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 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: ${\sigma }_{3Q}^{Abel}\simeq {\sigma }_{3Q}\simeq \sigma$. 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.

Comments: 8 pages, 8 figures