Instantaneous Bethe-Salpeter View of Goldstone-Type Pseudoscalar Mesons

TL;DR

This paper presents an instantaneous Bethe-Salpeter approach that effectively models light pseudoscalar mesons as near-massless quark-antiquark bound states, capturing essential relativistic effects and their Goldstone boson nature.

Contribution

It introduces a simplified Bethe-Salpeter formalism that retains key relativistic effects, improving the understanding of pseudoscalar mesons as Goldstone bosons.

Findings

Successfully models near-massless pseudoscalar mesons

Retains relativistic effects from the full quark propagator

Provides a simple yet effective framework for meson description

Abstract

Describing the lightest pseudoscalar mesons as bound states of quark and antiquark within the framework of an instantaneous Bethe-Salpeter formalism constructed such as to retain (in contrast to Salpeter's equation) as much information on the relativistic effects provided by the full quark propagator as conceivable allows for a surprisingly simple implementation of their near masslessness mandatory for their interpretability as pseudo-Goldstone bosons related to the spontaneous breaking of the chiral symmetries of quantum chromodynamics.