Intermediate effective interactions and dynamical fermion mass generation of QCD

TL;DR

This paper uses a two-loop functional renormalization group approach with an intermediate effective action to study dynamical fermion mass generation in QCD, revealing how certain four-fermion interactions influence mass degeneration.

Contribution

It introduces a two-loop FRG formulation with an intermediate effective action to analyze high-dimensional operators in QCD and their role in fermion mass generation.

Findings

Four types of fermion-4 interactions generate fermion mass.

Two types of interactions lead to fermion mass degeneration.

Flow patterns indicate mass degeneration at large dimensionless mass.

Abstract

The functional renormalization group equation is expanded to a two-loop form. This two-loop form equation involves one-loop effective action. An intermediate effective action perspective is adopted toward the one-loop effective action. That is to say, the intermediate effective action could not be of the same form of the bare action and one can make an ansatz to it. Thus by focusing on different high dimensional operators, effects of the chosen operators can be investigated. QCD through intermediate fermion-4 interactions is investigated. Of the 6 kinds of fermion-4 interactions generated by one-loop QCD, 4 kinds generate fermion mass while the other 2 kinds degenerate it. The net effect is fermion mass degeneration when dimensionless mass is large. Flow patterns on the $\tilde{m}^2_{\text{phys.}}-\tilde{g}^2$ plane are drawn.