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

TL;DR

This paper proposes a novel experiment using muon-electron scattering to directly measure the hadronic contribution to the muon g-2, aiming to improve the precision and independence of current theoretical estimates.

Contribution

It introduces a new space-like measurement method for the hadronic contribution to muon g-2 using high-energy muon scattering, providing an independent and competitive approach.

Findings

Achieves ~0.3% statistical uncertainty on the hadronic contribution after two years.

Uses 150 GeV muon beam at CERN with a high rate of muons.

Provides a direct measurement method complementary to existing approaches.

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 $a^{\rm{HLO}}_{\mu}$. By using a muon beam of 150 GeV, with an average rate of $\sim1.3\times 10^7$ muon/s, currently available at the CERN North Area, a statistical uncertainty of $\sim 0.3\%$ can be achieved on $a^{\rm{HLO}}_{\mu}$ after two years of data taking. This direct measurement of $a^{\rm{HLO}}_{\mu}$ 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.