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ISSN - 01709739, Zeitschrift f�r Physik C-Particles and Fields, 1995, vol. 67, p. 585-601

Hadronic contributions to (g-2) of the leptons and to the effective fine structure constant α(MZ 2)

Eidelman S., Jegerlehner F.

The new experiment planned at Brookhaven to measure the anomalous magnetic moment of the muon aμ≡(gμ-2)/2 will improve the present accuracy of 7 ppm by about a factor of 20. This requires a careful reconsideration of the theoretical uncertainties of the g-2 predictions, which are dominated by the error of the contribution from the light quarks to the photon vacuum polarization. This issue is cruicial also for the precise determination of the running fine structure constant at the Z-peak as LEP/SLC experiments continue to increase their precision. In this paper we present an updated analysis of the hadronic vacuum polarization using all presently available e+e- data. This seems to be justified because previous work on the subject was based to some extent on preliminary or incomplete experimental data. Contributions from different energy ranges are presented separately for g-2 of the muon and the τ-lepton and for α(MZ 2). We obtain the results aμ had*=(725±16)×10-10 and aτ had*=(351±10)×10-8, where the asterisk indicates the dressed (renormalization group improved) value. For the effective fine structure constant at MZ=91.1888 GeV we obtain Δαhad (5)=0.0280±0.0007 and α(MZ 2)-1=128.896±0.090. Further improvement in the accuracy of theoretical predictions which depend on the hadronic vacuum polarization requires more precise measurements of e+e- cross-sections at energies below about 12 GeV in future experiments. © 1995 Springer-Verlag.