Displaced Heavy Neutral Lepton from New Higgs Doublet

Heavy neutral leptons $N$ are introduced to explain the tiny neutrino masses via the seesaw mechanism. For proper small mixing parameter $V_{\ell N}$, the heavy neutral leptons $N$ become long-lived, which leads to the displaced vertex signature at colliders. In this paper, we consider the displaced heavy neutral lepton from the neutrinophilic Higgs doublet $\Phi_\nu$ decay. The new Higgs doublet with MeV scale VEV can naturally explain the tiny neutrino masses with TeV scale $N$. Different from current experimental searches via the $W^\pm\to \ell^\pm N$ decay, the new decays as $H^\pm\to \ell^\pm N$ are not suppressed by the small mixing parameter $V_{\ell N}$. Therefore, a larger parameter space is expected to be detected at colliders. We then investigate the promising region at the 14 TeV HL-LHC and the 3 TeV CLIC. According to our simulation, the DV signature could probe $|V_{\ell N}|^2\gtrsim10^{-19}$ with $m_N<m_{H^+}$, which covers the seesaw predicted value $|V_{\ell N}|^2\sim m_\nu/m_N$. We could probe $m_{H^+}\lesssim1200$ GeV at the 14 TeV HL-LHC and $m_{H^+}\lesssim1490$ GeV at the 3 TeV CLIC.