The three-quark potential and perfect Abelian dominance in SU(3) lattice QCD

Abstract

We study the static three-quark (3Q) potential for more than 300 different patterns of 3Q systems with high statistics, i.e., 1000-2000 gauge configurations, in SU(3) lattice QCD at the quenched level. For all the distances, the 3Q potential is found to be well described by the Y-ansatz, i.e., one-gluon-exchange (OGE) Coulomb plus Y-type linear potential. Also, we investigate Abelian projection of quark confinement in the context of the dual superconductor picture proposed by Yoichiro~Nambu~{\it et al.} in SU(3) lattice QCD. Remarkably, quark confinement forces in both Q$\bar{\mathrm{Q}}$ and 3Q systems can be described only with Abelian variables in the maximally Abelian gauge, i.e., ${\sigma }_{\mathrm{Q}\bar{\mathrm{Q}}}\simeq {\sigma }_{\mathrm{Q}\bar{\mathrm{Q}}}^{\mathrm{Abel}}\simeq {\sigma }_{3Q}\simeq {\sigma }_{3Q}^{\mathrm{Abel}}$, which we call ``perfect Abelian dominance'' of quark confinement.

Comments: 7 pages, 4 figures