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The Higgs trilinear coupling provides a unique opportunity to study thestructure of the Higgs sector and probe indirect signs of BSM Physics -- evenif new states are somehow hidden. In models with extended Higgs sectors, largedeviations in the Higgs trilinear coupling can appear at one loop because ofnon-decoupling effects in the radiative corrections involving the additionalscalar states. It is then natural to ask how two-loop corrections modify thisresult, and whether new large corrections can appear again. We present newresults on the dominant two-loop corrections to the Higgs trilinear coupling inseveral models with extended scalar sectors. We illustrate the analyticalexpressions with numerical examples and show that, while they remain smallerthan their one-loop counterparts and do not modify significantly thenon-decoupling effects observed at one loop, the two-loop corrections are notentirely negligible -- a typical size being 10-20% of the one-loop corrections.

Two-loop corrections to the Higgs trilinear coupling in models with extended scalar sectors