First constraints on the $L_{\mu }-L_{\tau }$ explanation of the muon $g-2$ anomaly from NA64-$e$ at CERN

Abstract

The inclusion of an additional $U(1)$ gauge $L_{\mu }-L_{\tau }$ 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 $Z^{\prime }$ vector boson, with dominant coupling to $\mu$ and $\tau$ leptons and interacting with electrons via a loop mechanism. The $L_{\mu }-L_{\tau }$ model can also explain the Dark Matter relic abundance, by assuming that the $Z^{\prime }$ 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 $Z^{\prime }$ search performed by the NA64-$e$ experiment at CERN SPS, that collected $\sim 9\times 10^{11}$ 100 GeV electrons impinging on an active thick target. Despite the suppressed $Z^{\prime }$ production yield with an electron beam, NA64-$e$ provides the first accelerator-based results excluding the $g-2$ preferred band of the $Z^{\prime }$ parameter space in the 1 keV $<m_{Z^{\prime }}\lesssim 2$ MeV range, in complementarity with the limits recently obtained by the NA64-$\mu$ experiment with a muon beam.

Comments: 15 pages, 5 figures. New version with extended exclusion limits down to 1 keV in Z' mass