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

Abstract

We propose a new experiment to measure the running of the fine-structure constant in the space-like region by scattering high-energy muons on atomic electrons of a low-Z target through the process $\mu e\to \mu e$. 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 $a_{\mu }^{\mathrm{HLO}}$. 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 $a_{\mu }^{\mathrm{HLO}}$ after two years of data taking. This direct measurement of $a_{\mu }^{\mathrm{HLO}}$ 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.

Comments: 8 pages, 4 figures