# Derivation of the effective Chiral Lagrangian for pseudoscalar, scalar, vector and axial-vector mesons from QCD

## TL;DR

This paper extends a derivation of the effective chiral Lagrangian from QCD to include scalar, vector, and axial-vector mesons, linking their properties to Bethe-Salpeter equations in the large Nc and Abelian approximations.

## Contribution

It generalizes previous work to incorporate additional meson types and relates their effective field equations to fundamental Bethe-Salpeter equations from QCD.

## Key findings

- Properties of added mesons are determined by Bethe-Salpeter equations.
- Masses in the equations are those from the Bethe-Salpeter solutions.
- Effective Lagrangian includes scalar, vector, and axial-vector mesons.

## Abstract

A previous formal derivation of the effective chiral Lagrangian for low-lying pseudoscalar mesons from first-principles QCD without approximations [Wang et al., Phys. Rev. D61, (2000) 54011] is generalized to further include scalar, vector, and axial-vector mesons. In the large Nc limit and with an Abelian approximation, we show that the properties of the newly added mesons in our formalism are determined by the corresponding underlying fundamental homogeneous Bethe--Salpeter equation in the ladder approximation, which yields the equations of motion for the scalar, vector, and axial-vector meson fields at the level of an effective chiral Lagrangian. The masses appearing in the equations of motion of the meson fields are those determined by the corresponding Bethe--Salpeter equation.