Novel Signatures of Heavy Neutral Lepton at Muon Collider

The Higgs-strahlung process $\ell^+\ell^-\to Z h$ is one of the most important production channels of the standard model Higgs boson $h$ at the lepton colliders. The cross section reaches the maximum value slightly above the threshold $\sqrt{s}\sim m_Z+m_h$, and decreases as $\sim 1/s$ at high energies. In the gauged extension models, the new gauge boson $Z'$ and heavy Higgs boson $H$ exist after the symmetry breaking. The heavy Higgs-strahlung process $\ell^+\ell^-\to Z' H$ would also reach the maximum cross section around the threshold $\sqrt{s}\sim m_{Z'}+m_H$. Therefore, the future high energy lepton colliders, such as the TeV scale muon collider, are promising to probe this new process. If heavy neutral lepton $N$ is introduced to generate the tiny neutrino masses via seesaw mechanism, novel signatures could arise from $\mu^+\mu^-\to Z' H \to NN +NN \to 4 \mu^\pm +4J$ and $\mu^+\mu^-\to Z' H \to \mu^+\mu^- +NN \to 3 \mu^\pm \mu^\mp +2J$, where the fat-jets $J$ come from the hadronic decay of $W$ bosons. In this paper, we investigate the same-sign tetralepton signature $4\mu^\pm+4J$ and the same-sign trilepton signature $3\mu^\pm \mu^\mp + 2J$ at the 3 TeV and 10 TeV muon collider.