Light Pseudoscalar Mesons: an Inverse Instantaneous Bethe-Salpeter Glimpse

TL;DR

This paper explores the use of inversion techniques on simplified Bethe-Salpeter equations to gain insights into the effective interactions responsible for the bound states of light pseudoscalar mesons like pions and kaons, which are linked to chiral symmetry breaking.

Contribution

It introduces a novel application of inversion methods to simplified Bethe-Salpeter equations to qualitatively analyze the effective interactions in light pseudoscalar mesons.

Findings

Provides a qualitative understanding of the effective interaction

Suggests a route to interpret meson bound states

Links meson properties to chiral symmetry breaking

Abstract

Achieving self-consistent simultaneous interpretations of pions and kaons as bound states of quark and antiquark and as the (almost) massless boson states related, according to Goldstone's theorem, to the dynamical (and explicit) breakdown of the chiral symmetries of QCD still represents a major challenge. Applying inversion techniques to conveniently simplified versions of the homogeneous Bethe-Salpeter equation, governing bound states in quantum field theory, enables us to get along a straightforward route a qualitative idea of how the underlying effective interaction might look like.