Leptonic scalar portal: Origin of muon g-2 anomaly and dark matter?

We present a model explaining both the 4.2 sigma muon g - 2 anomaly and the relic density of dark matter (DM) in which DM interacts with the Standard Model (SM) via a scalar portal boson phi carrying both dark and SM leptonic numbers, and mediating a nondiagonal interaction between the electron and muon that allows e <-> mu it transitions. The phi could be produced in high-energy electron scattering off a target nuclei in the reaction eZ -> mu Z phi followed by the prompt invisible decay phi -> DM particles and searched for in events with large missing energy accompanied by a single outgoing muon in the final state. Interestingly, several events with a similar signature have been observed in a data sample of similar or equal to 3 x 10(11) electrons on target collected during 2016-2018 for the search for light dark matter in the NA64 experiment at the CERN SPS [D. Banerjee et al. (NA64 Collaboration), Phys. Rev. Lett. 123, 121801 (2019).]. Attributing so far these events to background allows us to set first constraints on the phi mass and couplings while leaving at the same time decisively probing the origin of these events and a large fraction of the remaining parameter space to a near exiting future with the upgraded NA64 detector or other planned experiments.