Collider Phenomenology of $e^{-}e^{-}\to W^{-}W^{-}$

Whether in nature exists Majorana neutrino is one of the most fundamental questions in physics. It is directly related to the violation of accidental $U(1)$-lepton number symmetry(LNV). Enormous efforts had been put into such test and among them, one conventional experiment is the neutrinoless double-beta decay ($0\nu\beta\beta$). On the other hand, there have been proposals of future electron-positron colliders such as International Linear Collider (ILC) for precision measurements of Higgs boson or new discovered beyond SM particles and it can potentially be converted into an electron-electron collider. Such collider enables a new probe of Majorana neutrino via the inverse $0\nu\beta\beta$ process($e^{-}e^{-}\to W^- W^-$) as an alternative and complementary test to the conventional neutrinoless double-beta decay experiments. In this paper, we illustrate the searching strategies of $e^{-}e^{-}\to W^- W^-$ at future electron colliders, and find that the channels of pure hadronic, semi-leptonic with muon and pure leptonic with muons have the most discovery potential.