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

Abstract

We discuss the reaction π-e- → π-e-π0 with the purpose of obtaining information on the γπ → ππ anomalous amplitude $ \cal {F}$ 3π. We compare a full calculation at $ \cal {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 $ \cal {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 experimental cross-section as amplitudes $ \cal {F}$ 3π(0)extr = (9.9±1.1) GeV-3 and $ \cal {F}$ 3π(0)extr = (9.6±1.1) GeV-3, respectively, which have to be compared with the low-energy theorem $ \cal {F}$ 3π = e/(4π2Fπ3) = 9.72GeV-3. We emphasize the need for new data to allow for a comparison of experimental and theoretical distributions and to obtain $ \cal {F}$ 3π with smaller uncertainty.