Monopole Dominance of Confinement in SU(3) Lattice QCD

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 (Q$\bar{\rm Q}$) and three-quark (3Q) systems in SU(3) quenched lattice QCD in the maximally Abelian (MA) gauge. First, we examine Abelian dominance for the static Q$\bar{\rm Q}$ system in lattice QCD with various spacing $a$ at $\beta=5.8-6.4$ and various size $L^3 \times L_t$. For large physical-volume lattices with $La \ge 2{\rm fm}$, we find {\it perfect Abelian dominance} of the string tension for the Q$\bar{\rm Q}$ systems: $\sigma_{\rm Abel} \simeq \sigma$. 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: $(\beta, L^3 \times L_t)$=(5.8, $16^3 \times 32$) and (6.0, $20^3\times 32$). For all the distances, the static 3Q potential is found to be well described by the Y-Ansatz, i.e., two-body Coulomb term plus three-body Y-type linear term $\sigma L_{\rm min}$, where $L_{\rm min}$ is the minimum flux-tube length connecting the three quarks. We find {\it perfect Abelian dominance} of the string tension also for the 3Q systems: $\sigma^{\rm Abel}_{\rm 3Q} \simeq \sigma_{\rm 3Q} \simeq \sigma$. Finally, we accurately investigate monopole dominance in SU(3) lattice QCD at $\beta$=5.8 on $16^3 \times 32$ 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$\bar{\rm Q}$ and 3Q systems: $\sigma_{\rm Mo} \simeq 0.92 \sigma$. While the photon part has almost no confining force, the monopole part almost keeps the confining force.