Single $\pi^0$ production in $\mu e$ scattering at MUonE

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 prediction in radiative corrections to the $\mu e$ scattering as well as for robust quantitative estimates of all possible background processes. In this letter, the contribution due to the emission of a neutral pion through the process $\mu e \to \mu e \pi^0$ is studied and its numerical impact is discussed in different phase space configurations by means of the upgraded Monte Carlo event generator MESMER. In fact, single $\pi^0$ production could be a source of reducible background for the measurement of the QED running coupling constant at MUonE and it could be also an important background for possible New Physics searches at MUonE involving $2 \to 3$ processes, in phase space regions complementary to the ones characteristic of the elastic $\mu e$ scattering.