Functional renormalization flow and dynamical chiral symmetry breaking of QCD

TL;DR

This paper investigates the regulator dependence in functional renormalization group equations of QCD, deriving one-loop flow equations that include mass dependence, and explores conditions for chiral symmetry breaking and the conformal window.

Contribution

It introduces a regulator parameter to achieve regulator independence and derives novel mass-dependent flow equations for QCD.

Findings

Flow patterns vary with regulator parameter.

A mechanism for the absence of chiral symmetry breaking is proposed.

The conformal window is discussed via renormalization flow.

Abstract

The dependence of function renormalization group equation on regulators is investigated. A parameter is introduced to control the suppression of regulators. Functional renormalization group equations will become regulator-independent if this newly introduced parameter is sent to infinity in the end of calculation. One-loop renormalization flow equations of QCD are derived. The novelty is that both the coupling running equation and the mass running equation are mass-dependent. Different flow patterns are explored. A mechanism for non-occurrence of dynamical chiral symmetry breaking is arrived at. The existence of a conformal window is also discussed in the language of renormalization flow.