An overlooked WZW structure in the HLS formulation of vector mesons produces topological quantization of their anomalous couplings.
Dispersive analysis for $\eta\to \gamma\gamma^*$
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abstract
A dispersion integral is derived that connects data on $\eta\to \pi^+\pi^-\gamma$ to the $\eta\to \gamma\gamma^*$ transition form factor. A detailed analysis of the uncertainties is provided. We find for the slope of the $\eta$ transition form factor at the origin $b_\eta = (2.05 {}^{+0.22}_{-0.10})\, {\rm GeV}^{-2}$. Using an additional, plausible assumption, one finds for the corresponding slope of the $\eta'$ transition form factor, $b_{\eta'} = (1.58 {}^{+0.15}_{-0.08})\, {\rm GeV}^{-2}$. Both values are consistent with all recent data, but differ from some previous theoretical analyses.
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Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.
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Topological quantization of vector meson anomalous couplings
An overlooked WZW structure in the HLS formulation of vector mesons produces topological quantization of their anomalous couplings.
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Improved Standard-Model predictions for $\eta^{(\prime)}\to \ell^+ \ell^-$
Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.