Towards an improved understanding of $\eta \to \gamma^* \gamma^*$

TL;DR

High-quality data on the reaction $e^+e^- o ext{pi}^+ ext{pi}^- ext{eta}$ can enable model-independent determination of the $ ext{eta} o ext{gamma}^* ext{gamma}^*$ form factor, crucial for muon g-2 calculations, revealing effects of the $a_2$ meson.

Contribution

The paper highlights the potential of new data to determine the doubly-virtual $ ext{eta}$ form factor model-independently and examines the impact of the $a_2$ meson on existing assumptions.

Findings

Existing data suggests $a_2$ meson affects the form factor.

Better data are needed for definitive conclusions.

The $a_2$ meson breaks the factorization ansatz.

Abstract

We argue that high-quality data on the reaction $e^+e^-\to \pi^+\pi^-\eta$ will allow one to determine the doubly-virtual form factor $\eta\to \gamma^*\gamma^*$ in a model-independent way with controlled accuracy. This is an important step towards a reliable evaluation of the hadronic light-by-light scattering contribution to the anomalous magnetic moment of the muon. When analyzing the existing data for $e^+e^-\to\pi^+\pi^-\eta$ for total energies squared $k^2>1\text{GeV}^2$, we demonstrate that the effect of the $a_2$ meson provides a natural breaking mechanism for the commonly employed factorization ansatz in the doubly-virtual form factor $F_{\eta\gamma^*\gamma^*}(q^2,k^2)$. However, better data are needed to draw firm conclusions.