Type-III Seesaw: Phenomenological Implications of the Information Lost in Decoupling from High-Energy to Low-Energy

The type-III seesaw seems to explain the very minuteness of neutrino masses readily and naturally. The high-energy see-saw theories usually involve a larger number of effective parametres than the physical and measurable parametres appearing in the low-energy neutrino phenomenology. Casas-Ibarra parametrisation facilitates to encode the information lost in integrating the heavy fermions out in an arbitrary complex orthogonal matrix. The CMS collaboration has already searched for triplet fermions in the type-III seesaw model with only one generation of triplet fermion flavour democratically decaying into SM leptons. We reinterpret this CMS search in the context of a realistic type-III seesaw model with two or three generations of triplet fermions, and endeavour to comprehend the implications of the foregoing matrix on the $95\%$ CL lower limit on the mass of the triplet fermions. We also discuss the phenomenological implication of the aforesaid matrix in view of charged lepton flavour violating observables and displaced decays of the triplet fermions at colliders.