Reaction \gamma \pi \to \pi \pi in a confined quark model

Abstract

A confined quark model study in a couple of chirally anomalous processes is presented in comparison with effective meson Lagrangian approaches of various kind. The processes considered are \pi^0 \to \gamma \gamma and \gamma \to \pi^+ \pi^- \pi^0 (or the equivalent \pi \gamma \to \pi\pi) for which there is a well-known low energy theorem relating the latter amplitude with the former one by a very simple algebraic relation in the zero energy (or chiral, or soft pion) limit. Our quark model naturally generates the so-called contact term in the amplitude for the second process, but with the opposite sign to what effective chiral meson models indicate. A reinterpretation of our vector pole contribution restores the consistency, however. While the first reaction is observed to serve in it calibrating various models, it is found difficult, based upon the quality of the existing data in the second reaction, to single out the best model, which appears indispensable for testing the validity of the above low energy theorem. Thus the proposed experiments and their analyses should aim at attaining an optimal accuracy.