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

Abstract

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. While constraints on the $\eta ({\eta }^{\prime })\pi \pi$ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD $\theta$-term, our calculation means that whatever the origin of these couplings, The decays $\eta ({\eta }^{\prime })\to 2\pi$ will remain unobservable in the near future.

Comments: 8 hages, 3 figures