Phenomenological Estimate of Isospin Breaking in Hadronic Vacuum Polarization.

Puzzles in the determination of the hadronic-vacuum-polarization contribution currently impede a conclusive interpretation of the precision measurement of the anomalous magnetic moment of the muon at the Fermilab experiment. One such puzzle concerns tensions between evaluations in lattice QCD and using e^{+}e^{-}→hadrons cross-section data. In lattice QCD, the dominant isospin-symmetric part and isospin-breaking (IB) corrections are calculated separately, with very different systematic effects. Identifying these two pieces in a data-driven approach provides an opportunity to compare them individually and trace back the source of the discrepancy. Here, we estimate the IB component of the lattice-QCD calculations from phenomenology, based on a comprehensive study of exclusive contributions that can be enhanced via infrared singularities, threshold effects, or hadronic resonances, including, for the first time, in the e^{+}e^{-}→3π channel. We observe sizable cancellations among different channels, with a sum that even suggests a slightly larger result for the QED correction than obtained in lattice QCD. We conclude that the tensions between lattice QCD and e^{+}e^{-} data therefore cannot be explained by the IB contributions in the lattice-QCD calculations.

Improved Standard-Model Prediction for π

We present an improved standard-model (SM) prediction for the dilepton decay of the neutral pion. The loop amplitude is determined by the pion transition form factor for π^{0}→γ^{*}γ^{*}, for which we employ a dispersive representation that incorporates both spacelike and timelike data as well as short-distance constraints. The resulting SM branching fraction, Br[π^{0}→e^{+}e^{-}]=6.25(3)×10^{-8}, sharpens constraints on physics beyond the SM, including pseudoscalar and axial-vector mediators.

Pion-Pole Contribution to Hadronic Light-By-Light Scattering in the Anomalous Magnetic Moment of the Muon.

The π^{0} pole constitutes the lowest-lying singularity of the hadronic light-by-light (HLBL) tensor, and thus, it provides the leading contribution in a dispersive approach to HLBL scattering in the anomalous magnetic moment of the muon (g-2)_{µ}. It is unambiguously defined in terms of the doubly virtual pion transition form factor, which in principle, can be accessed in its entirety by experiment. We demonstrate that, in the absence of a direct measurement, the full spacelike doubly virtual form factor can be reconstructed very accurately based on existing data for e^{+}e^{-}→3π, e^{+}e^{-}→e^{+}e^{-}π^{0}, and the π^{0}→γγ decay width. We derive a representation that incorporates all the low-lying singularities of the form factor, matches correctly onto the asymptotic behavior expected from perturbative QCD, and is suitable for the evaluation of the (g-2)_{µ} loop integral. The resulting value, a_{µ}^{π^{0}-pole}=62.6_{-2.5}^{+3.0}×10^{-11}, for the first time, represents a complete data-driven determination of the pion-pole contribution with fully controlled uncertainty estimates. In particular, we show that already improved singly virtual measurements alone would allow one to further reduce the uncertainty in a_{µ}^{π^{0}-pole}.

Hadronic vacuum polarization and vector-meson resonance parameters from e + e - → π 0 γ.

We study the reaction e + e - → π 0 γ based on a dispersive representation of the underlying π 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of the π 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find a µ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of ω and ϕ . We observe good agreement with the e + e - → 3 π channel, explaining a previous tension in the ω mass between π 0 γ and 3 π by an unphysical phase in the fit function. Combining both channels we find M ¯ ω = 782.736 ( 24 ) MeV and M ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from the K ¯ K channel, demonstrating consistency with 3 π and π 0 γ . For the ω mass, our result is consistent but more precise, exacerbating tensions with the ω mass extracted via isospin-breaking effects from the 2 π channel.