Updated Estimate of the Muon Magnetic Moment Using Revised Results from e+e- Annihilation

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 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[had,LO] = (696.3 +- 6.2[exp] +- 3.6[rad])e-10 (e+e- -based) and a_mu[had,LO] = (711.0 +- 5.0[exp] +- 0.8[rad] +- 2.8[SU2])e-10 (tau-based), 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 = (11,659,180.9 +- 7.2[had] +- 3.5[LBL] +- 0.4[QED+EW])e-10 (e+e- -based) and a_mu = (11,659,195.6 +- 5.8[had] +- 3.5[LBL] +- 0.4[QED+EW])e-10 (tau-based), 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 +- 7.2 +- 3.5 +- 8.0)e-10 (1.9 sigma) and (7.4 +- 5.8 +- 3.5 +- 8.0)e-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.

Figures (4)

• Figure 1: Relative change in the $e^+e^-\rightarrow\pi^+\pi^-$ cross section of the revised CMD-2 analysis cmd2_new with respect to the one previously published cmd2.
• Figure 2: Relative comparison of the $\pi^+\pi^-$ spectral functions from $e^+e^-$ and isospin-breaking corrected $\tau$ data, expressed as a ratio to the $\tau$. The band shows the uncertainty on the latter. The $e^+e^-$ data are from CMD-2 cmd2_new, CMD cmd, OLYA cmdolya and DM1 dm1. The lower figure emphasizes the $\rho$ peak region.
• Figure 3: The measured branching ratios for $\tau^-\rightarrow\nu_\tau\pi^-\pi^0$ compared to the prediction from the $e^+e^-\rightarrow\pi^+\pi^-$applying the isospin-breaking correction factors discussed in Ref. dehz. The measured branching ratios are from ALEPH aleph_new, CLEO cleo_bpipi0 and OPAL opal_bpipi0. The L3 and OPAL results are obtained from their $h \pi^0$ branching ratio, reduced by the small $K \pi^0$ contribution measured by ALEPH aleph_ksum and CLEO cleo_kpi0.
• Figure 4: Comparison of the results (\ref{['eq_smres']}) with the BNL measurement bnl_2002. Also given are our estimates eidelmandh98 obtained before the CMD-2 data were available. For completeness, we show as triangles with dotted error bars the $e^+e^-$-based results dehzteubner derived with the previously published CMD-2 data cmd2.