Muon-electron scattering at next-to-leading order accuracy

The next-to-leading order electro-weak radiative corrections to the µ±e- → µ±e- process are reviewed and their relevance is discussed for the MUonE experiment, proposed at CERN. The aim of MUonE is the high precision measurement of the QED running coupling constant in the space-like region, from which the full hadronic contribution can be extracted and used to provide a new and independent determination of the leading-order hadronic correction to the muon g − 2. In this context, the required accuracy demands that radiative corrections are accounted for at the highest level of precision and implemented into a Monte Carlo event generator for data analysis. The first step towards the final goal of theoretical precision, which will require the full set of NNLO corrections and resummation of higher orders, is the inclusion of NLO electro-weak corrections.

The MUonE experiment

The precision measurement of the anomalous magnetic moment g − 2 of the muon at present exhibits a 3.5 σ deviation between theory and experiments. In the next few years it will be measured to higher precisions at Fermilab and J-PARC. The theoretical prediction can be improved by reducing the uncertainty on the leading hadronic correction $ a_\mu ^{HLO} $ to the g − 2. Here we present a new approach to determine $ a_\mu ^{HLO} $ with space-like data, by means of a precise measurement of the hadronic contribution to the effective electromagnetic coupling α, exploiting the elastic scattering of 150 GeV muons (currently available at CERN North area) on atomic electrons of a low-Z target. The direct measurement of $ a_\mu ^{HLO} $ in the space-like region will provide a new independent determination and will consolidate the theoretical prediction of 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.

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

The precision measurement of the anomalous magnetic moment g-2 of the muon presently exhibits a 3.5 σ deviation between theory and experiments. In the next few years the anomalous magnetic moment will be measured to higher precisions at Fermilab and J-PARC. The theoretical prediction can be improved by reducing the uncertainty on the leading hadronic correction HLO μ to the g-2. Here we present a novel approach to determine aHLO μ with space-like data, by means of precise measurement of the hadronic shift of the effective electromagnetic coupling α exploiting the elastic scattering of 150 GeV muons (currently available at CERN North area) on atomic electrons of a low-Z target. The direct measurement of aHLO μ in the space-like region will provide a new independent determination competitive with the time-like dispersive approach, and will consolidate the theoretical prediction of 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