A Geant4-based simulation study for a preliminary setup of the MUonE experiment

MUonE is a proposed experiment which aims at an independent and precise determination of the leading hadronic contribution to the muon $g-2$, based on the measurement of the hadronic running of the electromagnetic coupling in the space-like region. This can be achieved by measuring with extremely high accuracy the shape of the differential cross section of the $\mu e$ elastic scattering, using a 160$\,$GeV muon beam available at CERN, off atomic electrons of a light target. Geant4 simulations are required in order to estimate the backgrounds in the proposed experiment. For this reason, the MUonE setup has been simulated with the recent Geant4 versions containing relevant updates, mostly regarding the correct estimation of the angular distribution of the $e^{+}e^{-}$ production from muon interactions. In this work, two related studies utilizing the most accurate Geant4 physics list are presented, one involving standalone simulation tests and another one employing simulation and reconstruction using the new FairRoot release. In both cases, the latest Geant4 version has been validated comparing it with a previous version.