Effective Action Approach to Heavy Particle Contributions and Wilsonian Renormalization

We work in theories with both light and heavy particles. A method to obtain an effective low energy action with respect to the light particle is presented. Thanks to Wilsonian renormalization, we obtain effective actions with finite number of local operators describing possible non-decoupling effects of heavy particles. The validity of the method is first checked by explicit computation of a specific observable, the $\rho$ - parameter, in the framework of effective theory. Then we discuss a procedure to obtain the full effective action with respect to light particles in a typical example of the system of (t, b) doublet, gauge bosons and Higgs doublet, regarding only t quark as a heavy particle.