Improved Standard-Model predictions for η(′) → ℓ+ℓ−

A bstract The rare decays η ( ′ ) → ℓ + ℓ − , ℓ ∈ { e , μ }, are highly suppressed in the Standard Model, both by their chirality structure and the required loop attaching the lepton line to the η ( ′ ) → γ ∗ γ ∗ matrix element. The latter is described by a single scalar function, the transition form factor, which has recently been studied in great detail for η ( ′ ) in the context of the pseudoscalar-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon. Based on these results, we evaluate the corresponding prediction for the η ( ′ ) dilepton decays, supplemented by an improved evaluation of the asymptotic contributions including pseudoscalar mass effects. In particular, the dispersive representation for the η ( ′ ) transition form factors allows us, for the first time, to perform a robust evaluation of the imaginary parts due to subleading channels besides the dominant two-photon cut. Our final results are 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 , where the errors refer to the uncertainty in the normalized branching fraction, the one propagated from Br[ η ( ′ ) → γγ ], and the total uncertainty, respectively. The branching fraction for η → μ + μ − exhibits a mild 1.6 σ tension with experiment, and we explore the bounds that can be derived on physics beyond the Standard Model.