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

Ricard Alemany; Michel Davier; Andreas Höcker

doi:doi:10.1007/s100520050127

2021 Impact factor 4.991

Particles and Fields

Eur. Phys. J. C 2, 123-135

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

Ricard Alemany¹ - Michel Davier² - Andreas Höcker²

¹ CERN, CH-1211 Geneva 23, Switzerland (e-mail: alemany@alws.cern.ch)
² Laboratoire de l'Accélérateur Linéaire, IN2P3-CNRS et Université de Paris-Sud, F-91405 Orsay, France (e-mail: davier@lal.in2p3.fr, hoecker@lalcls.in2p3.fr)

Received: 6 March 1997

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 $a_\mu^{\mathrm had}$ =(695.0 $\,\pm\,$ 15.0) $\times10^{-10}$ and $\Delta\alpha_{\mathrm had}^{(5)}(M_{\mathrm Z}^2)$ =(280.9 $\,\pm\,$ 6.3) $\times10^{-4}$ using e⁺e^- data only. The corresponding results for combined e⁺e^- and $\tau$ data are $a_\mu^{\mathrm had}$ =(701.1 $\,\pm\,$ 9.4) $\times10^{-10}$ and $\Delta\alpha_{\mathrm had}^{(5)}(M_{\mathrm Z}^2)$ =(281.7 $\,\pm\,$ 6.2) $\times10^{-4}$ , where the latter is calculated using the contribution from the five lightest quarks.