The recently proposed MUonE experiment at CERN aims at providing a novel determination of the leading order hadronic contribution to the muon anomalous magnetic moment through the study of elastic muon-electron scattering at relatively small momentum transfer. The anticipated accuracy of the order of 10ppm demands for high-precision predictions, including all the relevant radiative corrections. The fixed-order NNLO radiative corrections due to the emission of virtual and real leptonic pairs are described and their numerical impact is discussed for typical event selections of the MUonE experiment, by means of the upgraded Monte Carlo code Mesmer.
The anomalous magnetic moment of the muon 𝑎 𝜇 = (𝑔 − 2) 𝜇 /2 has been measured at the Brookhaven National Laboratory in 2001 and recently at the Fermilab Muon 𝑔 − 2 Experiment. The results deviate by 4.2 𝜎 from the Standard Model predictions, where the dominant source of theoretical error comes from the Hadronic Leading Order contribution 𝑎 𝐻 𝐿𝑂 𝜇 . Moreover, recent calculations performed on the lattice seem to be more consistent with the experimental value for 𝑎 𝐻 𝐿𝑂 𝜇 . MUonE is a proposed experiment at CERN whose purpose is to provide a new and independent determination of 𝑎 𝐻 𝐿𝑂 𝜇 via elastic muon-electron scattering at low momentum transfer. To achieve a precision that is comparable to the standard timelike estimation of 𝑎 𝐻 𝐿𝑂 𝜇 , the experiment must reach an accuracy of about 10 parts per million on the differential cross section. This requires a similar level of accuracy also from the theoretical point of view: a precise calculation of the muon-electron scattering cross section with all the relevant radiative corrections as well as quantitative estimates of all possible background processes are needed. The state of the art of the theoretical calculation for 𝜇𝑒 scattering is presented. Then, the formulation for the next-to-next-to-leading order real and virtual lepton pair contributions is described as well as their numerical impact, obtained with the Monte Carlo event generator Mesmer. These contributions are crucial to reach the precision aim of MUonE.
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