Charged Higgs bosons produced either in top-quark decays or in association with a top-quark, subsequently decaying via $H^{\pm} \to \tau^{\pm}\nu_{\tau}$, are searched for in 140 $\text{fb}^{-1}$ of proton-proton collision data at $\sqrt{s}=13$ TeV recorded with the ATLAS detector. Depending on whether the top-quark produced together with the $H^{\pm}$ decays hadronically or semi-leptonically, the search targets $\tau$+jets or $\tau$+lepton final states, in both cases with a $\tau$-lepton decaying into a neutrino and hadrons. No significant excess over the Standard Model background expectation is observed. For the mass range of $80 \leq m_{H^{\pm}} \leq 3000$ GeV, upper limits at 95% confidence level are set on the production cross-section of the charged Higgs boson times the branching fraction $\mathrm{\cal{B}}(H^{\pm} \to \tau^{\pm}\nu_{\tau})$ in the range 4.5 pb-0.4 fb. In the mass range 80-160 GeV, assuming the Standard Model cross-section for $t\bar{t}$ production, this corresponds to upper limits between 0.27% and 0.02% on $\mathrm{\cal{B}}(t\to bH^{\pm}) \times \mathrm{\cal{B}}(H^{\pm} \to \tau^{\pm}\nu_{\tau})$.
A search for charged Higgs bosons decaying into a top quark and a bottom quark is presented. The data analysed correspond to 139 fb$^{-1}$ of proton-proton collisions at $\sqrt{s}$=13TeV, recorded with the ATLAS detector at the LHC. The production of a heavy charged Higgs boson in association with a top quark and a bottom quark, $pp\rightarrow tbH^{+}\rightarrow tbtb$, is explored in the $H^+$ mass range from 200 to 2000 GeV using final states with jets and one electron or muon. Events are categorised according to the multiplicity of jets and $b$-tagged jets, and multivariate analysis techniques are used to discriminate between signal and background events. No significant excess above the background-only hypothesis is observed and exclusion limits are derived for the production cross-section times branching ratio of a charged Higgs boson as a function of its mass; they range from 3.6 pb at 200 GeV to 0.036 pb at 2000 GeV at 95% confidence level. The results are interpreted in the hMSSM and $M_h^{125}$ scenarios.
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