Theoretical and phenomenological analyses from vacuum stability, perturbative unitarity, and oblique parameters in the Two Higgs Doublet Model

In light of the new results from experiments like the ones coming from the Large Hadron Collider (LHC), theoretical and phenomenological implications are comprehensively studied from an extended scalar sector given by the Two Higgs Doublet Model. A review and a brief status based on symmetries and Spontaneous Symmetry Breaking patterns are discussed. By using the hidden reparametrization invariance, we focused our analyses on Higgs potential behavior at tree level and Next to Leading Order. Particularly, positivity constraints to get a bounded from below Higgs potential are broadly analyzed. Moreover, since metastable states might be present even at tree level, compatible parameter space can be discussed from new limits; being this fact pointed out to an improvement of Next to Leading Order results. Exclusions over parameter space coming from to avoid limiting charge violation vacua scenarios are converted in complementary studies to whose associated with vacuum stability analyses. Besides these studies, we also consider the strongest conditions from perturbativity unitarity analyses in scattering processes for the scalar sector. Further, since brief surveys over unitarity is possible to introduce the concept of fermion mass scale as well as to study its realization in general Yukawa couplings in the 2HDMs. Besides, this treatment allows tackling the problem of perturbative unitarity in fermion-antifermion scattering. As a central point, we discussed unitarity bounds over flavor changing neutral currents couplings, which are compatible with those yielded by perturbativity in renormalization group equations. The most important feature of these bounds is the independence with Higgs masses and mixing angles. As a prototypical and realistic example incorporating all fundamentals described above, we present one complete scanning from vacuum analyses of several parameters spaces in an inert-2HDM with Z2 and U(1) symmetries. For scalar mass splittings in different zones of parameter space, we focused over stability bounds and described the evolution of instabilities and non-perturbative zones (yielding possible Landau poles). Moreover, we present new constraints to find one global minimum in the theory of the inert scenario. We apply a methodology based on reparameterization group formalism for the Higgs potential in 2HDMs. Bounds established by metastability analyses are evaluated regarding allowed zones compatible with one loop level studies for vacuum stability and unitarity systematics. All these regions are also analyzed from several phenomenological realizations and oblique parameters. Other archetypes scenarios to study the vacuum behavior of an extended Higgs sector are the two Higgs doublet models under the implementation of a softly broken U(1) global symmetry. The soft term is induced to forbid massless-axion particles arising when the global symmetry becomes spontaneously broken. 2HDMs with a soft breaking of U(1) global symmetry have metastability regions through the possible presence of multiple non-degenerate minima. Metastable states are unwanted from the phenomenological point of view if the other local minima are not long-lived enough. The analysis of this fact leads to find possible exclusion limits over parameter space of quartic couplings. It improves the individual behavior of initial conditions for renormalization group equations; also determining unstable zones for the Higgs potential at one loop level. Besides vacuum stability analyses, the influence of absence of charge violation minima is considered in all studies. Extremal cases for the model as well as criticality phenomena are comprehensively discussed using relation among Higgs masses or splittings among them. From vacuum behavior and LHC results, phenomenological aspects in the searching of charged and heavier Higgs bosons are considered to evaluate the scalar alignment regimen of the two Higgs doublet model.