# Monopole Dominance of Confinement in SU(3) Lattice QCD

## TL;DR

This study confirms monopole dominance in SU(3) lattice QCD, supporting the dual superconductor model of quark confinement by demonstrating that monopoles account for most of the confining force in both quark-antiquark and three-quark systems.

## Contribution

It provides the first detailed lattice QCD evidence of monopole dominance in SU(3), validating the dual superconductor picture of confinement for complex quark systems.

## Key findings

- Perfect Abelian dominance of string tension in large-volume lattices.
- The static 3Q potential fits the Y-Ansatz with three-body linear term.
- Monopole part reproduces approximately 92% of the full string tension.

## Abstract

To check the dual superconductor picture for the quark-confinement mechanism, we evaluate monopole dominance as well as Abelian dominance of quark confinement for both quark-antiquark and three-quark systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static $Q\bar Q$ system in lattice QCD with various spacing $a$ at $\beta$=5.8-6.4 and various size $L^3$x$L_t$. For large physical-volume lattices with $La \ge$ 2fm, we find perfect Abelian dominance of the string tension for the $Q\bar Q$ systems: $\sigma_{Abel} \simeq \sigma$. Second, we accurately measure the static 3Q potential for more than 300 different patterns of 3Q systems with 1000-2000 gauge configurations using two large physical-volume lattices: ($\beta$,$L^3$x$L_t$)=(5.8,$16^3$x32) and (6.0,$20^3$x32). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz: two-body Coulomb term plus three-body Y-type linear term $\sigma L_{min}$, where $L_{min}$ is the minimum flux-tube length connecting the three quarks. We find perfect Abelian dominance of the string tension also for the 3Q systems: $\sigma^{Abel}_{3Q}\simeq \sigma_{3Q} \simeq \sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $\beta$=5.8 on $16^3$x32 with 2,000 gauge configurations. Abelian-projected QCD in the MA gauge has not only the color-electric current $j^\mu$ but also the color-magnetic monopole current $k^\mu$, which topologically appears. By the Hodge decomposition, the Abelian-projected QCD system can be divided into the monopole part ($k_\mu \ne 0$, $j_\mu=0$) and the photon part ($j_\mu \ne 0$, $k_\mu=0$). We find monopole dominance of the string tension for $Q\bar Q$ and 3Q systems: $\sigma_{Mo}\simeq 0.92\sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.