Prospects for probing neutral vector-like leptons via pair production at muon collider

Vector-like leptons (VLLs) are well-motivated candidates for physics beyond the Standard Model. We investigate the sensitivity of the $6$ TeV muon collider to the neutral doublet VLL (denoted as $N$) via its pair production within a general VLL framework. Taking vector-like muon as a case study, we study the subsequent decay $N\rightarrow W^+ \mu$ and analyze two representative signals, namely $4j2\mu$ and $2\ell2\mu E\mkern-10.5 mu/$, arising from the hadronic and leptonic decays of the $W$ boson, respectively. The signal and background events are simulated within a complete Monte Carlo framework, and a cut-based analysis is performed at the $6$ TeV muon collider with an integrated luminosity $\mathcal{L}=4$ ab$^{-1}$ and beam polarizations $(P_{\mu^+},P_{\mu^-})=(-1,1)$. We consider VLL masses in the range of $1300-3000$ GeV and evaluate the corresponding search sensitivity. Our results show that the future $6$ TeV muon collider can effectively probe neutral doublet VLLs through the $4j2\mu$ and $2\ell2\mu E\mkern-10.5 mu/$ signals, with statistical significances exceeding $5\sigma$ over a broad mass range. These results demonstrate that the future $6$ TeV muon collider has excellent potential to search neutral doublet VLLs.