Hadronic vacuum polarization and vector-meson resonance parameters from $$\varvec{e^+e^-\rightarrow \pi ^0\gamma }$$

Abstract

AbstractWe study the reaction $$e^+e^-\rightarrow \pi ^0\gamma $$ e + e - → π 0 γ based on a dispersive representation of the underlying $$\pi ^0\rightarrow \gamma \gamma ^*$$ π 0 → γ γ ∗ transition form factor. As a first application, we evaluate the contribution of the $$\pi ^0\gamma $$ π 0 γ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find $$a_\mu ^{\pi ^0\gamma }\big |_{\le 1.35\,\text {GeV}}=43.8(6)\times 10^{-11}$$ a μ π 0 γ | ≤ 1.35 GeV = 43.8 ( 6 ) × 10 - 11 , in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of $$\omega $$ ω and $$\phi $$ ϕ . We observe good agreement with the $$e^+e^-\rightarrow 3\pi $$ e + e - → 3 π channel, explaining a previous tension in the $$\omega $$ ω mass between $$\pi ^0\gamma $$ π 0 γ and $$3\pi $$ 3 π by an unphysical phase in the fit function. Combining both channels we find $${\bar{M}}_\omega =782.736(24)\,\text {MeV}$$ M ¯ ω = 782.736 ( 24 ) MeV and $${\bar{M}}_\phi =1019.457(20)\,\text {MeV}$$ M ¯ ϕ = 1019.457 ( 20 ) MeV for the masses including vacuum-polarization corrections. The $$\phi $$ ϕ mass agrees perfectly with the PDG average, which is dominated by determinations from the $${\bar{K}} K$$ K ¯ K channel, demonstrating consistency with $$3\pi $$ 3 π and $$\pi ^0\gamma $$ π 0 γ . For the $$\omega $$ ω mass, our result is consistent but more precise, exacerbating tensions with the $$\omega $$ ω mass extracted via isospin-breaking effects from the $$2\pi $$ 2 π channel.