Measuring aμHLO with space-like data

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 measure- ment 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 determina- tion potentially competitive with the accuracy of the present results obtained with the dispersive approach via time-like data 1 αem 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 de- pends logarithmically on the energy scale (1). At zero mo- mentum transfer, the QED coupling constant α(0) is very accurately known from the measurement of the anoma- lous magnetic moment of the electron and from solid-state physics measurements: α −1 (0) = 137.03599976(50). (1) Vacuum polarization effects lead to a partial screen- ing of the charge in the low energy limit (Thomson limit) while at higher energies the strength of the electromag- netic 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 pen- etration 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