Long-lived sterile neutrino searches at future muon colliders

We explore the potential of studying sterile neutrinos at a future high-energy muon collider, where these particles can generate small active neutrino masses via the seesaw mechanism and exhibit long-lived particle signatures. A Dirac sterile neutrino model with U(1)Lμ-Lτ symmetry is introduced, where the heavy right-handed neutrino (NR) produces tiny active neutrino masses, and the light left-handed neutrino (NL) naturally behaves as a long-lived particle. The U(1)Lμ-Lτ gauge symmetry also enhances sterile neutrino pair production at a future high-energy muon collider. Using the displaced vertex method, the muon collider can search for heavy sterile neutrino, especially for mL>mW. We find that a muon collider with s=3(10) TeV and luminosity L=1(10) ab-1 can probe NL masses of mL∈[100,1500(5000)] GeV and mixing angles θνL∈[10-13,10-6].