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The vacuum stability condition of the Standard Model Higgs potential withmass in the range of 124-127 GeV puts an upper bound on the Dirac mass of theneutrinos. We study this constraint with the right-handed neutrino masses uptoTeV scale. The heavy neutrinos contribute to $\Delta L=2$ processes likeneutrinoless double beta decay and same-sign-dilepton production in thecolliders. The vacuum stability criterion also restricts the light-heavyneutrino mixing and constrains the branching ratio of lepton flavour violatingprocess, like $\mu \to e \gamma$ mediated by the heavy neutrinos. We show thatneutrinoless double beta decay with a lifetime $\sim 10^{25}$ years can beobserved if the the lightest heavy neutrino mass is $<$ 4.5 TeV. We show thatthe 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) associatedwith jets at the LHC needs much larger luminosity than available at present. Wehave estimated the possible maximum cross-section for this process at the LHCand show that with an integrated luminosity 100 $fb^{-1}$ it may be possible toobserve the SSD signals as long as $M_R <$ 400 GeV.

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