Probing an extra Higgs boson at future linear $e^+ e^-$ colliders

We investigate the possibility of probing an extra Higgs boson at future linear $e^+ e^-$ colliders. We consider the production process $e^+e^- \to H\nu \bar\nu$, followed by the decay $H \to W^+W^-$, where $H$ is the extra $\textit{CP}$-even Higgs boson of the general two Higgs doublet model (G2HDM). This process is governed by the $\textit{CP}$-even Higgs mixing angle, $\cos\gamma$, offering direct access to this parameter. We discuss constraints on $\cos\gamma$ using existing LHC data and test the viability of the G2HDM top-quark-driven scenario for electroweak baryogenesis. We perform a full Monte Carlo simulation of the signal and background, and show that an extra Higgs boson in the mass range $200 \leq m_H \leq 400$ GeV could be probed at high energy linear $e^+ e^-$ colliders. Promising results are found for CLIC running at 1.5 and 3 TeV collision energies.