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

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