Weak solution method of the non-perturbative renormalization group equation to describe dynamical chiral symmetry breaking and its application to beyond the ladder analysis in QCD

TL;DR

This paper introduces a weak solution approach to the non-perturbative renormalization group equation for analyzing dynamical chiral symmetry breaking in QCD, improving gauge dependence issues without bosonization.

Contribution

It presents a novel weak solution method for NPRG equations in QCD, avoiding bosonization and enhancing gauge invariance in chiral condensate calculations.

Findings

Weak solution method effectively describes DCSB in QCD.

Non-ladder approximation reduces gauge dependence.

Method simplifies evaluation via characteristic curves.

Abstract

The method of non-perturbative renormalization group (NPRG) is applied to the analysis of dynamical chiral symmetry breaking (DCSB) in QCD. We show that the DCSB solution of the NPRG flow equation can be obtained without the bosonization. The solution, having the singular point, can be authorized as the weak solution of partial differential equation, and can be easily evaluated using the method of the characteristic curve. Also we show that our non-ladder extended approximation improves almost perfectly the gauge dependence of the chiral condensates.