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It is well known that the Standard Model of the Electroweak interactionsrests on a metastable vacuum. This can only be fixed by means of new physics.Presently neutrino physics provides the most intriguing framework to formulatenew physics. This is so because, in addition to the problem of the lightness ofthe active standard neutrinos, currently MiniBooNE experimental result may beindicating that sterile neutrinos exist and are light, too. In this case, it isreasonable to expect that the framework that yields light active and sterileneutrinos could stabilize the vacuum, too. In order to achieve this goal, weconsider an extension of the standard model which involves new fermions in theform of right-handed neutrinos ($\nu_R$) and new scalars in the form of triplet($\Delta$) and singlet ($\sigma$). Within this framework, tiny masses areobtained when we consider that lepton number is spontaneously broken at lowenergy scale which means that $\Delta$ and $\sigma$, both, develop very smallvacuum expectation values. We investigate if this setting leads to a stablevacuum. For this we obtain the whole set of conditions over the Quartic Termsof the Potential that ensures that the model is Bounded From Below(BFB) andevaluate the RGE-evolution of the self coupling of the Higgs. We show that insuch a scenario the Quartic Coupling $\Phi^T \Delta \Phi \sigma$, where $\Phi$is the standard Higgs doublet, is responsible for the stability of theElectroweak Vacuum up to Planck scale. We also extract constraints over theparameters of the Potential by means of Lepton Flavor Violating(LFV) processesand from invisible decay of the standard-like Higgs.

Vacuum stability and spontaneous violation of the lepton number at low energy scale in a model for light sterile neutrinos