We study the most popular scalar extension of the Standard Model, namely the Two Higgs doublet model, extended by a complex triplet scalar (2HDMcT). Such considering model with a very small vacuum expectation value, provides a solution to the massive neutrinos through the so-called type II seesaw mechanism. We show that the 2HDMcT enlarged parameter space allow for a rich and interesting phenomenology compatible with current experimental constraints. In this paper the 2HDMcT is subject to a detailed scrutiny. Indeed, a complete set of tree level unitarity constraints on the coupling parameters of the potential is determined, and the exact tree-level boundedness from below constraints on these couplings are generated for all directions. We then perform an extensive parameter scan in the 2HDMcT parameter space, delimited by the above derived theoretical constraints as well as by experimental limits. We find that an important triplet admixtures are still compatible with the Higgs data and investigate which observables will allow to restrict the triplet nature most effectively in the next runs of the LHC. Finally, we emphasize new production and decay channels and their phenomenological relevance and treatment at the LHC.

Following the recent update measurement of the W boson mass performed by the CDF-II experiment at Fermilab which indicates 7σ deviation from the SM prediction. As a consequence, the open question is whether there are extensions of the SM that can carry such a remarkable deviation or what phenomenological repercussions this has. In this paper, we investigate what the theoretical constraints reveal about the 123-model. Also, we study the consistency of a CDF W boson mass measurement with the 123-model expectations, taking into account theoretical and experimental constraints. Both fit results of S and T parameters before and after m CDF W measurement are, moreover, considered in this study. Under these conditions, we found that the 123-model prediction is consistent with the measured m CDF W at a 95% Confidence Level (CL).

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