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

M. Davier; S. Eidelman; A. Höcker; Z. Zhang

doi:10.1140/epjc/s2003-01362-6

2023 Impact factor 4.2

Particles and Fields

Eur. Phys. J. C (2003) 31: 503-510
https://doi.org/10.1140/epjc/s2003-01362-6

experimental physics

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

M. Davier¹^*, S. Eidelman², A. Höcker¹ and Z. Zhang¹

¹ Laboratoire de l’Accélérateur Linéaire, IN2P3-CNRS et Université de Paris-Sud, 91898 , Orsay, France
² Budker Institute of Nuclear Physics, 630090, Novosibirsk, Russia

^* e-mail: davier@lal.in2p3.fr

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.