We discuss the future prospects of heavy neutrino searches at next generation lepton colliders. In particular, we focus on the planned electron-positron colliders, operating in two different beam modes, namely, $e^+e^-$ and $e^-e^-$. In the $e^+e^-$
beam mode, we consider various production and decay modes of the heavy neutrino ($N$), and find that the final state with $e+2j+{E!!!/}_T$, arising from the $e^+e^-to N u$ production mode, is the most promising channel. However, since this mode is insensitive to the Majorana nature of the heavy neutrinos, we also study a new production channel $e^+e^-to Ne^pm W^mp$, which leads to a same-sign dilepton plus four jet final state, thus directly probing the lepton number violation in $e^+e^-$ colliders. In the $e^-e^-$ beam mode, we study the prospects of the lepton number violating process of $e^-e^-to W^-W^-$, mediated by a heavy Majorana neutrino. We use both cut-based and multivariate analysis techniques to make a realistic calculation of the relevant signal and background events, including detector effects for a generic linear collider detector. We find that with the cut-based analysis, the light-heavy neutrino mixing parameter $|V_{eN}|^2$ can be probed down to $sim 10^{-4}$ at 95% C.L. for the heavy neutrino mass up to $400$ GeV or so at $sqrt s=500$ GeV with $100 rm{fb}^{-1}$ of integrated luminosity. For smaller mixing values, we show that a multivariate analysis can improve the signal significance by up to an order of magnitude. These limits will be at least an order of magnitude better than the current best limits from electroweak precision data, as well as the projected limits from $sqrt s=14$ TeV LHC.
We investigate the effect of introducing a sequential generation of chiral fermions in the Higgs Triplet Model with nontrivial mixing between the doublet and triplet Higgs. We use the available LHC data for Higgs boson production and decay rates, the
constraints on the fourth generation masses, and impose electroweak precision constraints from the S, T and U parameters. Our analysis shows that an SM-like Higgs boson state at ~125 GeV can be accommodated in the Higgs Triplet Model with four generations, and thus, that four generations survive collider and electroweak precision constraints in models beyond SM.
