Renormalization Flow of Bound States

TL;DR

This paper introduces a renormalization group flow framework that describes how bound states and fundamental particles can be viewed as scale-dependent entities, using the gauged Nambu--Jona-Lasinio model as an example.

Contribution

It develops a unified renormalization flow approach that captures the scale dependence of bound states and fundamental particles in quantum field theories.

Findings

Bound states and fundamental particles are classified by fixed points in the flow.

The approach applies to the gauged Nambu--Jona-Lasinio model at weak coupling.

The flow equations reveal the scale-dependent nature of bound states.

Abstract

A renormalization group flow equation with a scale-dependent transformation of field variables gives a unified description of fundamental and composite degrees of freedom. In the context of the effective average action, we study the renormalization flow of scalar bound states which are formed out of fundamental fermions. We use the gauged Nambu--Jona-Lasinio model at weak gauge coupling as an example. Thereby, the notions of bound state or fundamental particle become scale dependent, being classified by the fixed-point structure of the flow of effective couplings.