Search for a light $Z′$ in the $L_μ-L_τ$ scenario with the NA64-$e$ experiment at CERN

The extension of Standard Model made by inclusion of additional <math display="inline"><mi>U</mi><mo stretchy="false">(</mo><mn>1</mn><mo stretchy="false">)</mo></math> gauge <math display="inline"><msub><mi>L</mi><mi>μ</mi></msub><mo>-</mo><msub><mi>L</mi><mi>τ</mi></msub></math> symmetry can explain the difference between the measured and the predicted value of the muon magnetic moment and solve the tension in <math display="inline"><mi>B</mi></math> meson decays. This model predicts the existence of a new, light <math display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> 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 <math display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> parameter space, obtained from the analysis of the data collected by the NA64-<math display="inline"><mi>e</mi></math> experiment at CERN SPS, that performed a search for light dark matter with <math display="inline"><mn>2.84</mn><mo>×</mo><msup><mn>10</mn><mn>11</mn></msup></math> electrons impinging with 100 GeV on an active thick target. The resulting limits touch the muon <math display="inline"><mi>g</mi><mo>-</mo><mn>2</mn></math> preferred band for values of the <math display="inline"><msup><mi>Z</mi><mo>′</mo></msup></math> mass of order of 1 MeV, while the sensitivity projections for the future high-statistics NA64-<math display="inline"><mi>e</mi></math> runs demonstrate the power of the electrons/positron beam approach in this theoretical scenario.