Improved Evaluation of the Hadronic Vacuum Polarization Contributions to Muon $g-2$ and ${\bar{\alpha }}_{\mathrm{QED}}(M_Z)$ Using High Order QCD Calculations

Abstract

We use recently evaluated radiative and nonperturbative corrections to production of heavy quarks by a vector current to give very precise theoretical calculations of the high energy ($t^{1/2}\ge \sqrt{2}$ GeV) imaginary part of the photon vacuum polarization function, $\mathrm{Im}\Pi (t)$. This allows us to improve the corresponding contributions to the muon (or any other lepton) $g-2$ anomaly and to the running QED constant on the $Z$, ${\bar{\alpha }}_{\mathrm{QED}}(M_Z)$. This decreases the error in the evaluations by a factor between two and six for the high energy contribution, and by some 50\% for the overall result. We find for the hadronic contributions $a_h=6993.4\pm 110.0\times 10^{-11}$ and $\Delta {\alpha }_h=272.59\pm 4.09\times 10^{-4}.$

Comments: 12 pages, uses RevTeX, 1 postscript figure appended