The Rare Decays πee, ηee and ηmumu in Chiral Perturbation Theory

Martin J. Savage , Michael Luke , Mark B. Wise

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classification ✦ hep-ph

keywords etaeeetamumupieechiralperturbationtheorytimesamplitudes

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We calculate the decay rates for $\piee$, $\etaee$ and $\etamumu$ in chiral perturbation theory. The linear combination of counterterms necessary to render these amplitudes finite is fixed by the recently measured branching fraction for $\etamumu$. We find $\Br(\piee ) = 7\pm 1\times 10^{-8}$ and $\Br(\etaee )=5\pm 1\times 10^{-9}$.

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Improved Standard-Model predictions for $\eta^{(\prime)}\to \ell^+ \ell^-$
hep-ph 2025-12 accept novelty 5.0

Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.