Special Fixed Target Cross talk: MUonE
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,The MUonE experiment aims to measure the differential cross section of the 𝜇-e elastic scattering using the CERN SPS muon beam with mean energy of 160 GeV onto atomic electrons of a low-Z target. Thanks to the intense M2 beam with in-spill intensity of 5 ✕ 107 muons/s, a precise measurement of the scattering angles allows to extract the hadronic contribution to the running of the QED coupling, and by a novel approach the leading hadronic contribution to the muon anomalous magnetic moment. This determination will be completely independent from the usual data-driven method, based on measurements of the R-ratio in e+e- annihilations, and could clarify the discrepancy between these results and the theory-based estimates from recent lattice QCD calculations. The main theoretical motivations, the experiment design and the strategies to extract the hadronic running will be presented.