Dispersive analysis of the pion transition form factor

Abstract

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 e+e-→3π cross section, generalizing previous studies on ω,ϕ→3π decays and γπ→ππ scattering, and verify our result by comparing to e+e-→π0γ data. We perform the analytic continuation to the space-like region, predicting the poorly-constrained space-like transition form factor below 1 GeV, and extract the slope of the form factor at vanishing momentum transfer aπ = (30.7±0.6)×10-3. 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.