bounds on rare decays of $\eta$ and $\eta^\prime$ mesons from the neutron EDM

Understand

We provide model-independent bounds on the rates of rare decays $\eta (\eta^\prime) \to \pi\pi$ based on experimental limits on the neutron electric dipole moment (nEDM).

• Starting from phenomenological $\eta(\eta^\prime) \pi\pi$ couplings, the nEDM arises at two loop level.
• The leading-order relativistic ChPT calculation with the minimal photon coupling to charged pions and a proton inside the loops leads to a finite, counter term-free result.
• This is an improvement upon previous estimates which used approximations in evaluating the two loop contribution and were plagued by divergences.