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Towards an improved understanding of $\eta \to \gamma^* \gamma^*$
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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.
Forward citations
Cited by 5 Pith papers
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Precision evaluation of the $\eta$- and $\eta'$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
A new dispersive analysis of the eta and eta-prime transition form factors gives a_mu(eta-pole) = 14.7(9) x 10^-11 and a_mu(eta'-pole) = 13.5(7) x 10^-11, with combined pseudoscalar poles at 91.2(+2.9,-2.4) x 10^-11.
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Dispersive Analysis of $D$- and $B$-Meson Form Factors with Chiral and Heavy-Quark Constraints
The isovector D/D*/B/B* electromagnetic form factors are reconstructed dispersively with ππ rescattering, yielding ρ(770) coupling constants from pole residues.
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Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
Using a dispersive formalism with experimental transition form factors and short-distance constraints, the authors obtain a_mu^HLbL = 101.9(7.9) x 10^-11, halving the previous uncertainty.
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Dispersion relation for hadronic light-by-light scattering: $\eta$ and $\eta'$ poles
A dispersive analysis of the eta and eta' transition form factors yields data-driven pole contributions to the muon g-2 of 14.7(9) x 10^-11 and 13.5(7) x 10^-11.
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Dispersion relation for hadronic light-by-light scattering: subleading contributions
A dispersive evaluation gives a_mu^HLbL subleading = 33.2(7.2) x 10^-11 and total = 101.9(7.9) x 10^-11.
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