Constraint for a light charged Higgs boson and its neutral partners from top quark pairs at the LHC

The charged Higgs boson plays an essential role in distinguishing between a wide variety of standard model extensions with multiple Higgs doublets, and has been searched for in various collider experiments. This paper expands our previous work to a broader Higgs mass space with discussions on subsequent issues. We study the prospect of a light charged Higgs boson, produced by top quark pairs at the Large Hadron Collider (LHC), and decaying into a $W$ boson (can be off shell) and a pair of bottom quarks via on-shell production of an intermediate neutral Higgs boson. We reinterpret the cross sections of $WWbb\bar{b}\bar{b}$ final states measured by the ATLAS collaboration at LHC 13 TeV in the presence of the decay chain: $t \rightarrow H^+ b, H^+ \rightarrow W^+ H_i, H_i \rightarrow b \bar{b}$, and H.c., where $H_i$ is a neutral Higgs boson variably lighter than the charged Higgs boson. We find improved agreements with the data and obtain limits on the total branching ratio of the aforementioned decay chain. The limits impose the strongest constraints on the parameter space of type-I two-Higgs-doublet model for most Higgs masses sampled when $H_i$ is the $CP$-odd Higgs boson $A$. We also calculate potential constraints with pseudodata in high-luminosity runs of the LHC.