We study new physics effects on the couplings of weak gauge bosons with the lightest CP-even Higgs boson ($h$), $hZZ$, and the trilinear coupling of the lightest Higgs boson, $hhh$, at the one-loop order, as predicted by the two Higgs doublet model. Those renormalized coupling constants can deviate from the standard model (SM) predictions due to two distinct origins: the tree level mixing effect of Higgs bosons and the quantum effect of additional particles in loop diagrams. The latter can be enhanced in the renormalized $hhh$ coupling constant when the additional particles show the nondecoupling property. Therefore, even in the case where the $hZZ$ coupling is close to the SM value, deviation in the $hhh$ coupling from the SM value can become as large as plus 100%, while that in the $hZZ$ coupling is at most minus 1% level. Such large quantum effect on the Higgs trilinear coupling is distinguishable from the tree level mixing effect, and is expected to be detectable at a future linear collider.

We analyze the theoretical and phenomenological considerations for the electroweak phase transition and dark matter in an extension of the standard model with a complex scalar singlet (cxSM). In contrast with earlier studies, we use a renormalization group improved scalar potential and treat its thermal history in a gauge-invariant manner. We find that the parameter space consistent with a strong first-order electroweak phase transition (SFOEWPT) and present dark matter phenomenological constraints is significantly restricted compared to results of a conventional, gauge-noninvariant analysis. In the simplest variant of the cxSM, recent LUX data and a SFOEWPT require a dark matter mass close to half the mass of the standard model-like Higgs boson. We also comment on various caveats regarding the perturbative treatment of the phase transition dynamics.