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
Kento Asai, Koichi Hamaguchi, Natsumi Nagata, Shih-Yen Tseng, Juntaro Wada
Abstract
We discuss the prospects of probing the ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ gauge boson at the MUonE experiment. The ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ gauge boson ${Z}^{\ensuremath{'}}$ with a mass of $\ensuremath{\lesssim}200\text{ }\text{ }\mathrm{MeV}$, which can explain the discrepancy between the measured value of the muon $g\ensuremath{-}2$ and the value calculated in the Standard Model, can be produced at the MUonE experiment through the process $\ensuremath{\mu}e\ensuremath{\rightarrow}\ensuremath{\mu}e{Z}^{\ensuremath{'}}$. The ${Z}^{\ensuremath{'}}$ in the final state decays into a pair of neutrinos, and therefore we cannot observe the decay of ${Z}^{\ensuremath{'}}$ 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 $\ensuremath{\mu}e\ensuremath{\rightarrow}\ensuremath{\mu}e$ as well as radiative process $\ensuremath{\mu}e\ensuremath{\rightarrow}\ensuremath{\mu}e\ensuremath{\gamma}$ 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 $\ensuremath{\mu}e\ensuremath{\rightarrow}\ensuremath{\mu}e\ensuremath{\nu}\overline{\ensuremath{\nu}}$ are negligible. With our selection criteria, the number of signal events $\ensuremath{\mu}e\ensuremath{\rightarrow}\ensuremath{\mu}e{Z}^{\ensuremath{'}}$ is found to be as large as $\ensuremath{\sim}{10}^{3}$, assuming an integrated luminosity of $15\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$, in the parameter region motivated by the muon $g\ensuremath{-}2$ discrepancy. It is, therefore, quite feasible to probe the ${L}_{\ensuremath{\mu}}\ensuremath{-}{L}_{\ensuremath{\tau}}$ gauge boson at the MUonE experiment---without introducing additional devices---and we strongly recommend recording the events relevant to this ${Z}^{\ensuremath{'}}$ production process.