Probing the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>L</mml:mi><mml:mi>μ</mml:mi></mml:msub><mml:mo>−</mml:mo><mml:msub><mml:mi>L</mml:mi><mml:mi>τ</mml:mi></mml:msub></mml:math> gauge boson at the MUonE experiment

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