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Exploring the tension between nature and the Standard Model: the muon g-2

Anomalous magnetic moment of the muon (muon g-2) is one of the most precisely measured quantities in particle physics. At the same time, it can be evaluated in the Standard Model with an unprecedented accuracy. The Muon g-2 experiment at Fermilab has started the major data collection and the aimed four-fold increase in precision will shed light on the current discrepancy between the theory prediction and the measured value. This renders a comparable improvement of the precision in the SM theory an essential ingredient in order to fully exploit the expected increase of precision in experimental results. For all these reasons, the muon g-2 is considered to be a great testing ground for new physics. Hadronic contributions are the dominant sources of uncertainty in the theoretical prediction of the muon g-2. A reciprocal effort to a precise determination of the leading hadronic contribution to the muon g-2 using lattice gauge theories is a direct measurement of the hadronic contributions to the running of the fine structure constant recently proposed by the MUonE experiment. A hybrid strategy including both experimental and lattice data sets is expected to give an independent check of the dispersive results from $e^+e^-$ annihilation, which dominate the current world average.