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 α(s) at s = M 2 Z . We incorporated new data from hadronic τ 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 τ 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 had µ = (695.0 ± 15.0)×10 −10 and ∆α (5) had (M 2 Z ) = (280.9 ± 6.3)×10 −4 using e + e − data only. The corresponding results for combined e + e − and τ data are a had µ = (701.1 ± 9.4)×10 −10 and ∆α (5) had (M 2 Z ) = (281.7 ± 6.2) ×10 −4 , where the latter is calculated using the contribution from the five lightest quarks.

Theoretical precision in estimates of the hadronic contributions to (g − 2)μ and αQED(Mz)

“…The most recent BNL (g µ − 2) measurement [2] gives (world average) The new analysis [14] is "data-driven" like [21,13] and confirms a substantial discrepancy between e + e − -and τ -data. The τ -based result agrees with the corresponding result of [13].…”

“…The most important ingredient of our analysis are the e + e − -data which we described in detail in [21] (see also [13]) and the new data which have become available since then [33]. The distribution of hadronic contributions to ∆α had in the e + e − -data based approach in shown in Fig.…”

“…This has been pioneered by Ref. [13]. Here one utilizes the fact that the vector-current hadronic τ -decay spectral functions are related to the iso-vector part of the e + e − -annihilation cross-section via an isospin rotation:…”

Results and techniques of multi-loop calculations

“…τ data [155]. τ data from ALEPH have been used in order to get more information about R(s) for energies below roughly 1.8 GeV.…”

“…Their incorporation into the analysis has been performed in [155] leading to a slight reduction of the error on ∆α (5) had 23 . Perturbative QCD (pQCD).…”