The process of gluon-initiated double Higgs production is sensitive to non-linear interactions of the Higgs boson. In the context of the Standard Model, studies of this process focused on the extraction of the Higgs trilinear coupling. In a general parametrization of New Physics effects, however, an even more interesting interaction that can be tested through this channel is the (ttbar hh) coupling. This interaction vanishes in the Standard Model and is a genuine signature of theories in which the Higgs boson emerges from a strongly-interacting sector. In this paper we perform a model-independent estimate of the LHC potential to detect anomalous Higgs couplings in gluon-fusion double Higgs production. We find that while the sensitivity to the trilinear is poor, the perspectives of measuring the new (ttbar hh) coupling are rather promising.

22 pages, 9 figures. v2: plots of Figs.8 and 9 redone to include experimental uncertainty on the Higgs couplings, references added