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The η meson provides a laboratory to study isospin violation and search for new flavor-conserving sources of C and CP violation with a sensitivity approaching 10−6 of the isospin-conserving strong amplitude. Some of the most interesting rare η decays are the neutral modes, yet the effective loss of photons from the relatively common decay η → 3π0 → 6γ (33%) has largely obscured rare decays producing 3-5γ's. Particularly important relevant branches include the highly suppressed η → π02γ → 4γ, which provides a rare window on testing models of O(p6) contributions in ChPTh, and η → 3γ and η → 2π0γ → 5γ which provide direct constraints on C violation in flavor-conserving processes. The substitution of lead tungstate in the forward calorimeter of the GluEx setup in Jefferson Lab's new Hall D would allow dramatically improved measurements. The main niche of this facility, which we call the JLab Eta Factory (JEF), would be η decay neutral modes. However, this could likely be expanded to rare η′(958) decays for low energy QCD studies as well as η decays involving muons for new physics searches

Physics and outlook for rare, all-neutral Eta decays