Light Pseudoscalar Mesons in Bethe-Salpeter Equation with Instantaneous Interaction

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.

14 pages, 4 figures

References in corpus (2)

• Exact Solutions of Bethe-Salpeter Equations with Instantaneous Interactions
• Stability in the instantaneous Bethe-Salpeter formalism: harmonic-oscillator reduced Salpeter equation

Cited by in corpus (7)

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• Goldstonic pseudoscalar mesons in Bethe-Salpeter-inspired setting
• Goldstone-Type Pseudoscalar Mesons: Instantaneous Bethe-Salpeter Models
• Simplified Bethe-Salpeter Description of Basic Pseudoscalar-Meson Features