Constraining minimal Type-III Seesaw Model from naturalness, Lepton Flavor Violation and Electroweak Vacuum stability

We study the minimal type-III seesaw model in which we extend the SM by adding two $SU(2)_L$ triplet fermions with zero hypercharge to explain the origin of the non-zero neutrino masses. We show that the naturalness conditions and the limits from lepton flavor violating decays provide very stringent bounds on the model parameters along with the constraints from the stability/metastability of the electroweak vacuum. We perform a detailed analysis of the model parameter space including all the constraints for both normal as well as inverted hierarchies of the light neutrino masses. We find that most of the region that are allowed by lepton flavor violating decays and naturalness fall in the stable/metastable region depending on the values of the standard model parameters.