Search for charged Higgs bosons through vector-like top quark pair production at the LHC

We investigate the discovery prospects for a vector-like top partner (VLT) in the Type-II Two-Higgs-Doublet Model (2HDM-II) extended by a vector-like quark doublet ($TB$) at the 14~TeV LHC. The study focuses on the pair production process $pp \to T\bar{T} \to bH^+\, \bar{b}H^- \to b(tb)\, \bar{b}(\bar{t}b)$, yielding fully hadronic final states characterized by high $b$-jet multiplicity. Two analysis strategies are employed, requiring at least four or five $b$-tagged jets (4$b$ and 5$b$), to exploit the signal topology. Assuming a charged Higgs mass of $m_{H^\pm} \sim 600$~GeV and a systematic uncertainty of $\delta = 5\%$, the 4$b$ channel enables discovery up to $m_T \sim 1200$~GeV at $\mathcal{L} = 300~\text{fb}^{-1}$, while the 5$b$ analysis extends the reach to $m_T \sim 1300$~GeV. At higher luminosities of 1000--3000~fb$^{-1}$, the 5$b$ strategy achieves discovery sensitivity up to $m_T \sim 1400$~GeV. The reach is significantly reduced as $m_{H^\pm}$ increases, due to the suppression of the $\text{BR}(T \to H^+ b)$: for $m_{H^\pm} \sim 1000$~GeV, discovery becomes unattainable across all luminosity and systematic uncertainty configurations. Sensitivity is also strongly impacted by systematic uncertainties: for $\delta = 10\%$ and $m_{H^\pm} < 1000$~GeV, discovery remains viable up to $m_T \sim 1200$~GeV in the 5$b$ analysis, while for $\delta = 20\%$, no discovery is achievable for $m_T \geq 1000$~GeV.