Search for a light muon-philic $Z^{\prime }$ with the NA64-$e$ experiment at CERN

Abstract

The extension of Standard Model made by inclusion of additional $U(1)$ gauge $L_{\hat{I}}¼-L_{\ddot{I}}„$ 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 $Z^{\prime }$ 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 $Z^{\prime }$ 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 $2.84\times 10^{11}$ electrons impinging with 100 GeV on an active thick target. The resulting limits, despite being included in a region already investigated by neutrino experiments,touch the muon $g-2$ preferred band for values of the $Z^{\prime }$ mass of order of 1 MeV. The sensitivity projections for the future high-statistics NA64-$e$ runs demonstrate the power of the electrons/positron beam approach in this theoretical scenario.

11 pages, 9 figures. This version was accepted for publication