Sketching the Bethe-Salpeter kernel

TL;DR

This paper derives an exact, symmetry-preserving form of the axial-vector Bethe-Salpeter equation with dressed quark-gluon vertices, enabling analysis of meson mass responses and chiral symmetry effects.

Contribution

It introduces a novel, exact formulation of the Bethe-Salpeter kernel with dressed vertices, preserving symmetries and allowing detailed meson spectrum analysis.

Findings

Dynamical chiral symmetry breaking enhances spin-orbit splitting.

The derived equations form a closed, symmetry-preserving system.

Comparison of pseudoscalar and scalar meson responses to vertex dressing.

Abstract

An exact form is presented for the axial-vector Bethe-Salpeter equation, which is valid when the quark-gluon vertex is fully dressed. A Ward-Takahashi identity for the Bethe-Salpeter kernel is derived therefrom and solved for a class of dressed quark-gluon vertex models. The solution provides a symmetry-preserving closed system of gap and vertex equations. The analysis can be extended to the vector equation. This enables a comparison between the responses of pseudoscalar- and scalar meson masses to nonperturbatively dressing the quark-gluon vertex. The result indicates that dynamical chiral symmetry breaking enhances spin-orbit splitting in the meson spectrum.