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The Higgs sector of models beyond the standard model requires specialattention and study, since through them, a natural explanation can be offeredto current questions such as the big differences in the values of the masses ofthe quarks (hierarchy of masses), the possible generation of flavor changingneutral currents (inspired by the evidence about the oscillations ofneutrinos), besides the possibility that some models, with more complicatedsymmetries than those of the standard model, have a non standard low energylimit. The simplest extension of the standard model known as thetwo-Higgs-doublet-model (2HDM) involves a second Higgs doublet. The 2HDMpredicts the existence of five scalar particles: three neutral ($A^{0}$),($h^{0}$, $H^{0}$) and two charged ($H^{\pm}$). The purpose of this work is todetermine in a natural and easy way the mass eigenstates and masses of thesefive particles, in terms of the parameters $\lambda_{i}$ introduced in theminimal extended Higgs sector potential that preserves the CP symmetry. Wediscuss several cases of Higgs mixings and the one in which two neutral statesare degenerate. As the values of the quartic interactions between the scalardoublets are not theoretically determined, it is of great interest to exploreand constrain their values, therefore we analize the stability and trivialitybounds using the Lagrange multipliers method and numerically solving therenormalization group equations. Through the former results one can establishthe region of validity of the model under several circumstances considered inthe literature.

Outlook on the Higgs particles, masses and physical bounds in the Two Higgs-Doublet Model