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

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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 β=5.8 on 16³32 and at β=6.0 on 20³32 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 σ₃Q Lmin, where Lmin is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension σ₃Q and its Abelian part σ₃Q Abel with an accuracy within a few percent deviation, i.e., σ₃Q ≃ σ₃Q Abel, which means Abelian dominance of the quark-confining force in 3Q systems.