Abstract
In this paper, we consider a minimal extension to the standard model by a scalar triplet field with hypercharge Y = 2. This model relies on the seesaw mechanism which provides a consistent explication of neutrino mass generation. We show from naturalness considerations that the Veltman condition is modified by virtue of the additional scalar charged states and that quadratic divergencies at one loop can be driven to zero within the allowed parameter space of the model; the latter is severely constrained by unitarity and boundedness from below, and it is consistent with the di-photon Higgs decay data of the LHC. Furthermore, we analyze the naturalness condition effects to the masses of heavy Higgs bosons H^0, A^0, H^± and H^±±, providing a drastic reduction of the ranges of variation of mH± and mH±± with an upper bounds at 288 and 351 GeV, respectively, while predicting almost a degeneracy for the other neutral Higgs bosons H^0, A^0 at about 207 GeV.