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Abstract

Previous calculations of the rate of the decay η → π⁰ γγ have fallen short of the experimental result, 0.84 ± 0.18 eV. One such calculation, that of vector meson dominance (VMD), is included herein (giving 0.29₋₀.₁₂⁺⁰¹⁶ eV), and moreover is modified by the inclusion of an added ingredient, the scalar meson α₀. The added mechanism does not adequately fix the result; assuming constructive interference the calculated rate becomes 0.37₋₀.₁₅⁺⁰²⁰ eV. The rate is then calculated according to a quark-box mechanism, where the ηqq and πqq couplings are fixed by the rates of the η→γγ and π⁰→ γγ decays. With constituent quark masses of 300 MeV for u and d quarks the calculated rate is 0.70±0.12 eV, which is in good agreement with experiment. Lower bounds (the unitarity limits) for the decays η → π⁰ e⁺e⁻ and η → π⁰ μ⁺ μ⁻ are calculated, using the intermediate state π⁰ γγ. The available experimental information is inadequate for purposes of a model-free calculation of these unitarity limits; therefore, the models considered for η → π⁰ γγ are used in these calculations. Using the quark box mechanism as above, the unitarity limits are 2.9 ± 0.5 μeV and 4.3 ± 0.7 μeV, for η → π⁰e⁺e⁻ and η → π⁰ μ⁺ μ⁻ respectively. These results show that the measurement of these (as yet unseen) modes at η factories such as that of Saturne can be expected.