Measuring the leading hadronic contribution to the muon g-2 via $$\mu e$$ μ e scattering

We propose a new experiment to measure the running of the electromagnetic coupling constant in the space-like region by scattering high-energy muons on atomic electrons of a low-Z target through the elastic process $$\mu \, e \rightarrow \mu \, e$$ . The differential cross section of this process, measured as a function of the squared momentum transfer $$t=q^2<0$$ , provides direct sensitivity to the leading-order hadronic contribution to the muon anomaly $$a^\mathrm{{HLO}}_{\mu }$$ . By using a muon beam of 150 GeV, with an average rate of $$\sim $$ 1.3 $$\times 10^7$$ muon/s, currently available at the CERN North Area, a statistical uncertainty of $$\sim $$ 0.3% can be achieved on $$a^\mathrm{{HLO}}_{\mu }$$ after two years of data taking. The direct measurement of $$a^\mathrm{{HLO}}_{\mu }$$ via $$\mu e$$ scattering will provide an independent determination, competitive with the time-like dispersive approach, and consolidate the theoretical prediction for the muon g-2 in the Standard Model. It will allow therefore a firmer interpretation of the measurements of the future muon g-2 experiments at Fermilab and J-PARC.