Quark confinement and color transparency in a gauge-invariant formulation of QCD

TL;DR

This paper explores a gauge-invariant formulation of QCD, revealing how nonlocal interactions between quark color charges diminish in singlet states and analyzing their behavior in an SU(2) model, with implications for understanding confinement and transparency.

Contribution

It introduces a gauge-invariant approach to QCD interactions, showing how color-singlet configurations weaken interactions and providing a nonperturbative evaluation method in an SU(2) model.

Findings

Color-singlet quark packets experience reduced interactions as they shrink.

Residual interactions increase with the expansion of quark packets.

Nonperturbative evaluation of nonlocal interactions in an SU(2) model.

Abstract

We examine a nonlocal interaction that results from expressing the QCD Hamiltonian entirely in terms of gauge-invariant quark and gluon fields. The interaction couples one quark color-charge density to another, much as electric charge densities are coupled to each other by the Coulomb interaction in QED. In QCD, this nonlocal interaction also couples quark color-charge densities to gluonic color. We show how the leading part of the interaction between quark color-charge densities vanishes when the participating quarks are in a color singlet configuration, and that, for singlet configurations, the residual interaction weakens as the size of a packet of quarks shrinks. Because of this effect, color-singlet packets of quarks should experience final state interactions that increase in strength as these packets expand in size. For the case of an SU(2) model of QCD based on the {\em ansatz} that the gauge-invariant gauge field is a hedgehog configuration, we show how the infinite series that represents the nonlocal interaction between quark color-charge densities can be evaluated nonperturbatively, without expanding it term-by-term. We discuss the implications of this model for QCD with SU(3) color and a gauge-invariant gauge field determined by QCD dynamics.