Muon collider signatures for a $Z^{\prime }$ with a maximal $\mu -\tau$ coupling in $U(1{)}_{L_{\mu }-L_{\tau }}$

Abstract

The gauged $U(1{)}_{L_{\mu }-L_{\tau }}$ model is a candidate model for explaining the muon g-2 anomaly because the $Z^{\prime }$ in the model has a natural normal coupling to muon. Due to other experimental data constraints the viable mass range for the usual $Z^{\prime }$ is constrained to be lower than a few hundred MeV. It has been shown that if the $Z^{\prime }$ has a maximal off-diagonal mixing, $(\bar{\mu }{\gamma }^{\mu }\tau +\bar{\tau }{\gamma }^{\mu }\mu )Z_{\mu }^{\prime }$, a large mass for $Z^{\prime }$ is possible. This class of models has a very interesting signature for detection, such as ${\mu }^{-}{\mu }^{+}\to {\tau }^{-}{\tau }^{+}$ pair, ${\mu }^{-}{\mu }^{+}\to {\mu }^{\pm }{\mu }^{\pm }{\tau }^{\mp }{\tau }^{\mp }$ at a muon collider. In this work we study in detail these processes. We find that the in the parameter space solving the muon g-2 anomaly, t-channel ${\tau }^{-}{\tau }^{+}$ pair production can easily be distinguished at more than 5$\sigma$ level from the s-channel production as that predicted in the standard model. The smoking gun signature of doubly same sign ${\mu }^{\pm }{\mu }^{\pm }+{\tau }^{\mp }{\tau }^{\mp }$ pairs production can have a 5$\sigma$ sensitivity, at a muon collider of 3 TeV with $\mathcal{O}$($f{b}^{-1}$) luminosity.

Comments: 10 pages, 7 figures