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 $5 \times 10^7$ 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.

Riccardo Nunzio Pilato is an experimental physicist, member of the MUonE Collaboration. He graduated at the University of Pisa, and obtained the PhD at the same university. He is now a postdoctoral research associate at the University of Liverpool. He is involved in the feasibility studies on the MUonE experiment since the master's degree, and contributed to the simulations of the MUonE detector, to the analysis strategy of the experiment and to the data taking operations.

Matteo Fael is fellow at CERN TH. He did a joint PhD between the University of Padova and Zurich with a thesis on the electromagnetic dipole moments of fermions. He held postdoctoral appointments in Bern, Siegen and Karlsruhe before joining CERN. Matteo is a member of the MUonE theory initiative, which aims at providing the best possible theoretical description of elastic electron-muon scattering.