Anomalous decay and scattering processes of the $$\eta $$ η meson

Abstract

We amend a recent dispersive analysis of the anomalous $$\eta $$ decay process $$\eta \rightarrow \pi ^+\pi ^-\gamma $$ by the effects of the $$a_2$$ tensor meson, the lowest-lying resonance that can contribute in the $$\pi \eta $$ system. While the net effects on the measured decay spectrum are small, they may be more pronounced for the analogous $$\eta '$$ decay. There are nonnegligible consequences for the $$\eta $$ 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 $$\gamma \pi ^-\rightarrow \pi ^-\eta $$ , which could be measured in Primakoff reactions in the future.