Revealing the origin of neutrino masses through the Type II Seesaw mechanism at high-energy muon colliders

The future muon collider can play as an ideal machine to search for new physics at high energies. In this work, we study the search potential of the heavy Higgs triplet in the Type II Seesaw mechanism at muon colliders with high collision energy and high luminosity. The latest neutrino oscillation data are taken into account for realizing the leptonic decay modes of the charged Higgs bosons $(H^{\pm\pm},~H^{\pm})$ in the Type II Seesaw. We show the impact of neutrino mass and mixing parameters on the purely leptonic decays. The pair production of doubly charged Higgs $H^{++}H^{--}$ is through direct $\mu^+\mu^-$ annihilation and vector boson fusion (VBF) processes at muon collider. The associated production $H^{\pm\pm}H^{\mp}$ can only be induced by VBF processes. We simulate both the purely leptonic and bosonic signal channels of charged Higgs bosons in Type II Seesaw, together with the Standard Model backgrounds. We show the required luminosity for the discovery of the charged Higgses and the reachable limits on the leptonic decay branching fractions.