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

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We discuss the reaction π- e- → π- e- π⁰ with the purpose of obtaining information on the γπ→ ππ anomalous amplitude F₃π. We compare a full calculation at O(p⁶) 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 O(p⁶) 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 the experimental cross section as amplitudes F₃π(0) extr = (9.9 ± 1.1) GeV⁻³ and F₃π(0) extr = (9.6 ± 1.1) GeV⁻³, respectively, which have to be compared with the low-energy theorem F₃π=e/(4π² Fπ³)=9.72 GeV⁻³. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain F₃π with smaller uncertainty.