Contribution of exclusive $(π^0π^0, π^0η, ηη)γ$ channels to the leading order HVP of the muon $g-2$

Abstract

We evaluate the contributions of (π 0 π 0 , π 0 η, ηη)γ exclusive channels to the dispersion integral of the leading order HVP of the muon anomalous magnetic moment. These channels are included in some way in previous evaluations of the π 0 ω, ηω and ηφ contributions to a had,LO µ , where the vector resonances (decaying into π 0 /η + γ) are assumed to be on-shell. Since the separation of resonance and background contributions in a given observable is, in general, a model-dependent procedure, here we use pseudoscalar mesons and the photon as the in and out states of the e + e − → (π 0 π 0 , π 0 η, ηη)γ S-matrix, such that the cross section contains the interferences among different contributing to the amplitudes. We find a had,LO µ (P 0 1 P 0 2 γ) = (1.13 ± 0.13) × 10 −10 , where uncertainties stem mainly from vector meson dominance model parameters. Improved experimental studies of these exclusive channels in the whole range below 2 GeV would reduce model-dependency.