An update of the ALEPH non-strange spectral functions from hadronic $tau$ decays is presented. Compared to the 2005 ALEPH publication, the main improvement is related to the use of a new method to unfold the measured mass spectra from detector effect
s. This procedure also corrects a previous problem in the correlations between the unfolded mass bins. Results from QCD studies and for the evaluation of the hadronic vacuum polarisation contribution to the anomalous muon magnetic moment are derived using the new spectral functions. They are found in agreement with published results based on the previous set of spectral functions.
In a recent paper cite{benayoun} M.Benayoun {it et al.} use a specific model to compare results on the existing data for the cross section of the process $e^+e^-rightarrow pi^+pi^-$ and state conclusions about the inconsistency of the BABAR results w
ith those from the other experiments. We show that a direct model-independent comparison of the data at hand contradicts this claim. Clear discrepancies with the results of Ref. cite{benayoun} are pointed out. As a consequence we do not believe that the lower value and the smaller uncertainty obtained for the prediction of the muon magnetic anomaly are reliable results.
The BABAR collaboration has nearly completed a program of precise measurements of the cross sections for the dominant channels of e+e- --> hadrons from threshold to an energy of 3-5 GeV using the initial-state radiation (ISR) method, i.e. the measure
ment of the cross sections e+e- --> gamma hadrons with the energetic photon detected at large angle to the beams. These data are used as input to vacuum polarization dispersion integrals, in particular the hadronic contribution to the muon g-2 anomaly. In addition to the recently measured pi+pi- cross section, giving the dominant contibution, many multihadronic channels have been investigated, with some recent examples presented here. We give preliminary results for the process e+e- --> K+K-(gamma) using 232 fb-1 of data collected with the BABAR detector at e+e- center-of-mass energies near 10.6 GeV. The lowest-order contribution to the hadronic vacuum polarization term in the muon magnetic anomaly is obtained for this channel: amu-KK-LO=(22.95 +-0.14(stat) +-0.22(syst)) 10^-10, which is about a factor of three more precise than the previous world average value.
We reevaluate the hadronic contributions to the muon magnetic anomaly, and to the running of the electromagnetic coupling constant at the Z-boson mass. We include new pi+pi- cross-section data from KLOE, all available multi-hadron data from BABAR, a
reestimation of missing low-energy contributions using results on cross sections and process dynamics from BABAR, a reevaluation of all experimental contributions using the software package HVPTools, together with a reanalysis of inter-experiment and inter-channel correlations, and a reevaluation of the continuum contributions from perturbative QCD at four loops. These improvements lead to a decrease in the hadronic contributions with respect to earlier evaluations. For the muon g-2 we find lowest-order hadronic contributions of (692.3 +- 4.2) 10^-10 and (701.5 +- 4.7) 10^-10 for the e+e- based and tau-based analyses, respectively, and full Standard Model predictions that differ by 3.6 sigma and 2.4 sigma from the experimental value. For the e+e- based five-quark hadronic contribution to alpha(MZ) we find Delta_alpha_had[5](MZ)=(275.7 +- 1.0) 10^-4. The reduced electromagnetic coupling strength at MZ leads to an increase by 7 GeV in the most probable Higgs boson mass obtained by the standard Gfitter fit to electroweak precision data.
