Analytic Bethe-Salpeter Description of the Lightest Pseudoscalar Mesons

TL;DR

This paper presents an analytic Bethe-Salpeter approach to describe the lightest pseudoscalar mesons, capturing their near-masslessness, asymptotic behavior, and confinement features within a quark-antiquark bound state framework.

Contribution

It introduces a fully analytic Bethe-Salpeter method to model pseudoscalar mesons, emphasizing their Goldstone boson nature, asymptotic properties, and confinement characteristics.

Findings

Successfully models near-massless pions and kaons as Goldstone bosons.

Reproduces correct asymptotic behavior of Bethe-Salpeter amplitudes.

Ensures pointwise behavior consistent with color confinement.

Abstract

Within the Bethe-Salpeter formalism for instantaneous interactions, we describe, along a totally analytic route, the lightest pseudoscalar mesons by quark-antiquark bound states which show at least three indispensable general features, namely, the (almost) masslessness required for pions and kaons to be interpretable as (pseudo) Goldstone bosons, the suitable asymptotic behaviour in the limit of large spacelike relative momenta as determined by the relationship between quark mass function and Bethe-Salpeter amplitudes, and a pointwise behaviour for finite spacelike relative momenta suited for guaranteeing colour confinement.