Charged Higgs Study through Triple or Double Higgs Production in a General Two Higgs Doublet Model at Future Lepton Collide

In this study the charged Higgs signal through triple or double Higgs production in a general two Higgs doublet model (2HDM) is investigated. The main production process is $e^+e^- \rightarrow H^+H^-H^0$ followed by the charged Higgs decay to a pair of $\tau \nu$ and the neutral Higgs decay to $b\bar{b}$. The alternative process $H^+W^-H^0$ is also included as a source of charged Higgs signal in the analysis having comparable cross-section. The focus is on a future $e^+e^-$ linear collider operating at $\sqrt{s}=1.5$ TeV. The final state under consideration ($\tau^+ \tau^- b \bar{b} E^{\textnormal{miss}}_{T}$) is suitable for electroweak background rejection using the $b-$tagging tools. It is shown that although the signal cross section is small, with a reasonable background suppression, high signal significance values are achievable at an integrated luminosity $500 fb^{-1}$ depending on the charged Higgs mass, $\tan\beta~$ and the CP-odd neutral Higgs mass. Finally results are quoted in terms of the signal significance for charged Higgs in the mass range $170<m_{H^{\pm}}<400$ GeV.