Dispersive analysis of the pion transition form factor

Hoferichter, Martin; Kubis, Bastian; Leupold, Stefan; Niecknig, Franz; Schneider, Sebastian P. (2014). Dispersive analysis of the pion transition form factor. European physical journal. C - particles and fields, C74(11), p. 3180. EDP Sciences 10.1140/epjc/s10052-014-3180-0

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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 1GeV, 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.

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