Dilepton events with displaced vertices, double beta decay, and resonant leptogenesis with Type-II seesaw dominance, TeV scale $Z'$ and heavy neutrinos

Abstract: In a class of Type-II seesaw dominated $SO(10)$ models proposed recently with heavy neutrinos, extra $Z'$ boson, and resonant leptogenesis, at first we show that the lightest first generation sterile neutrino that mediates dominant contributions to neutrinoless double beta decay also generates the displaced vertex leading to verifiable like-sign di-electron as well as di-muon production events outside the LHC detectors having suppressed standard model back-ground and missing energy. Resonant leptogenesis in this case is implemented by a pair of quasi-degenerate sterile neutrinos of the second and the third generations having masses of ${\cal O}(500)$ GeV. Then we predict a new alternative scenario where the models allow the second generation sterile neutrino mass to be ${\cal O}(10)$ GeV capable of mediating the dominant double beta decay as well as the displaced vertices for significantly improved number of like-sign dilepton events in different channels. Resonant leptogenesis in this alternative scenario is mediated by a pair of heavy quasi-degenerate sterile neutrino masses of the first and the third generations. In addition to QD type light neutrino mass hierarchy, we also show how these results are derived for the NH case. We also discuss $Z'$ production cross sections at $\sqrt s =14 $ TeV run-II of LHC and also at ILC. While the lepton flavour violating branching ratios are only few to four orders less than the current experimental bounds, proton lifetime predictions are accessible to ongoing Super K. or Hyper K. searches.