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The inclusion of an additional U (1) gauge L_ - L_ symmetry would release the tension between the measured and the predicted value of the anomalous muon magnetic moment: this paradigm assumes the existence of a new, light Z' vector boson, with dominant coupling to and and interacting with electrons via a loop mechanism. The L_ - L_ model can also explain the Dark Matter relic abundance, by assuming that the Z' boson acts as a "portal" to a new Dark Sector of particles in Nature, not charged under known interactions. In this work we present the results of the Z' search performed by the NA64-e experiment at CERN SPS, that collected 9 10^11 100-GeV electrons impinging on an active thick target. Despite the suppressed Z' production yield with an electron beam, the limits sets by NA64-e are competitive with other experimental searches, and partially exclude the g-2 preferred model parameter values for Z' masses lighter than 2 MeV. This result proves the complementarity of this search with NA64-, the parallel effort of the NA64 collaboration with a muon beam.
Andreev et al. (Wed,) studied this question.