Leading Higgs Mass Dependent Corrections to the Standard Model Lagrangian and its Two Higgs Doublet Extension

We present an alternative calculation for the leading Higgs mass dependent one--loop corrections to the standard model Lagrangian, using a background field technique. Cross--sections computed from our one--loop Lagrangian provide a check of and reproduce results already obtained in the existing literature using diagrammatic methods, as well as allowing an analysis of other processes involving longitudinally polarized $W^\pm$s and $Z^0$s. We concentrate on the processes $WW\rightarrow f\bar{f}$ and $f\bar{f}\rightarrow WW$. We extend our result to the case of a two Higgs doublet model, when one of the physical Higgs is much heavier than the other particles and analyze the tree+one--loop unitarity bounds on the scale at which signs of a strongly interacting sector (or the heaviest Higgs) must turn up.