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

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 $16^332$ and at $β=6.0$ on $20^332$ 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 $σ_{3\mathrm{Q}} L_{\mathrm{min}}$, where $L_{\mathrm{min}}$ is the minimum flux-tube length connecting the three quarks. We find equivalence between the three-body string tension $σ_{3\mathrm{Q}}$ and its Abelian part $σ_{3\mathrm{Q}}^{\rm Abel}$ with an accuracy within a few percent deviation, i.e., $σ_{3\mathrm{Q}} \simeq σ_{3\mathrm{Q}}^{\rm Abel}$, which means Abelian dominance of the quark-confining force in 3Q systems.

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