Naturalness in Type II seesaw model and implications for physical scalars

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 space parameter of the model, the latter is severely constrained by unitarity, boundedness from below and is consistent with the di-photon Higgs decay data of LHC. Furthermore, we analyse the naturalness condition effects to the masses of heavy Higgs bosons $H^0$, $A^0$, $H^\pm$ and $H^{\pm\pm}$, providing a drastic reduction of the ranges of variation of $m_{H^{\pm}}$ and $m_{H^{\pm\pm}}$ with an upper bounds at $288$ and $351$~GeV respectively, while predicting an almost degeneracy for the other neutral Higgs bosons $H^0$, $A^0$ at about $207$~GeV.