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In composite Higgs models the Higgs boson arises as a pseudo-Goldstone bosonfrom a strongly-interacting sector. Fermion mass generation is possible throughpartial compositeness accompanied by the appearance of new heavy fermionicresonances. The Higgs couplings to the Standard Model (SM) particles andbetween the Higgs bosons themselves are modified with respect to the SM. Higgspair production is sensitive to the trilinear Higgs self-coupling but also toanomalous couplings like the novel 2-Higgs-2-fermion coupling emerging incomposite Higgs models. The QCD corrections to SM Higgs boson pair productionare known to be large. In this paper we compute, in the limit of heavy loopparticle masses, the next-to-leading order (NLO) QCD corrections to Higgs pairproduction in composite Higgs models without and with new heavy fermions. Therelative QCD corrections are found to be almost insensitive both to thecompositeness of the Higgs boson and to the details of the heavy fermionspectrum, since the leading order cross section dominantly factorizes. With theobtained results we investigate the question if, taking into account Higgscoupling constraints, new physics could first be seen in Higgs pair production.We find this to be the case in the high-luminosity option of the LHC forcomposite Higgs models with heavy fermions. We also investigate the invariantmass distributions at NLO QCD. While they are sensitive to the Higgsnon-linearities and hence anomalous couplings, the influence of the heavyfermions is much less pronounced.

Signs of Composite Higgs Pair Production at Next-to-Leading Order