6533b86ffe1ef96bd12ce6e4

RESEARCH PRODUCT

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

subject

description

We provide model-independent bounds on the rates of rare decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\pi}$ based on experimental limits on the neutron electric dipole moment (nEDM). Starting from phenomenological $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ 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 $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\pi}\ensuremath{\pi}$ couplings in our phenomenological approach are somewhat milder than in the picture with the QCD $\ensuremath{\theta}$ term, our calculation means that whatever the origin of these couplings, the decays $\ensuremath{\eta}({\ensuremath{\eta}}^{\ensuremath{'}})\ensuremath{\rightarrow}2\ensuremath{\pi}$ will remain unobservable in the near future.