Higgs boson pair production through gauge boson fusion at linear colliders within the general 2HDM

Inclusive Higgs boson pair production through the mechanism of gauge boson fusion e+e−→V∗V∗→hh+X (V=W±,Z) in the general Two-Higgs-Doublet Model (2HDM), with h=h0,H0,A0,H±, is analyzed at O(αew4) in the linear colliders ILC and CLIC. This kind of processes is highly sensitive to the trilinear (3H) Higgs boson self-interactions and hence can be a true keystone in the reconstruction of the Higgs potential. For example, in the ILC at 1 TeV, the most favorable scenarios yield cross-sections up to roughly 1 pb, thus entailing 105 events per 100 fb−1 of integrated luminosity, whilst remaining fully consistent with the perturbativity and unitarity bounds on the 3H couplings, the electroweak precision data and the constraints from B(b→sγ). Comparing with other competing mechanisms, we conclude that the Higgs boson-pair events could be the dominant signature for Higgs-boson production in the TeV-class linear colliders for a wide region of the 2HDM parameter space, with no counterpart in the Minimal Supersymmetric Standard Model (MSSM). Owing to the extremely clean environment of these colliders, inclusive 2H events should allow a comfortable tagging and might therefore open privileged new vistas into the structure of the Higgs potential.