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We study the vacuum behavior at one loop level in extended Higgs sectors withtwo doublets (2HDM), where $U(1)$ and $Z_{2}$ symmetries are considered toprotect the $CP$ symmetry in the Higgs potential and to avoid Flavor ChangingNeutral Currents at tree level in the Yukawa sector. In the Inert Higgs Modelcase, a detailed comparison is made between both models by using the energyevolution of couplings, which should satisfy energy scale dependent relationsdeduced for minima and stationary points of the Higgs potential at tree level.Besides, perturbative unitarity constraints at tree level are considered togenerate the allowed parameter space compatible with perturbativity (absence ofLandau poles). Our studies illustrate exclusion regions for Higgs masses andother combinations of couplings in the scalar sector, in particular forsplittings of mass square for neutral scalars $A^{0}$ and $H^{0}$, as well asthe difference between the sum of these and the charged Higgs mass square. Fromthe vacuum stability for inert-2HDM at the tree and one loop levels, analyseslead us to find out new hierarchical structures for scalar masses. To completevacuum studies on the Inert model, and based on reparameterization invarianceof the Higgs potential, we compute original discriminants that allow ensuringthe presence of a global electroweak minimum at tree level. Moreover, thebehavior in high energy scales drives out analyzing criticality phenomena forthe additional parameters of extended Higgs sectors. Finally, and using theconsistency with the electroweak precision analyses of oblique parameters, wedescribe several implications from different regimes of the inert model oncharged and pseudoscalar Higgs searches.

Study of vacuum behavior for inert models with discrete $Z_{2}$-like and abelian $U(1)$ symmetries