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Using the present upper bound on the neutron electric dipole moment, we givean estimate for the upper limit of the CP-violating couplings of the eta(eta')to the nucleon. Using this result, we then derive constraints on theCP-violating eta(eta')-pi-pi couplings, which define the two-pion CP-violatingdecays of the eta and eta' mesons. Our results are relevant for the running andplanned measurements of rare decays of the eta and eta' mesons by the GlueXCollaboration at JLab and the LHCb Collaboration at CERN.

CP-violating decays of the pseudoscalars eta and eta' and their connection to the electric dipole moment of the neutron