Measurement of the $e^+e^-\to\pi^+\pi^-\pi^0$ cross section in the energy region from 0.56 to 1.1 GeV with the SND detector

TL;DR

This paper reports a precise measurement of the $e^+e^- o ext{pi}^+ ext{pi}^- ext{pi}^0$ cross section in the 0.56 to 1.1 GeV range using the SND detector, refining parameters of vector mesons and calculating the hadronic contribution to muon g-2.

Contribution

The study provides the most accurate cross section measurements in the specified energy range and improves the precision of vector meson parameters and the hadronic contribution to muon g-2.

Findings

Cross section measurement with 0.9-1.2% systematic uncertainty.

Calculated hadronic contribution to muon g-2 as (45.95±0.06±0.46)×10^{-10}.

Refined parameters of $ ho$, $ ho$, and $ ext{omega}$ resonances.

Abstract

The precise measurement of the $e^+e^-\to\pi^+\pi^-\pi^0$ cross section is performed in the center-of-mass energy range $E = 560$--1100 MeV using a data sample of 66 pb$^{-1}$ collected in the experiment with the SND detector at the VEPP-2000 $e^+e^-$ collider. The systematic uncertainty of the cross section measurement is 0.9\% at the maximum of the $\omega$ resonance and 1.2\% at the maximum of the $\phi$ resonance. The leading-order hadronic contribution to the muon magnetic anomaly calculated using the $e^+e^-\to\pi^+\pi^-\pi^0$ cross section measured by SND from 0.62 to 1.975 GeV is $(45.95\pm0.06\pm 0.46)\times 10^{-10}$. From the fit to the cross section data with the vector meson dominance model, the parameters of the $\omega$, $\rho$, and $\phi$ resonances are obtained. The obtained values of ${\cal B}(\omega\to e^+e^-) {\cal B}(\omega\to 3\pi)$, mass and width of the $\omega$ meson, and ${\cal B}(\rho\to 3\pi)$ have accuracy better than the current world average values.