Muon collider signatures for a $Z'$ with a maximal $μ-τ$ coupling in $U(1)_{L_μ-L_τ}$
The gauged $U(1)_{L_μ- L_τ}$ model is a candidate model for explaining the muon g-2 anomaly because the $Z'$ in the model has a natural normal coupling to muon. Due to other experimental data constraints the viable mass range for the usual $Z'$ is constrained to be lower than a few hundred MeV. It has been shown that if the $Z'$ has a maximal off-diagonal mixing, $(\bar μγ^μτ+ \bar τγ^μμ) Z'_μ$, a large mass for $Z'$ is possible. This class of models has a very interesting signature for detection, such as $μ^-μ^+ \to τ^- τ^+$ pair, $μ^- μ^+ \to μ^\pmμ^\pm τ^\mp τ^\mp$ 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 $τ^- τ^+$ pair production can easily be distinguished at more than 5$σ$ level from the s-channel production as that predicted in the standard model. The smoking gun signature of doubly same sign $μ^\pm μ^\pm + τ^\mpτ^\mp$ pairs production can have a 5$σ$ sensitivity, at a muon collider of 3 TeV with $\mathcal{O}$($fb^{-1}$) luminosity.