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

A more precise determination of the effective fine structure constant alpha(eff) (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, alpha(eff) (E) plays the role the static zero momentum alpha = alpha(eff) (0) plays in low energy physics. However, by going to the effective version of a one loses about a factor 2 x 10(2) at E = m mu to 10(5) at E = M-Z in precision, such that for physics at the gauge boson mass scale and beyond alpha(eff) (E) is the least known basic parameter, about a factor 20 less precise than the neutral gauge boson mass M-Z and by about a factor 60 less precise than the Fermi constant G(F). Examples of precision limitations are alpha(eff) (m mu) which limits the theoretical precision of the muon anomalous magnetic moment a(mu) and alpha(eff) (M-Z) which limits the accuracy of the prediction of the weak mixing parameter sin(2) Theta(f) and indirectly the upper bound on the Higgs mass m(H). An optimal exploitation of a future linear collider for precision physics requires an improvement of the precision of alpha(eff) (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 sigma(hadronic) in a wide energy range as well as efforts in theory and in particular improving the precision of the QCD parameters alpha(s), m(c) and m(b) 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 alpha(eff) (M-Z) as well as alpha(eff) (m mu). Using the Adler function as a monitor, one observes that we may obtain the hadronic shift Delta alpha((5))(had) (M-Z(2)) as a sum Delta alpha((5))(had) (-s(0))(data) + Delta alpha((5))(had) (s(0), M-Z(2))(pQCD) where the first term includes the full non-perturbative part with the choice s(0) = (2.5 GeV)(2) 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 Delta alpha((5))(had) (M-Z(2)) = 0.027593 +/- 0.000169 [alpha(-1) (M-Z(2)) = 128.938 +/- 0.023] (splitting with s(0) = (10 GeV)(2) to reduce dependence on m(c)), Delta alpha((5))(had) (M-Z(2)) = 0.027607 +/- 0.000225 [alpha(-1)(M-Z(2)) = 128.947 +/- 0.035] (standard approach), and a(mu)(had) = (692.0 +/- 6.0) x 10(-10). The continuation of alpha(eff) (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 VPP-2000 and DANAE/KLOE-2 projects.