AbstractWe argue that high-quality data on the reaction $$e^+e^-\rightarrow \pi ^+\pi ^-\eta $$ e + e - → π + π - η will allow one to determine the doubly-virtual form factor $$\eta \rightarrow \gamma ^*\gamma ^*$$ η → 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 $$e^+e^-\rightarrow \pi ^+\pi ^-\eta $$ e + e - → π + π - η for total energies squared $$k^2>1\,\text {GeV}^2$$ k 2 > 1 GeV 2 , we demonstrate that the effect of the $$a_2$$ a 2 meson provides a natural breaking mechanism for the commonly employed factorization ansatz in the doubly-virtual form factor $$F_{\eta \gamma ^*\gamma ^*}(q^2,k^2)$$ F η γ ∗ γ ∗ ( q 2 , k 2 ) . However, better data are needed to draw firm conclusions.