Measurement of the $e^+e^-\to\pi^+\pi^-\pi^0\pi^0$ cross section using initial-state radiation at BaBar

TL;DR

This paper reports a highly precise measurement of the $e^+e^- o ext{4-pion}$ cross section using initial-state radiation at BaBar, significantly improving the accuracy of contributions to muon g-2 and the running of the fine-structure constant.

Contribution

It provides the most precise measurement to date of the $e^+e^- o ext{4-pion}$ cross section in the 1.5 GeV region, refining calculations of fundamental constants.

Findings

Measured the cross section with 3.6% uncertainty.

Calculated the contribution to muon g-2 as $(17.9 imes 10^{-10})$.

Determined impact on the running of the fine-structure constant.

Abstract

The process $e^+e^- \to \pi^+\pi^-2\pi^0\gamma$ is investigated by means of the initial-state radiation technique, where a photon is emitted from the incoming electron or positron. Using $454.3 \rm{fb}^{-1}$ of data collected around a center-of-mass energy of $\sqrt{s} = 10.58 \rm{GeV}$ by the BaBar experiment at SLAC, approximately 150000 signal events are obtained. The corresponding non-radiative cross section is measured with a relative uncertainty of $3.6\%$ in the energy region around $1.5 \rm{GeV}$, surpassing all existing measurements in precision. Using this new result, the channel's contribution to the leading order hadronic vacuum polarization contribution to the anomalous magnetic moment of the muon is calculated as $(g_\mu^{\pi^+\pi^-2\pi^0}-2)/2 = (17.9 \pm 0.1_\mathrm{stat} \pm 0.6_\mathrm{syst}) \times 10^{-10}$ in the energy range $0.85\rm{GeV} < E_\mathrm{CM} < 1.8\rm{GeV}$. In the same energy range, the impact on the running of the fine structure constant at the $Z^0$-pole is determined as $\Delta\alpha^{\pi^+\pi^-2\pi^0}(M^2_\mathrm{Z}) = (4.44 \pm 0.02_\mathrm{stat} \pm 0.14_\mathrm{syst}) \times 10^{-4}$. Furthermore, intermediate resonances are studied and especially the cross section of the process $e^+e^- \to \omega\pi^0 \to \pi^+\pi^-2\pi^0$ is measured.