Updated estimate of the muon magnetic momentusing revised results from e + e-annihilation

By M. Davier. 2003

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Abstract.A new evaluation of the hadronic vacuum polarization contribution to the muon magnetic moment is presented. We take into account the reanalysis of the low-energy e + e-annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e + e-and $\tau$ spectral functions in the $\pi\pi$ channel is found to be much improved. Nevertheless, significant discrepancies remain in the center-of-mass energy range between 0.85 and $1.0\;{\rm GeV}$, so that we refrain from averaging the two data sets. The values found for the lowest-order hadronic vacuum polarization contributions are $$ a_\mu^{\rm had,LO} = \left\{ \begin{array}{@{}ll@{}} (696.3\pm6.2_{\exp}\pm3.6_{\mathrm{rad}})\,10^{-10} & \quad [e^+e^-{\rm -based}],\\ (711.0\pm5.0_{\exp}\pm0.8_{\mathrm{rad}} \pm2.8_{\rm SU(2)})\,10^{-10} & \quad [\tau {\rm -based}], \\ \end{array} \right. $$ where the errors have been separated according to their sources: experimental, missing radiative corrections in e + e-data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read $$ a_\mu = \left\{ \begin{array}{@{}ll@{}} (11\,659\,180.9\pm7.2_{\rm had} \pm3.5_{\rm LBL}\pm0.4_{\rm QED+EW})\,10^{-10} & \quad [e^+e^-{\rm -based}], \\ (11\,659\,195.6\pm5.8_{\rm had} \pm3.5_{\rm LBL}\pm0.4_{\rm QED+EW})\,10^{-10} & \quad [\tau {\rm -based}], \\ \end{array} \right. $$ where the errors account for the hadronic, light-by-light (LBL) scattering and electroweak contributions. The deviations from the measurement at BNL are found to be $(22.1 \pm 7.2 \pm 3.5 \pm 8.0) 10^{-10}$ (1.9 $\sigma$) and $(7.4 \pm 5.8 \pm 3.5 \pm 8.0) 10^{-10}$ (0.7 $\sigma$) for the e + e-- and $\tau$-based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.

View Paper: https://www.semanticscholar.org/paper/c5ff0b002fc25104b738a1fc2ba35a84e8b31958

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Aspects of the Stueckelberg extension (2005, background): “Numerically, the deviations from the SM are significantly smaller than the SM Z contribution and thus not discernible at the current level of hadronic error [23, 24] and experimental accuracy [25] in the determination of gμ − 2.”