Probing the $L_{\mu }$-$L_{\tau }$ Gauge Boson at the MUonE Experiment

Abstract

We discuss the prospects of probing the $L_{\mu }-L_{\tau }$ gauge boson at the MUonE experiment. The $L_{\mu }-L_{\tau }$ gauge boson $Z^{\prime }$ with a mass of $\lesssim 200$ MeV, which can explain the discrepancy between the measured value of the muon $g-2$ and the value calculated in the Standard Model, can be produced at the MUonE experiment through the process $\mu e\to \mu e{Z}^{\prime }$. The $Z^{\prime }$ in the final state decays into a pair of neutrinos, and therefore we cannot observe the decay of $Z^{\prime }$ directly. It is, however, still possible to probe this signature by searching for events with a large scattering angle of muon and a less energetic final-state electron. The background events coming from the elastic scattering $\mu e\to \mu e$ as well as radiative process $\mu e\to \mu e\gamma$ can be removed by the kinematical cuts on the muon scattering angle and the electron energy, in addition to a photon veto. The background events from the electroweak process $\mu e\to \mu e\nu \bar{\nu }$ are negligible. With our selection criteria, the number of signal events $\mu e\to \mu e{Z}^{\prime }$ is found to be as large as $\sim 10^3$ in the parameter region motivated by the muon $g-2$ discrepancy. It is, therefore, quite feasible to probe the $L_{\mu }-L_{\tau }$ gauge boson at the MUonE experiment -- without introducing additional devices -- and we strongly recommend recording the events relevant to this $Z^{\prime }$ production process.

6pages, 3 figures, published version

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