Measurement of $\sigma(e^+e^- \to \pi^+\pi^-)$ at DA$\Phi$NE with the radiative return

TL;DR

This paper reports on the measurement of the $e^+e^- o ext{pi}^+ ext{pi}^-$ cross section at low energies using the radiative return method at DA$ ext{Phi}$NE, providing data relevant for muon magnetic moment calculations.

Contribution

The study introduces a novel measurement approach using radiative return at DA$ ext{Phi}$NE, offering an independent cross check with different systematic errors.

Findings

Differential cross section for $e^{+}e^{-} o ext{pi}^+ ext{pi}^- ext{gamma}$ measured.

Total cross section for $e^{+}e^{-} o ext{pi}^+ ext{pi}^-$ obtained.

Results support existing data and improve precision in the low-energy region.

Abstract

The measurement of hadronic cross sections at low centre-of-mass energies is currently attracting much interest because of the r\^o{}le these measurements play in the theoretical evaluation of the anomalous magnetic moment of the muon. The KLOE experiment at the DA$\Phi$NE $\phi$-factory in Frascati aims to determine the cross section of the dominant contribution $e^{+}e^{-} \to \pi^{+}\pi^{-}$ at energies below 1 GeV exploiting the radiative return from the $\phi$ to the $\rho$ and $\omega$ mesons. This method has systematic errors completely different from previous measurements and allows a cross check of existing data in this energy region. The method and results on both the differential cross section for $e^{+}e^{-} \to \pi^{+}\pi^{-}\gamma$ and the total cross section for $e^{+}e^{-} \to \pi^{+}\pi^{-}$ are presented.