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We discuss the reaction $\pi^- e^- \to \pi^- e^- \pi^{0}$ with the purpose ofobtaining information on the $\gamma \pi \to \pi\pi$ anomalous amplitude ${\calF}_{3\pi}$. We compare a full calculation at ${\cal O}(p^6)$ in chiralperturbation theory and various phenomenological predictions with the existingdata of Amendolia {\em et al}. By integrating our theory results using MonteCarlo techniques we obtain $\sigma= 2.05 $ nb at ${\cal O}(p^6)$ and $\sigma=2.17 $ nb after including the dominant electromagnetic correction. Both resultsare in good agreement with the experimental cross section of $\sigma= (2.11 \pm0.47)$ nb. On the basis of the ChPT results one would extract from the theexperimental cross section as amplitudes ${\cal F}_{3\pi}^{(0)\rm extr} = (9.9\pm 1.1)$ GeV$^{-3}$ and ${\cal F}_{3\pi}^{(0)\rm extr} = (9.6 \pm 1.1)$GeV$^{-3}$, respectively, which have to be compared with the low-energy theorem${\cal F}_{3\pi}=e/(4\pi^2 F_\pi^3)=9.72 {GeV}^{-3}$. We emphasize the need fornew data to allow for a comparison of experimental and theoreticaldistributions and to obtain ${\cal F}_{3\pi}$ with smaller uncertainty.Comment: 23 pages, 14 figures, discussion of the ChPT calculation extende

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