Probing Charged Higgs Bosons in the 2-Higgs Doublet Model Type-II with Vector-Like Quarks

We study the phenomenology of charged Higgs bosons ($H^\pm$) and Vector-Like Quarks (VLQs), denoted as $T$, the latter possessing a charge identical to the top quark one, within the framework of the Two Higgs Doublet Model Type-II (2HDM-II). Upon examining two scenarios, one featuring a singlet $(T)$ (2HDM-II+$(T)$) and another a doublet $(TB)$ (2HDM-II+$(TB)$), we discover that the presence of VLQs has a significant effect on the (pseudo)scalar sector of the 2HDM-II. In particular, this leads to a reduction in the strict constraint on the mass of the charged Higgs boson, which is imposed by $B$-physics observables, specifically $B\to X_s\gamma$. {The observed reduction stems from modifications in the charged Higgs couplings to the Standard Model (SM) top and bottom quarks}. Notably, the degree of this reduction varies distinctly between the singlet 2HDM+$(T)$ and doublet 2HDM+$(TB)$ scenarios. Additionally, our investigation extends to constraints imposed by the oblique parameters $S$ and $T$ on the VLQ mixing angles. Furthermore, to facilitate efficient exploration of the '2HDM-II+VLQ' parameter space, we present results on pair production of VLQs $T$ ($pp\to T\bar T$), followed by $T\to H^\pm b$ and $H^\pm \to tb$ decays, yielding a distinctive $2t4b$ final state. This investigation thus provides valuable insights guiding the search for extended Higgs and quark sectors at the Large Hadron Collider (LHC) at CERN.