Measuring the leading hadronic contribution to the muon g-2 via the -e elastic scattering.
The precision measurement of the anomalous magnetic moment g-2 of the muon presently exhibits a 3.5 σ deviation between theory and experiments. In the next few years the anomalous magnetic moment will be measured to higher precisions at Fermilab and J-PARC. The theoretical prediction can be improved by reducing the uncertainty on the leading hadronic correction HLO μ to the g-2. Here we present a novel approach to determine aHLO μ with space-like data, by means of precise measurement of the hadronic shift of the effective electromagnetic coupling α exploiting the elastic scattering of 150 GeV muons (currently available at CERN North area) on atomic electrons of a low-Z target. The direct measurement of aHLO μ in the space-like region will provide a new independent determination competitive with the time-like dispersive approach, and will consolidate the theoretical prediction of the muon g-2 in the Standard Model. It will allow therefore a firmer interpretation of the measurements of the future muon g-2 experiments at Fermilab and J-PARC