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 $H^{\pm }\to {\tau }^{\pm }\nu$ : $ c b \to H^\pm \to \tau^\pm \bar \nu $. 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.