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

The MUonE experiment at CERN aims at determining the leading-order hadronic vacuum polarisation (HLO) contribution to the muon anomalous magnetic moment, $a_{\mu}=(g-2)_{\mu}/2$. At the moment, the Standard Model theoretical prediction of $a_{\mu}$ presents a tension of $4.2\sigma$ with the experimental results. Such a discrepancy can point to possible New Physics (NP) signals. The MuonE experiment will provide an independent determination of the HLO contribution, one of the dominant terms to the theoretical uncertainty on $a_{\mu}$, via the study of elastic muon-electron scattering at small momentum transfer, with a precision of the order of $10 {ppm}$. In this contribution, the analysis of a potential source of reducible background at MUonE, coming from the $\pi^0$ production in $\mu\mbox{-}e$ scattering, is presented, motivated by the fact that the $\pi^0$ production is dynamically enhanced in the region of small electron and muon scattering angles, which is particularly interesting for MUonE. Moreover, the effects of this same process as a background to possible NP searches at MUonE are analysed, such as the production of a light new gauge boson $Z^{\prime}$ or of a dark photon $A^{\prime}$.