Abstract. After reviewing the traditional way of computing the leading order hadronic correction to the muon (g-2) through a dispersive approach via time-like data, I will present a novel approach, based on the measurement of the effective electromagnetic coupling in the space-like region extracted from Bhabha scattering data. We argue that this new method may become feasible at flavor factories, resulting in an alternative determination potentially competitive with the accuracy of the present results obtained with the dispersive approach via time-like data 1 α em running and the Vacuum Polarization Precision physics requires appropriate inclusion of higher order effects and the knowledge of very precise parameters of the electroweak Standard Model SM. One of the basic input parameters is the fine structure constant which depends logarithmically on the energy scale [1]. At zero momentum transfer, the QED coupling constant α(0) is very accurately known from the measurement of the anomalous magnetic moment of the electron and from solid-state physics measurements:(1)Vacuum polarization effects lead to a partial screening of the charge in the low energy limit (Thomson limit) while at higher energies the strength of the electromagnetic interaction grows. This is due to virtual lepton and quark loop corrections to the photon propagator. This effect can also be understood as an increasing penetration of the polarized cloud of virtual particles which screen the bare electric charge of a particle. Thus, at large distances, we observe a reduced bare charge due to this effect of screening. As we probe closer we penetrate into the cloud of virtual particles, decreasing the screening effect and observing more of the bare charge and thus a strengthening of the coupling The charge has to be replaced by a running charge: e 2 → e 2 (q 2 ) = e 2 Z 1 + Π γ (q 2 ) .The wave function renormalization factor Z is fixed by the condition that for q 2 → 0 one obtains the classical charge (charge renormalization in the Thomson limit) [2]. Thus the renormalized charge is: a e-mail: graziano.venanzoni@lnf.infn.it e 2 → e 2 (q 2 ) = e 2 1 + (Π γ (q 2 ) − Π γ (0)) (2) where, in the perturbation theory, the lowest order diagram which contributes to Π γ (q 2 ) is: which describes virtual creation and reabsorption of fermion pairs:in leading order. In terms of the fine structure constant α = e 2 /4π:The shift Δα is large due to the large change in scale going from zero momentum to the Z-mass scale μ = M Z and due to the many species of fermions contributing. Zero momentum more precisely means the light fermion mass thresholds [1]. The various contributions to the shift in the fine structure constant come from the leptons (lep=e,μ and τ) the 5 light quarks (u,b,s,c and the corresponding hadrons =had) and from the top quark:While the leptonic contributions are calculable with very high precision in QED by the perturbation theory, the hadronic ones are more problematic as they involve the quark masses and hadronic physics at low momentum scales. B...