Quark-Antiquark Bound States in the Relativistic Spectator Formalism

TL;DR

This paper develops a relativistic covariant framework using the spectator formalism to analyze quark-antiquark bound states, ensuring confinement and applying it to pions and kaons with promising results.

Contribution

It introduces a covariant formalism for confined quark-antiquark states using the relativistic spectator equations, including regularization and chiral symmetry considerations.

Findings

Proves the linear potential yields zero decay amplitudes, consistent with confinement.

Improves regularization of singularities in the potential.

Successfully describes properties of pions and kaons.

Abstract

The quark-antiquark bound states are discussed using the relativistic spectator (Gross) equations. A relativistic covariant framework for analyzing confined bound states is developed. The relativistic linear potential developed in an earlier work is proven to give vanishing meson$\to$ $q+\bar{q}$ decay amplitudes, as required by confinement. The regularization of the singularities in the linear potential that are associated with nonzero energy transfers (i.e. $q^2=0,q^{\mu}\neq0$) is improved. Quark mass functions that build chiral symmetry into the theory and explain the connection between the current quark and constituent quark masses are introduced. The formalism is applied to the description of pions and kaons with reasonable results.