Anomalous decay and scattering processes of the eta meson

TL;DR

This paper refines the dispersive analysis of eta meson decay by including the $a_2$ tensor meson effects, impacting the transition form factor and related scattering processes relevant to muon g-2 calculations.

Contribution

It introduces the effects of the $a_2$ tensor meson into the dispersive analysis of eta decay, providing more accurate predictions for decay spectra and scattering observables.

Findings

Small effects on decay spectrum but significant for eta' decay.

Impacts on the eta transition form factor relevant for muon g-2.

Predicted cross sections and asymmetries for future measurements.

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 $\eta'$ 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.