Light charged Higgs boson production via $cb-$fusion at the Large Hadron Collider

We analyse the production of a light charged Higgs boson at the Large Hadron Collider (LHC) via the quark-fusion mechanism $c \bar{b} \to H^- $ considering the decay channel $H^- \to \tau \bar \nu_\tau$ in the final state. We study this process in the framework of the 2-Higgs Doublet Model Type III (2HDM-III) with lepton-specific Yukawa couplings and assess the LHC sensitivity to such $H^\pm$ signals against the dominant irreducible background. We show that BR$(H^\pm \to cb) \sim 0.1- 0.2$ and BR$(H^\pm \to \tau \nu) \sim 0.7-0.9$ so that, under these conditions, the prospects for $H^\pm$ detection in the 2HDM-III in the aforementioned production and decay channels are excellent assuming standard collider energy and luminosity conditions.