The distribution of gluon fields in a baryon is of fundamental interest in QCD. We have observed the formation of gluon flux-tubes within baryons using lattice QCD techniques. In particular we use a high-statistics approach, based on the translational and rotational symmetries of the four-dimensional lattice, which enables us to observe correlations between the vacuum action density and the quark positions in a completely gauge independent manner. This contrasts with earlier studies which needed to use gauge-dependent smoothing techniques. We use 200 $\mathcal{O}(a^2)$-improved quenched QCD gauge-field configurations on a ${16}^3\times 32$ lattice with a lattice spacing of 0.123 fm. Vacuum field fluctuations are observed to be suppressed in the presence of static quarks such that flux tubes represent the suppression of gluon-field fluctuations. We considered numerous different link paths in the creation of the static quark sources in order to investigate the dependence of the flux tubes on the source shape. 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 do observe an expulsion of gluon-field fluctuations in the shape of a filled triangle with maximal expulsion at the center of the triangle. Having identified the precise geometry of the flux distribution, we are able to perform a 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 characteristic flux tube radius of the baryonic ground state potential is found to be $0.38\pm 0.03\mathrm{fm}$, with vacuum fluctuations suppressed by $7.2\pm 0.6\%$. The node connecting the flux tubes is 25% larger at $0.47\pm 0.02\mathrm{fm}$ with a larger suppression of the vacuum by $8.1\pm 0.7\%$

• Received 29 June 2006

DOI:https://doi.org/10.1103/PhysRevD.76.114512