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 $\lesssim 200\mathrm{MeV}$, 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 $\mu e\to \mu e\nu \overline{\nu }$ 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 $\sim {10}^3$, assuming an integrated luminosity of $15{\mathrm{fb}}^{-1}$, 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.

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在 MUonE 实验中探测 Lμ−Lτ 玻色子

我们讨论了探索的前景${\mathrm{大号}}_{\mu }-{\mathrm{大号}}_{\tau }$在 MUonE 实验中测量玻色子。这${\mathrm{大号}}_{\mu }-{\mathrm{大号}}_{\tau }$规范玻色子$Z^{\text{'}}$有大量的$\lesssim 200\mathrm{电子伏特}$，这可以解释μ子的测量值之间的差异$G-2$以及在标准模型中计算的值，可以通过该过程在 MUonE 实验中产生$\mu e\to \mu e{Z}^{\text{'}}$. 这$Z^{\text{'}}$在最终状态下衰变为一对中微子，因此我们无法观察到中微子的衰变$Z^{\text{'}}$直接地。然而，仍然可以通过搜索具有大的 μ 子散射角和能量较低的最终态电子的事件来探测这一特征。来自弹性散射的背景事件$\mu e\to \mu e$以及辐射过程$\mu e\to \mu e\gamma$除了光子否决之外，还可以通过对 μ 子散射角和电子能量的运动学削减来消除。电弱过程的背景事件$\mu e\to \mu e\nu \overline{\nu }$可以忽略不计。根据我们的选择标准，信号事件的数量$\mu e\to \mu e{Z}^{\text{'}}$被发现是一样大$～{10}^3$，假设综合光度为$15{\mathrm{脸书}}^{-1}$，在介子激发的参数区域$G-2$差异。因此，探查是完全可行的${\mathrm{大号}}_{\mu }-{\mathrm{大号}}_{\tau }$在 MUonE 实验中测量玻色子——不引入额外的设备——我们强烈建议记录与此相关的事件$Z^{\text{'}}$生产过程。