The Lowest Order Hadronic Contribution to the Muon $g-2$ Value with Systematic Error Correlations

Abstract

We have performed a new evaluation of the hadronic contribution to $a_{\mu}=(g-2)/2$ of the muon with explicit correlations of systematic errors among the experimental data on $\sigma( e^+e^- \to hadrons )$. Our result for the lowest order hadronic vacuum polarization contribution is $ a_{\mu}^{had} = 702.6(7.8)(14.0) \times 10^{-10}$ where the the first error is statistical and the second is systematic. The total systematic error contributions from below and above $\sqrt{s} = 1.4$ GeV are $(13.1) \times 10^{-10}$ and $(5.1) \times 10^{-10}$ respectively, and are hence dominated by the low energy region. Therefore, new measurements on $\sigma( e^+e^- \to hadrons )$ below 1.4 GeV can significantly reduce the total error on $a_{\mu}^{had}$. In particular, the effect on the total errors of new hypothetical data with 3 \% statistical and 0.5 - 1.0 \% systematic errors is presented.