Implications of light charged Higgs boson at the LHC Run III in the 2HDM

In this study, we focus on the bosonic decays of light charged Higgs boson (i.e., with $M_{H^\pm}<m_t$) in the 2-Higgs Doublet Model (2HDM) Type-I. To study the signal of such a charged Higgs state at the Large Hadron Collider (LHC), in a scenario where the $H^0$ boson is the Standard Model (SM)-like one already discovered, we assume that it decays mainly via $h^0W^{\pm *}$ and/or $H^\pm\to A^0W^{\pm *}$ (i.e., via an off-shell $W^{\pm}$ boson), which can reach a sizable Branching Ratio (BR) for $\tan\beta\geq4$, when the exclusion bounds from $H^\pm\to\tau\nu$ and $c{s}$ searches get weaker. By using six Benchmark Points (BPs), which are consistent with current LHC constraints, we perform a Monte Carlo (MC) study and examine the sensitivity of the LHC to light charged Higgs boson decaying via the above bosonic modes and produced in top decay following both single top and top pair production processes. Our findings demonstrate that, when the integrated luminosity can reach 100 fb$^{-1}$, the LHC has the potential to either discover or rule out most of these BPs via either of these two production and decay channels or both.