We use the present upper bound on the neutron electric dipole moment to give an estimate for the upper limit of the CP-violating couplings of the $eta(eta)$ meson to the neutron. Using this result, we derive constraints on the CP-violating two-pion decays of the $eta(eta)$. Our results are relevant for the running and planned GlueX and LHCb measurements of rare meson decays.
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