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Phenomenological studies of a CP-violating two-Higgs-doublet Model with type-II Yukawa couplings are presented. In the light of recent LHC data, an update on the viable parameter space that survives both the experimental and theoretical constraints is provided. In addition, the scope of the LHC in exploring this model through the discovery of a charged Higgs boson that decays in the tauonic mode is analysed. For this, various production channels were investigated, with emphasis on the boson-associated channel $gg\to H_i\to H^\pm W^\mp$ and the fermion-associated channels $gb\to H^\pm t$ and $gg\to H^\pm bt$. For the latter, a signal-over-background analysis is performed.

From realistic 2HDM-II CPV benchmarks to the $H^\pm \to\tau \nu$ decay at the LHC