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

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 $16^{3}32$ and at $\beta =6.0$ on $20^{3}32$ 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 ${\sigma }_{3\mathrm{Q}}{L}_{\min }$, where $L_{\min }$ 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 ${\sigma }_{3\mathrm{Q}}^{\mathrm{Abel}}$ with an accuracy within a few percent deviation, i.e., ${\sigma }_{3\mathrm{Q}}\simeq {\sigma }_{3\mathrm{Q}}^{\mathrm{Abel}}$, which means Abelian dominance of the quark-confining force in 3Q systems.

Comments: 7pages, 7figures, 3tables; published version