Improved determination of the hadronic contribution to the muon (${g-2}$) and to ${\alpha(M_{\mathrm Z}^2)}$ Using new data from hadronic $\tau$ decays

Abstract.

We have reevaluated the hadronic contribution to the anomalous magnetic moment of the muon $(g-2)$ and to the running of the QED fine structure constant $\alpha (s)$ at $s=M_{\mathrm Z}^2$. We incorporated new data from hadronic $\tau$ decays, recently published by the ALEPH Collaboration. In addition, compared to previous analyses, we use more extensive $e^+e^-$ annihilation data sets. The integration over the total hadronic cross section is performed using experimental data up to 40 GeV and results from perturbative QCD above 40 GeV. The improvement from $\tau$ data concerns mainly the pion form factor, where the uncertainty in the corresponding integral could be reduced by more than a factor of two. We obtain for the lowest order hadronic vacuum polarization graph $a^{\rm had}_\mu =(695.0\pm 15.0)\times10^{-10}$ and $\Delta \alpha ^{(5)}_{\rm had} (M^2_{\rm Z}) =(280.9 \pm 6.3) \times 10^{-4}$ using $e^+e^-$ data only. The corresponding results for combined $e^+e^-$ and $\tau$ data are $a^{\rm had}_\mu=(701.1 \pm 9.4)\times 10^{-10}$ and $\Delta \alpha ^{(5)}_{\rm had} (M^2_{\rm Z}) =(281.7 \pm 6.2) \times10^{-4}$, where the latter is calculated using the contribution from the five lightest quarks.