Research of Extra Charged Gauge Boson $W^{\mathrm{\prime }}$ in Alternative Left-Right Model at Future Muon Collider

The study of extra charged gauge boson beyond the Standard Model has always been of great interest. Future muon colliders will have a significant advantage in discovering exotic particles. In this paper, by studying the ${\mu }^{+}{\mu }^{-}\to W^{\mathrm{\prime }+}{W}^{\mathrm{\prime }-}\to e^{+}{e}^{-}{n}_e{\bar{n}}_e$ process, we explore the properties of $W^{\mathrm{\prime }}$ in the alternative left-right model. The cross section and angular distribution of the final electron are investigated in the scenario of different $W^{\mathrm{\prime }}$ mass and right-handed coupling constant. The forward-backward asymmetry is also an important observable to reflect the properties of $W^{\mathrm{\prime }}$. We provide a method to effectively suppress the background processes. With specific kinematic cuts, the significance can reach $5.17\sigma$ for 4.8 TeV $W^{\mathrm{\prime }}$ at the collision energy of 10 TeV.