A new determination of the γπ → ππ anomalous amplitude via πe^- → π^-e^-π⁰ data

We discuss the reaction π^- e ^- → π^- e ^-π⁰ with the purpose of obtaining information on the γπ → ππ anomalous amplitude ℱ _3π. We compare a full calculation at script O sign (p ⁶) in chiral perturbation theory and various phenomenological predictions with the existing data of Amendolia et al. By integrating our theory results using Monte Carlo techniques, we obtain σ = 2.05 nb at script O sign (p ⁶) and σ = 2.17 nb after including the dominant electromagnetic correction. Both results are in good agreement with the experimental cross-section of σ = (2.11±0.47) nb. On the basis of the ChPT results one would extract from the experimental cross-section as amplitudes ℱ _3π ^(0)extr = (9.9±1.1) GeV^-3 and ℱ _3π ^(0)extr = (9.6±1.1) GeV^-3, respectively, which have to be compared with the low-energy theorem ℱ _3π = e/(4π² F _π ³) = 9.72GeV^-3. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain ℱ _3π with smaller uncertainty.