Abstract. We study the three-pion decays of the lightest isoscalar vector mesons, ω and φ, in a dispersive framework that allows for a consistent description of final-state interactions between all three pions. Our results are solely dependent on the phenomenological input for the pion-pion P-wave scattering phase shift. We predict the Dalitz plot distributions for both decays and compare our findings to recent measurements of the φ → 3π Dalitz plot by the KLOE and CMD-2 collaborations. Dalitz plot parameters for future precision measurements of ω → 3π are predicted. We also calculate the ππ P-wave inelasticity contribution from ωπ intermediate states. PACS

The pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon (g − 2) µ is fully determined by the doubly-virtual pion transition form factor. Although this crucial input quantity is, in principle, directly accessible in experiment, a complete measurement covering all kinematic regions relevant for (g − 2) µ is not realistic in the foreseeable future. Here, we report in detail on a reconstruction from available data, both space-and time-like, using a dispersive representation that accounts for all the low-lying singularities, reproduces the correct high-and low-energy limits, and proves convenient for the evaluation of the (g − 2) µ loop integral. We concentrate on the systematics of the fit to e + e − → 3π data, which are key in constraining the isoscalar dependence, as well as the matching to the asymptotic limits. In particular, we provide a detailed account of the pion transition form factor at low energies in the time-and space-like region, including the error estimates underlying our final result for the pion-pole contribution, a π 0 -pole µ = 62.6 +3.0 −2.5 × 10 −11 , and demonstrate how forthcoming singly-virtual measurements will further reduce its uncertainty.

We calculate the ! ! 0 Ã and ! 0 Ã electromagnetic transition form factors based on dispersion theory, relying solely on a previous dispersive analysis of the corresponding three-pion decays and the pion vector form factor. We compare our findings to recent measurements of the ! ! 0 þ À decay spectrum by the NA60 collaboration, and strongly encourage experimental investigation of the OkuboZweig-Iizuka forbidden ! 0 ' þ ' À decays in order to understand the strong deviations from vectormeson dominance found in these transition form factors.

We analyze the pion transition form factor using dispersion theory. We calculate the singly-virtual form factor in the time-like region based on data for the cross section, generalizing previous studies on decays and scattering, and verify our result by comparing to data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below , and extract the slope of the form factor at vanishing momentum transfer . We derive the dispersive formalism necessary for the extension of these results to the doubly-virtual case, as required for the 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}.