  We develop a systematic and general approach to study the effective Higgs
Lagrangian in a supersymmetric framework in which the Higgs fields in the
visible sector couple weakly to another sector. The extra sector may be
strongly coupled in general. It is assumed to be superconformal in the
ultraviolet, but develop a mass-gap with supersymmetry breaking in the
infrared. The main technique used in our approach is that of the operator
product expansion (OPE). By using OPE methods we are able to compute the
parameters in the Higgs Lagrangian to quadratic order and make general
statements that are applicable to many classes of models. Not only does this
approach allow us to understand the traditional problems plaguing simple models
from a different perspective, it also reveals new possibilities for solutions
of these problems. The methods and results of our work should be useful in
constructing a viable and natural model of physics beyond the Standard Model.
