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We study the search potential of heavy triplet leptons in Type III Seesawmechanism at future high-energy and high-luminosity muon colliders. The impactof up-to-date neutrino oscillation results is taken into account on neutrinoparameters and the consequent decay patterns of heavy leptons in Type IIISeesaw. The three heavy leptons in the Casas-Ibarra parametrization withdiagonal unity matrix are distinguishable in their decay modes. We consider thepair production of charged triplet leptons $E^+ E^-$ through both $\mu^+\mu^-$annihilation and vector boson fusion (VBF) processes. The leading-orderframework of electroweak parton distribution functions are utilized tocalculate the VBF cross sections. The charged triplet leptons can be probed formasses above $\sim 1$ TeV. The $E^+E^-\to ZZ\ell^+\ell^-$ channel can befurther utilized to fully reconstruct the three triplet leptons and distinguishneutrino mass patterns. The pair production of heavy neutrinos $N$ and theassociated production $E^\pm N$ are only induced by VBF processes and lead tolepton-number-violating (LNV) signature. We also study the search potential ofLNV processes at future high-energy muon collider with $\sqrt{s}=30$ TeV.

Probing heavy triplet leptons of the type-III seesaw mechanism at future muon colliders