New Physics Search via the Higgs Self-Coupling
  We discuss quantum corrections of new physics to the triple coupling of the lightest CP-even Higgs boson in the Two Higgs Doublet Model (THDM) and also in the Minimal Supersymmetric Standard Model (MSSM). In the THDM, quartic contributions of the mass of heavy particles in the loop can appear, which are not absorbed by renormalization of the Higgs boson mass. Such non-decoupling effects on the self-coupling can give corrections of ${\cal O}(100%)$, even when all measured Higgs couplings with gauge bosons and fermions are consistent with the Standard Model prediction. In the MSSM, the loop-corrections decouple in such a scenario. 
Shinya Kanemura, Shingo Kiyoura, Yasuhiro Okada, Eibun Senaha, C.-P.   Yuan