Chiral Lagrangian and chiral quark model from confinement in QCD

TL;DR

This paper derives the effective chiral Lagrangian from QCD using confinement, computes its coefficients, and connects it to the chiral quark model, extending low-energy descriptions to higher momenta.

Contribution

It provides a derivation of the chiral Lagrangian from QCD with confinement, calculating coefficients directly from quark Green's functions and linking to the chiral quark model.

Findings

Coefficients of the chiral Lagrangian match experimental data.

Derived GOR relations and quark decay constants from QCD.

Extended low-energy Lagrangian to arbitrary momenta.

Abstract

The effective chiral Lagrangian in both nonlocal form $L_{ECCL}$ and standard local form $L_{ECL}$ are derived in QCD using the confining kernel, obtained in the vacuum correlator formalism. As a result all coefficients of $L_{ECL}$ can be computed via $q\bar q$ Green's functions. In the $p^2$ order of $L_{ECL}$ one obtains GOR relations and quark decay constants $f_a$ are calculated $a=1,...8$, while in the $p^4$ order the coefficients $L_1, L_2, L_3,L_4, L_5, L_6$ are obtained in good agreement with the values given by data. The chiral quark model is shown to be a simple consequence of $L_{ECCL}$ with defined coefficients. It is demonstrated that $L_{ECCL}$ gives an extension of the limiting low-energy Lagrangian $L_{ECL}$ to arbitrary momenta.