Instantaneous Bethe-Salpeter Kernel for the Lightest Pseudoscalar Mesons

TL;DR

This paper reconstructs an instantaneous Bethe-Salpeter kernel from Dyson-Schwinger solutions to accurately describe the lightest pseudoscalar mesons as nearly massless quark-antiquark bound states, capturing their Goldstone boson nature.

Contribution

It provides a detailed reconstruction of the interaction kernel for the instantaneous Bethe-Salpeter equation based on Dyson-Schwinger solutions, enabling better modeling of pseudoscalar mesons.

Findings

Successfully describes light pseudoscalar mesons as (pseudo) Goldstone bosons.

Reveals the structure of the interaction kernel needed for accurate meson modeling.

Supports the connection between chiral symmetry breaking and meson properties.

Abstract

Starting from a phenomenologically successful, numerical solution of the Dyson-Schwinger equation that governs the quark propagator, we reconstruct in detail the interaction kernel that has to enter the instantaneous approximation to the Bethe-Salpeter equation to allow us to describe the lightest pseudoscalar mesons as quark-antiquark bound states exhibiting the (almost) masslessness necessary for them to be interpretable as the (pseudo) Goldstone bosons related to the spontaneous chiral symmetry breaking of quantum chromodynamics.