Precision measurements of sigma_hadronic for alpha_eff(E) at ILC energies and (g-2)_mu

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Abstract
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. 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 alpha one loses about a factor 2 times 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. We discuss a strategy which should be able to reach a factor 10 improvement 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. 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). 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_had^(5)(M_Z) = 0.027593 +/- 0.000169 [alpha^-1(M_Z) = 128.938 +/- 0.023] and a_mu^had=(692.1 +/- 5.6) x 10^{-10}. We emphasize the very high improvement potential of the VEPP-2000 and DANAE/KLOE-2 projects.

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