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

We study the vacuum behavior of an extended Higgs sector with two doublets in a scenario with a softly broken \texorpdfstring{$U(1)$}{lg} global symmetry. The soft-violation term is introduced to avoid massless-axion particles arising when the global symmetry becomes spontaneously broken. This model has metastable states through the possible presence of multiple non-degenerate minima, which is unwanted from the phenomenological point of view if the metastable state is not long-lived enough. The analysis of this fact leads to find possible exclusion limits over parameter space of quartic couplings. Results improve the individual behavior of initial conditions for renormalization group equations; also determining unstable zones for the effective Higgs potential at one loop level. Besides vacuum stability analyses, the influence of absence of charge violation minima is considered as a limiting case excluding zones in the parameter space. Extremal cases for the model as well as criticality phenomena are discussed with the aid of 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.