Gluon flux-tube distribution and linear confinement in baryons

TL;DR

This study uses lattice QCD to visualize and analyze gluon flux-tube formations in baryons, confirming Y-shaped flux tubes at large separations and quantifying their properties, advancing understanding of confinement mechanisms.

Contribution

It provides the first gauge-independent observation of flux-tube geometries in baryons and quantitatively compares flux-tube length with static quark potential, confirming the Y-shape configuration at large distances.

Findings

Y-shaped flux tubes form at large quark separations

Flux tube radius is approximately 0.38 fm

Potential energy correlates with flux-tube length

Abstract

We have observed the formation of gluon flux-tubes within baryons using lattice QCD techniques. A high-statistics approach, based on translational and rotational symmetries of the four-dimensional lattice, enables us to observe correlations between vacuum action density and quark positions in a completely gauge independent manner. This contrasts with earlier studies which used gauge-dependent smoothing techniques. We used 200 O(a^2) improved quenched QCD gauge-field configurations on a 16^3x32 lattice with a lattice spacing of 0.123 fm. In the presence of static quarks flux tubes representing the suppression of gluon-field fluctuations are observed. We have analyzed 11 L-shapes and 8 T and Y shapes of varying sizes in order to explore a variety of flux-tube topologies, including the ground state. At large separations, Y-shape flux-tube formation is observed. T-shaped paths are observed to relax towards a Y-shaped topology, whereas L-shaped paths give rise to a large potential energy. We do not find any evidence for the formation of a Delta-shaped flux-tube (empty triangle) distribution. However, at small quark separations, we observe an expulsion of gluon-field fluctuations in the shape of a filled triangle with maximal expulsion at the centre of the triangle. Having identified the precise geometry of the flux distribution, we are able to perform quantitative comparison between the length of the flux-tube and the associated static quark potential. For every source configuration considered we find a universal string tension, and conclude that, for large quark separations, the ground state potential is that which minimizes the length of the flux-tube. The flux tube radius of the baryonic ground state potential is found to be 0.38 \pm 0.03 fm, with vacuum fluctuations suppressed by 7.2 \pm 0.6 %.