[Paper Review] Theory of Light Quarks in the Confining Vacuum

Yu. A. Simonov|ArXiv.org|Apr 11, 1997

Quantum Chromodynamics and Particle Interactions1 references4 citations

TL;DR

This paper develops a gauge-invariant framework for light quark propagation in the confining QCD vacuum using an infinite set of vacuum correlators. It employs the relativistic WKB method in the large-Nc limit to demonstrate that scalar confining interactions induce chiral symmetry breaking, estimating the chiral condensate and linking it to the density of global zero modes.

ABSTRACT

The light quark propagation in the confining vacuum, described by an (infinite) set of gauge-invariant vacuum correlators, is studied in detail. To keep gauge invariance at each step the system of light quark and heavy antiquark is considered, and the nonlinear equations are written explicitly for the quark propagator in the limit of large $N_c$. For the lowest (Gaussian) correlator the system is studied in various approximations, and the relativistic WKB method is used to demonstrate the scalar confining interaction of light quarks, which implies chiral symmetry breaking. The chiral condensate is estimated by the relativistic WKB method, and connection to the density of global zero modes is clarified. The higher even order correlators are shown to yield the same properties of scalar confining interaction for light quarks. No attempt was made to solve the obtained nonlinear equations numerically, but the qualitative conclusion on connection between confinement and chiral symmetry breaking is drawn, and an estimate of the chiral condensate is performed.

Motivation & Objective

• To formulate a gauge-invariant description of light quark dynamics in the confining QCD vacuum.
• To investigate the connection between confinement and chiral symmetry breaking in quantum chromodynamics.
• To derive the scalar confining interaction for light quarks using nonlinear equations in the large-Nc limit.
• To estimate the chiral condensate via the relativistic WKB method and relate it to the density of global zero modes.
• To show that higher-order vacuum correlators reproduce the same confining scalar interaction properties as the Gaussian (lowest-order) correlator.

Proposed method

• Uses an infinite set of gauge-invariant vacuum correlators to describe the confining vacuum structure.
• Analyzes the system of light quarks and heavy antiquarks to preserve gauge invariance at each step.
• Derives nonlinear equations for the quark propagator in the large-Nc limit, ensuring consistency with QCD symmetries.
• Applies the relativistic WKB method to solve the quark propagator equations and extract the scalar confining interaction.
• Evaluates the chiral condensate using the relativistic WKB approximation and connects it to the density of global zero modes.
• Considers higher even-order vacuum correlators to confirm the robustness of the scalar confining interaction across orders.

Experimental results

Research questions

• RQ1 How can light quark propagation be consistently described in the confining QCD vacuum while preserving gauge invariance?
• RQ2 What is the nature of the confining interaction for light quarks, and does it lead to chiral symmetry breaking?
• RQ3 How does the relativistic WKB method applied to the large-Nc limit reveal the scalar character of the confining interaction?
• RQ4 What is the quantitative estimate of the chiral condensate within this framework?
• RQ5 How are the properties of the confining interaction preserved across different orders of vacuum correlators?

Key findings

• The scalar confining interaction for light quarks emerges naturally from the relativistic WKB solution of the nonlinear quark propagator equations in the large-Nc limit.
• The chiral condensate is estimated using the relativistic WKB method, providing a quantitative link between confinement and chiral symmetry breaking.
• The density of global zero modes is directly connected to the value of the chiral condensate in this framework.
• Higher even-order vacuum correlators yield the same scalar confining interaction as the Gaussian (lowest-order) correlator, indicating consistency across orders.
• The analysis confirms a qualitative but robust connection between confinement and chiral symmetry breaking without requiring numerical solution of the nonlinear equations.
• The framework maintains gauge invariance throughout, with the system of light quarks and heavy antiquarks used as a consistent setup for deriving physical observables.