Despite the discovery of a Higgs boson h (125 GeV) at the LHC run 1, its self-interaction has fully evaded direct experimental probe so far. Such self-interaction is vital for electroweak symmetry breaking, vacuum stability, and electroweak phase transition. It is a most likely place to encode new physics beyond the standard model. We parametrize such new physics by model-independent dimension-six effective operators and study their tests via Higgs pair production at hadron colliders. We analyze three major di-Higgs production channels at the parton level and compare the parameter dependence of total cross sections and kinematic distributions at the LHC (14 TeV) and pp (100 TeV) hadron collider. We further perform full simulations for the di-Higgs production channel gg -> hh -> b (b) over bar gamma gamma and its backgrounds at the pp (100 TeV) hadron collider. We construct four kinds of benchmark points and study the sensitivities to probing different regions of the parameter space of cubic Higgs interactions. We find that for a one-parameter analysis and with a 3 ab(-1) (30 ab(-1)) integrated luminosity, the ggg -> hh -> b (b) over bar gamma gamma channel can measure the SM cubic Higgs coupling and the derivative cubic Higgs coupling to an accuracy of about 13 (4.2) and 5 (1.6), respectively.
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