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

Abstract

We study the search potential of heavy triplet leptons in a type-III seesaw mechanism at future high-energy and high-luminosity muon colliders. The impact of up-to-date neutrino oscillation results is taken into account on neutrino parameters and the consequent decay patterns of heavy leptons in a type-III seesaw. The three heavy leptons in the Casas-Ibarra parametrization with diagonal unity matrix are distinguishable in their decay modes. We consider the pair production of charged triplet leptons ${E}^{+}{E}^{\ensuremath{-}}$ through both ${\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ annihilation and vector boson fusion (VBF) processes. The leading-order framework of electroweak parton distribution functions is utilized to calculate the VBF cross sections. The charged triplet leptons can be probed for masses above $\ensuremath{\sim}1\text{ }\text{ }\mathrm{TeV}$. The ${E}^{+}{E}^{\ensuremath{-}}\ensuremath{\rightarrow}ZZ{\ensuremath{\ell}}^{+}{\ensuremath{\ell}}^{\ensuremath{-}}$ channel can be further utilized to fully reconstruct the three triplet leptons and distinguish neutrino mass patterns. The pair production of heavy neutrinos $N$ and the associated production ${E}^{\ifmmode\pm\else\textpm\fi{}}N$ are only induced by VBF processes and lead to a lepton-number-violating (LNV) signature. We also study the search potential of LNV processes at future high-energy muon colliders with $\sqrt{s}=30\text{ }\text{ }\mathrm{TeV}$.