Abstract
A new experiment is proposed to determine the leading-order hadronic contribution to the muon $g$-2 based on the measurement of the effective electromagnetic coupling in the space-like region at low-momentum transfer. This can be achieved by scattering a 150 GeV muon beam, available at CERN, on a low-Z fixed target and measuring with very high precision the differential cross section of the elastic $\mu$e scattering. This novel approach could provide an independent determination, competitive with the usual time-like dispersive approach, thus consolidating the theoretical prediction for the muon $g$-2 in the Standard Model.
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