Precision measurements of σhadronic for αeff(E) at ILC energies and (g−2)μ

A more precise determination of the effective fine structure constant αeff(E) is mandatory for confronting data from future precision experiments with precise SM predictions. Higher precision would help a lot in monitoring new physics by increasing the significance of any deviation from theory. At a future e+e−–collider like the ILC, as at LEP before, αeff(E) plays the role the static zero momentum α=αeff(0) plays in low energy physics. However, by going to the effective version of α one loses about a factor 2×102 at E=mμ to 105 at E=MZ in precision, such that for physics at the gauge boson mass scale and beyond αeff(E) is the least known basic parameter, about a factor 20 less precise than the neutral gauge boson mass MZ and by about a factor 60 less precise than the Fermi constant GF. Examples of precision limitations are αeff(mμ) which limits the theoretical precision of the muon anomalous magnetic moment aμ and αeff(MZ) which limits the accuracy of the prediction of the weak mixing parameter sin2Θf and indirectly the upper bound on the Higgs mass mH. An optima exploitation of a future linear collider for precision physics requires an improvement of the precision of αeff(E) by something like a factor ten. We discuss a strategy which should be able to reach this goal by appropriate efforts in performing dedicated measurements of σhadronic in a wide energy range as well as efforts in theory and in particular improving the precision of the QCD parameters αs, mc and mb by lattice QCD and/or more precise determinations of them by experiments and perturbative QCD efforts. Projects at VEPP-2000 (Novosibirsk) and DANAE/KLOE-2 (Frascati) are particularly important for improving on αeff(MZ) as well as αeff(mμ). Using the Adler function as a monitor, one observes that we may obtain the hadronic shift as a sum where the first term includes the full non-perturbative part with the choice or larger. In such a determination low-energy machines play a particularly important role in the improvement program. We present an up-to-date analysis including the recent data from KLOE, SND, CMD-2 and BABAR. The analysis based on e+e−–data yields (splitting with to reduce dependence on mc), [] (standard approach), and . The continuation of αeff(E) from the Z mass scale to ILC energies may be obtained by means of perturbative QCD. We emphasize the very high improvement potential of the VEPP-2000 and DANAE/KLOE-2 projects.