The MUonE experiment aims at an independent and very precise determination of the leading hadronic contribution to the muon magnetic moment, based on an alternative method, complementary to the existing ones. This can be achieved by measuring with unprecedented precision the shape of the differential cross section of muon-electron elastic scattering, using the intense muon beam available at CERN, with energy of 150-160 GeV, off atomic electrons of a light target. The status of the project is presented, with recent results in preparation for the test run scheduled in 2021 with a reduced detector.
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