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

TL;DR

This paper uses a dispersive approach to analyze the $e^+e^- o\pi^0\gamma$ reaction, determining resonance parameters and evaluating its contribution to the muon's anomalous magnetic moment with high precision.

Contribution

It provides a novel dispersive analysis of the $\pi^0 o\gamma\gamma^*$ transition form factor and refines the resonance parameters of $\omega$ and $\phi$ mesons.

Findings

The $\pi^0 o\\gamma\\gamma^*$ transition form factor contribution to $a_\mu$ is $43.8(6)\times 10^{-11}$.

Resonance parameters of $\\omega$ and $\\phi$ are determined with high precision, consistent with previous data.

The $\\phi$ mass agrees with PDG, while the $\\omega$ mass is more precise but shows tension with other measurements.

Abstract

We study the reaction $e^+e^-\to\pi^0\gamma$ based on a dispersive representation of the underlying $\pi^0\to\gamma\gamma^*$ transition form factor. As a first application, we evaluate the contribution of the $\pi^0\gamma$ channel to the hadronic-vacuum-polarization correction to the anomalous magnetic moment of the muon. We find $a_\mu^{\pi^0\gamma}\big|_{\leq 1.35\,\text{GeV}}=43.8(6)\times 10^{-11}$, in line with evaluations from the direct integration of the data. Second, our fit determines the resonance parameters of $\omega$ and $\phi$. We observe good agreement with the $e^+e^-\to3\pi$ channel, explaining a previous tension in the $\omega$ mass between $\pi^0\gamma$ and $3\pi$ by an unphysical phase in the fit function. Combining both channels we find $\bar M_\omega=782.736(24)\,\text{MeV}$ and $\bar M_\phi=1019.457(20)\,\text{MeV}$ for the masses including vacuum-polarization corrections. The $\phi$ mass agrees perfectly with the PDG average, which is dominated by determinations from the $\bar K K$ channel, demonstrating consistency with $3\pi$ and $\pi^0\gamma$. For the $\omega$ mass, our result is consistent but more precise, exacerbating tensions with the $\omega$ mass extracted via isospin-breaking effects from the $2\pi$ channel.