  We present a comprehensive study on Higgs pair production in various
archetypical extended Higgs sectors such as the real and the complex
2-Higgs-Doublet Model, the 2-Higgs-Doublet Model augmented by a real singlet
field and the Next-to-Minimal Supersymmetric extension of the Standard Model.
We take into account all relevant theoretical and experimental constraints, in
particular the experimental limits on non-resonant and resonant Higgs pair
production. We present the allowed cross sections for Standard Model (SM)-like
Higgs pair production and the ranges of the SM-like Yukawa and trilinear Higgs
self-coupling that are still compatible with the applied constraints.
Furthermore, we give results for the pair production of a SM-like with a
non-SM-like Higgs boson and for the production of a pair of non-SM-like Higgs
bosons. We find that di-Higgs production in the models under investigation can
exceed the SM rate substantially, not only in the non-resonance region but also
due to resonant enhancement. We give several benchmarks with interesting
features such as large cross sections, the possibility to test CP violation,
Higgs-to-Higgs cascade decays or di-Higgs production beating single Higgs
production. In all of our benchmark points, the next-to-leading order QCD
corrections are included in the large top-mass limit. For these points, we
found that, depending on the model and the Higgs pair final state, the
corrections increase the leading order cross section by a factor of 1.79 to
2.24. We also discuss the relation between the description of Higgs pair
production in an effective field theory approach and in the specific models
investigated here.
