The value of the anomalous magnetic moment of the muon, aμ=(g−2)μ/2, is a fundamental quantity in particle physics. Its most precise experimental measurement
yields a deviation of 4.2σ from the theoretical prediction within the Standard Model. In this context, the recently proposed MUonE experiment at CERN aims at
providing a novel and independent determination of the main source of theoretical uncertainty on the muon anomaly, namely the leading order hadronic
contribution aHLOμ, through the study
of elastic muon-electron scattering at small momentum
transfer. The anticipated accuracy of the order of 10 ppm demands for
high-precision calculations of the relevant radiative corrections to μe scattering, as well as for robust quantitative estimates of all possible background processes. The contribution due to the emission of a neutral pion through the process μe→μeπ0 is here studied as a source of reducible background for the measurement of the QED running coupling constant
at MUonE, and as a background for possible New Physics searches at MUonE involving 2→3 processes, in phase space regions complementary to the ones characteristic of the elastic μe scattering. Its numerical impact is discussed by means of the Monte Carlo event generator MESMER.