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

Abstract

\n 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\n + \ne\n-annihilation cross section into hadrons by the CMD-2 Collaboration. The agreement between e\n + \ne\n-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 \n \n$$ a_\\mu^{\\rm had,LO} = \\left\\{\n \\begin{array}{@{}ll@{}}\n (696.3\\pm6.2_{\\exp}\\pm3.6_{\\mathrm{rad}})\\,10^{-10} & \\quad [e^+e^-{\\rm\n -based}],\\\\ (711.0\\pm5.0_{\\exp}\\pm0.8_{\\mathrm{rad}} \\pm2.8_{\\rm\n SU(2)})\\,10^{-10} & \\quad [\\tau {\\rm -based}], \\\\\n \\end{array}\n \\right. $$\n\n where the errors have been separated according to their sources: experimental, missing radiative corrections in e\n + \ne\n-data, and isospin breaking. The corresponding Standard Model predictions for the muon magnetic anomaly read \n \n$$ a_\\mu = \\left\\{\n \\begin{array}{@{}ll@{}}\n (11\\,659\\,180.9\\pm7.2_{\\rm had} \\pm3.5_{\\rm LBL}\\pm0.4_{\\rm\n QED+EW})\\,10^{-10} & \\quad [e^+e^-{\\rm -based}], \\\\\n (11\\,659\\,195.6\\pm5.8_{\\rm had} \\pm3.5_{\\rm LBL}\\pm0.4_{\\rm\n QED+EW})\\,10^{-10} & \\quad [\\tau {\\rm -based}], \\\\\n \\end{array}\n \\right. $$ \n\n 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\n + \ne\n-- and $\\tau$-based estimates, respectively, where the second error is from the LBL contribution and the third one from the BNL measurement.\n