Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction

TL;DR

This paper develops an analytical approach within the Bethe-Salpeter formalism to connect the chiral symmetry properties and the bound state wave functions of light pseudoscalar mesons, providing exact solutions and insights into their interactions.

Contribution

It introduces a method to derive exact Bethe-Salpeter solutions for pseudoscalar mesons using chiral symmetry constraints in an instantaneous approximation.

Findings

Established the relationship between interactions and Bethe-Salpeter amplitudes.

Derived analytical solutions for pseudoscalar meson bound states.

Linked chiral symmetry properties with bound state wave functions.

Abstract

The light pseudoscalar mesons play a twofold role: they may or have to be regarded both as low-lying bound states of the fundamental degrees of freedom of quantum chromodynamics as well as the (pseudo-) Goldstone bosons of the spontaneously broken chiral symmetries of quantum chromodynamics. We interrelate these aspects in a single quantum-field-theoretic approach relying on the Bethe-Salpeter formalism in instantaneous approximation by very simple means: the shape of the pseudoscalar-meson Bethe-Salpeter wave function dictated by chiral symmetry is used in Bethe-Salpeter equations for bound states of vanishing mass, in order to deduce analytically the interactions which govern the bound states under study. In this way, we obtain exact Bethe-Salpeter solutions for pseudoscalar mesons, in the sense of establishing the rigorous relationship between, on the one hand, the relevant interactions and, on the other hand, the Bethe-Salpeter amplitudes that characterize the bound states.