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We study the vacuum behavior of an extended Higgs sector with two doublets ina scenario with a softly broken \texorpdfstring{$U(1)$}{lg} global symmetry.The soft-violation term is introduced to avoid massless-axion particles arisingwhen the global symmetry becomes spontaneously broken. This model hasmetastable states through the possible presence of multiple non-degenerateminima, which is unwanted from the phenomenological point of view if themetastable state is not long-lived enough. The analysis of this fact leads tofind possible exclusion limits over parameter space of quartic couplings.Results improve the individual behavior of initial conditions forrenormalization group equations; also determining unstable zones for theeffective Higgs potential at one loop level. Besides vacuum stability analyses,the influence of absence of charge violation minima is considered as a limitingcase excluding zones in the parameter space. Extremal cases for the model aswell as criticality phenomena are discussed with the aid of relation amongHiggs masses or splittings among them. From vacuum behavior and LHC results,phenomenological aspects in the searching of charged and heavier Higgs bosonsare considered to evaluate the scalar alignment regimen of the two Higgsdoublet model.

Phenomenological aspects from vacuum stability and metastability in  models with soft breaking of a \texorpdfstring{$U\left( 1\right)$}{lg} global  symmetry