Constraints on TeV scale Majorana neutrino phenomenology from the Vacuum Stability of the Higgs

The vacuum stability condition of the Standard Model Higgs potential with mass in the range of 124-127 GeV puts an upper bound on the Dirac mass of the neutrinos. We study this constraint with the right-handed neutrino masses upto TeV scale. The heavy neutrinos contribute to $\Delta L=2$ processes like neutrinoless double beta decay and same-sign-dilepton production in the colliders. The vacuum stability criterion also restricts the light-heavy neutrino mixing and constrains the branching ratio of lepton flavour violating process, like $\mu \to e \gamma$ mediated by the heavy neutrinos. We show that neutrinoless double beta decay with a lifetime $\sim 10^{25}$ years can be observed if the the lightest heavy neutrino mass is $<$ 4.5 TeV. We show that the vacuum stability condition and the experimental bound on $\mu \rightarrow e \gamma$ together put a constrain on heavy neutrino mass $M_R >$ 3.3 TeV. Finally we show that the observation of same-sign-dileptons (SSD) associated with jets at the LHC needs much larger luminosity than available at present. We have estimated the possible maximum cross-section for this process at the LHC and show that with an integrated luminosity 100 $fb^{-1}$ it may be possible to observe the SSD signals as long as $M_R <$ 400 GeV.