Anomalous decay and scattering processes of the eta meson

Abstract

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 ${\eta }^{\prime }$ 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.

Comments: 12 pages, 11 figures; v2 matches version published in EPJC