Three-quark potential and Abelian dominance of confinement in SU(3) QCD

TL;DR

This study demonstrates that the three-quark potential in SU(3) QCD can be accurately described by the Abelian projection, showing Abelian dominance in the confinement mechanism through lattice simulations.

Contribution

It provides the first detailed lattice QCD evidence that the Abelian projected potential reproduces the three-quark confinement force with high accuracy.

Findings

The three-quark potential follows the Y ansatz with Coulomb and linear terms.

The Abelian part of the potential closely matches the non-Abelian potential.

Abelian dominance of the quark-confining force is confirmed within a few percent accuracy.

Abstract

We study the baryonic three-quark (3Q) potential and its Abelian projection in terms of the dual-superconductor picture in SU(3) quenched lattice QCD. The non-Abelian SU(3) gauge theory is projected onto Abelian U(1)$^2$ gauge theory in the maximal Abelian gauge. We investigate the 3Q potential and its Abelian part for more than 300 different patterns of static 3Q systems in total at $\beta=5.8$ on $16^332$ and at $\beta=6.0$ on $20^332$ with 1000-2000 gauge configurations. For all the distances, both the 3Q potential and Abelian part are found to be well described by the Y ansatz, i.e., two-body Coulomb term plus three-body Y-type linear term $\sigma_{3\mathrm{Q}} L_{\mathrm{min}}$, where $L_{\mathrm{min}}$ is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension $\sigma_{3\mathrm{Q}}$ and its Abelian part $\sigma_{3\mathrm{Q}}^{\rm Abel}$ with an accuracy within a few percent deviation, i.e., $\sigma_{3\mathrm{Q}} \simeq \sigma_{3\mathrm{Q}}^{\rm Abel}$, which means Abelian dominance of the quark-confining force in 3Q systems.