Search for a light <math><msup><mi>Z</mi><mo>′</mo></msup></math> in the <math><msub><mi>L</mi><mi>μ</mi></msub><mo>−</mo><msub><mi>L</mi><mi>τ</mi></msub></math> scenario with the NA64-<math><mi>e</mi></math> experiment at CERN

The extension of Standard Model made by inclusion of additional U(1) gauge Lμ−Lτ symmetry can explain the difference between the measured and the predicted value of the muon magnetic moment and solve the tension in B meson decays. This model predicts the existence of a new, light Z′ vector boson, predominantly coupled to second and third generation leptons, whose interaction with electrons is due to a loop mechanism involving muons and taus. In this work, we present a rigorous evaluation of the upper limits in the Z′ parameter space, obtained from the analysis of the data collected by the NA64-e experiment at CERN SPS, that performed a search for light dark matter with 2.84&#215;1011 electrons impinging with 100 GeV on an active thick target. The resulting limits touch the muon g−2 preferred band for values of the Z′ mass of order of 1 MeV, while the sensitivity projections for the future high-statistics NA64-e runs demonstrate the power of the electrons/positron beam approach in this theoretical scenario.