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Production of charged Higgs $H^\pm$ through $cb$-fusion at LHC

Considering the framework of the 2-Higgs Doublet Model Type III (2HDM-III), wherein two doublets are coupled both to up as down fermions, and the Flavour Changin Currents (FCNCs) is controlled by a four-zero Texture approach in the Yukawa matrices. We study the production of charged Higgs ($H^\pm$) by means of $cb$ quark fusion followed by channel decay $H^\pm \to τ^\pm ν$ : $ c b \to H^\pm \to τ^\pm \bar ν$. Taking in account the experimental bounds, as well as the theoretical constraints analysed in previous work arXiv:2003.06263[hep-ph]. One can show that in a lepton-specific-like incarnation of the model, we obtain a significant sensitivity for the LHC machine. We consider in the aforementioned study to both irreducible and reducible backgrounds of the SM.