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

Abstract

We propose a new experiment to measure the running of the electromagnetic coupling constant in the spacelike region by scattering high-energy muons on atomic electrons of a low-Z target through the elastic process μ e → μ 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 HLO μ . By using a muon beam of 150 GeV, with an average rate of ∼1.3 ×10 7 muon/s, currently available at the CERN North Area, a statistical uncertainty of ∼0.3% can be achieved on a HLO μ after two years of data taking. The direct measurement of a HLO μ via μe 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. a

A proposal to measure the hadronic contribution to the g-2 in the space-like region

“…Always within the space-like approach, an alternative possibility has been investigated [2]. It consists in using a fixed target μ → e scattering process and to analyse the elastic muon distribution in the forward region.…”

“…A series of preliminary considerations on the detector have been discussed [2]. In order to perform the planned measurement to the required precision, a dedicated detector is necessary.…”

“…The motivation of this work [1,2] is due to a long-standing discrepancy between experiment and the Standard Model (SM) prediction for a μ , the muon anomalous magnetic moment. For this reason the hadronic corrections have been kept under close scrutiny [3][4][5][6].…”

Mellin-Barnes approach to hadronic vacuum polarization and gμ−2

“…[10][11][12][13][14][15][16][17][18][19]), or on new dedicated experiments as proposed in ref. [20]. The standard representation of a HVP μ used in the experimental determinations is the one in terms of a weighted integral of the hadronic spectral function and therefore [21,22] which is the one proposed for LQCD evaluations [23].…”

Measuring the leading hadronic contribution to the muon g-2 via the -e elastic scattering.

“…The proposal described here is to determine a HLO μ from a measurement of the effective electromagnetic coupling α in the space-like region, where the vacuum polarization is expectd to be a smooth function of the squared momentum transfer. In this approach the hadronic contribution to the running of α can be measured by means of the t-channel μ − e elastic scattering process, from which a HLO μ can be determined directly [17] 1 .…”