Eur. Phys. J. A (2005) 25: 229-240
https://doi.org/10.1140/epja/i2005-10116-1

Original Article

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

¹ School of Physics and Astronomy, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Tel Aviv, Israel
² Institut für Kernphysik, Johannes Gutenberg-Universität, J.J. Becher-Weg 45, D-55099, Mainz, Germany

^* e-mail: scherer@kph.uni-mainz.de

Received: 23 March 2005
Accepted: 5 July 2005
Published online: 5 September 2005

Abstract

We discuss the reaction π^- e ^- → π^- e ^-π⁰ with the purpose of obtaining information on the γπ → ππ anomalous amplitude _3π. We compare a full calculation at (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 (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 _3π ^(0)extr = (9.9±1.1) GeV^-3 and _3π ^(0)extr = (9.6±1.1) GeV^-3, respectively, which have to be compared with the low-energy theorem _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 _3π with smaller uncertainty.