Triple Higgs boson production in the linear collider

Triple Higgs boson production (3H) may provide essential information to reconstruct the Higgs potential. We consider 3H-production in the International Linear Collider (ILC) both in the Minimal Supersymmetric Standard Model (MSSM) and in the general Two-Higgs-Doublet Model (2HDM). We compute the total cross-section for the various 3H final states, such as H+H 12h0, H0A0h0, etc., and compare with the more traditional double Higgs (2H) boson production processes. While the cross-sections for the 2H final states lie within the same order of magnitude in both the MSSM and 2HDM, we find that for the 3H states the maximum 2HDM cross-sections, being of order 0.1 pb, are much larger than the MSSM ones which, in most cases, are of order 10 126 pb or less. Actually, the 3H processes could be the dominant mechanism for Higgs boson production in the 2HDM. Ultimately, the origin of the remarkable enhancement of the 3H channels in the 2HDM case (for both type I and type II models) originates in the structure of the trilinear Higgs boson couplings. The extremely clean environment of the ILC should allow a relatively comfortable tagging of the three Higgs boson events. In view of the fact that the MSSM contribution is negligible, these events should manifest themselves mainly in the form of 6 heavy-quark jet final states. Some of these signatures could be spectacular, and in case of being detected would constitute strong evidence of an extended Higgs sector of non-supersymmetric origin