Anomalous decay and scattering processes of the eta meson

Abstract

We amend a recent dispersive analysis of the anomalous $η$ decay process $η\toπ^+π^-γ$ by the effects of the $a_2$ tensor meson, the lowest-lying resonance that can contribute in the $πη$ system. While the net effects on the measured decay spectrum are small, they may be more pronounced for the analogous $η'$ decay. There are nonnegligible consequences for the $η$ transition form factor, which is an important quantity for the hadronic light-by-light scattering contribution to the muon's anomalous magnetic moment. We predict total and differential cross sections, as well as a marked forward-backward asymmetry, for the crossed process $γπ^-\toπ^-η$ that could be measured in Primakoff reactions in the future.