Unravelling the left-right mixing using $0\nu \beta\beta$ decay and collider probes

In the context of the minimal left-right symmetric model, we study the interplay between current and future neutrinoless double beta ($0\nu\beta\beta$) decay experiments, long-lived particle searches at the LHC main detectors ATLAS/CMS, and the proposed far detector MATHUSLA. The heavy Majorana neutrino can be produced in association with an electron from the decay of $W$ boson for a non-zero left-right mixing and subsequently decays into another electron with the same charge and jets. Owing to the suppression of large right-handed charged gauge boson $W_R$ mass, the heavy neutrinos could be long-lived. We show that long-lived particle (LLP) searches for heavy Majorana neutrinos in the same-sign dilepton channel at the LHC can be used to extend $W_R$ boson mass reach relative to the reach of the Keung-Senjanovic (KS) process. Finally, we show that sensitivities of LLP searches at the high-luminosity LHC with main detectors ATLAS/CMS are competitive with those of future $0\nu\beta\beta$ decay searches.