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.

LaTeX with REVTeX style and options: multicol,aps,psfig. 18 pages, postscript figures included after text. Accepted in Phys. Rev. D (~ Sept 1996)

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