The precision measurement of the anomalous magnetic moment g-2 of the muon presently exhibits a 3.5 deviation between theory and experiments. In the next few years the anomalous magnetic moment will be measured with higher precision (0.14 ppm) at Fermilab and J-PARC. Theoretical predictions are limited instead by the uncertainty on the leading order hadronic contribution to the g-2 due to the non perturbative QCD regime involved at this scale.
We have proposed a novel approach to determine the hadron leading contribution with space-like data, by means of a very precise measurement of the elastic scattering of 150 GeV muons (currently available at CERN North area) on atomic electrons of a low-Z target.
On this basis one can determine the hadronic shift of the effective electromagnetic coupling and the hadronic contribution to the g-2 of the muon. The direct measurement of the hadronic leading contribution in the space-like region will provide an 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 rmer interpretation of the measurements of the future muon g-2 experiments at Fermilab and J-PARC
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