Towards an improved understanding of $η\to γ^* γ^*$

Abstract

We argue that high-quality data on the reaction $e^+e^-\to π^+π^-η$ will allow one to determine the doubly-virtual form factor $η\to γ^*γ^*$ 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 $e^+e^-\toπ^+π^-η$ 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 $F_{ηγ^*γ^*}(q^2,k^2)$. However, better data are needed to draw firm conclusions.