A newly released doctoral dissertation evaluates the LHC data to determine the current experimental constraints on the Higgs boson's self-coupling, K, in which the Standard Model expectation set to exactly 1 by definition. (The paper also has a well done 40 page summary of the physics of the Standard Model including the values of its experimentally measured constants and the outstanding unresolved issues in the Standard Model generally, in its introduction.) The results are consistent with the Standard Model expectation at the one sigma level although they aren't terribly tight. The pertinent part of the abstract is as follows:
Under the assumption that new physics affects only the Higgs-boson self-coupling, the combined H+HH best-fit value of the coupling modifier is: , excluding values outside the interval at 95% confidence level. Results with less stringent assumptions are also provided, decoupling the Higgs-boson self-coupling and the other Standard Model couplings. The final results of this thesis provide the most stringent constraint on from experimental measurements to date.