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.

arXiv comment8 hages, 3 figures

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• New ideas for handling of loop and angular integrals in D-dimensions in QCD
• Patterns of CP violation from mirror symmetry breaking in the $\eta \to {\pi }^{+}{\pi }^{-}{\pi }^0$ Dalitz plot
• Lepton Phenomenology of Stueckelberg Portal to Dark Sector
• Study of the interactions of the axion with mesons and photons using a chiral effective Lagrangian model
• Updated limits on the CP violating $\eta \pi \pi$ and ${\eta }^{\prime }\pi \pi$ couplings derived from the neutron EDM
• Patterns of $C$- and $CP$-violation in hadronic $\eta$ and ${\eta }^{\prime }$ three-body decays
• Deuteron EDM induced by CP violating couplings of pseudoscalar mesons
• Static electric dipole moment of the francium atom induced by axionlike particle exchange
• Dark SU(2) Stueckelberg portal
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• Probing leptophobic dark sector with a pseudoscalar portal in the NA64 experiment at CERN