Anomalous decay and scattering processes of the eta meson

Understand

We amend a recent dispersive analysis of the anomalous $\eta$ decay process $\eta\to\pi^+\pi^-\gamma$ 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 $\gamma\pi^-\to\pi^-\eta$ that could be measured in Primakoff reactions in the future.