Search for a light muon-philic $Z'$ with the NA64-e experiment at CERN

The inclusion of an additional U(1) gauge Lμ - Lτ 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 μ and τ and interacting with electrons via a loop mechanism. The Lμ - Lτ 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 × 10¹¹ 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-μ, the parallel effort of the NA64 collaboration with a muon beam.