Description
We propose a new approach to measure very precisely
the hadronic leading order corrections to the muon $g-2$,
%the $\mu - e$ differential cross section in order to determine
$a_{\mu}^{HLO}$, with space-like data,
measuring the hadronic contribution to the effective electromagnetic coupling
$\alpha$, by means of the elastic scattering $\mu - e$ of 150 GeV muons
(currently available at CERN North area) off atomic electrons.
Such a direct measurement of $a_{\mu}^{HLO}$ will provide a new independent
determination and will consolidate the theoretical prediction
of the muon $g-2$ in the Standard Model, which currently shows a
3.5~$\sigma$ discrepancy between theory and experiments.
This project is part of the Physics Beyond Colliders Working Group.
