Effective Action Approach to Heavy Particle Contributions and Wilsonian Renormalization

TL;DR

This paper presents a Wilsonian renormalization method to derive effective low-energy actions that incorporate non-decoupling effects of heavy particles, demonstrated through the $ ho$-parameter and top quark contributions.

Contribution

It introduces a systematic approach to obtain effective actions with finite local operators accounting for heavy particle effects in theories with both light and heavy particles.

Findings

Effective actions with finite local operators are derived.

The method accurately reproduces the $ ho$-parameter in the presence of heavy particles.

The approach is applied to the (t, b) doublet system, considering only the top quark as heavy.

Abstract

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.