Detailed analysis of the three-quark potential in SU(3) lattice QCD

The static three-quark (3Q) potential is studied in detail using SU(3) lattice QCD with 12³×24 at β=5.7 and 16³×32 at β=5.8,0ex0ex6.0 at the quenched level. For more than 300 different patterns of the 3Q systems, we perform the accurate measurement of the 3Q Wilson loop with the smearing method, which reduces excited-state contaminations, and present the lattice QCD data of the 3Q ground-state potential V3Q. We perform the detailed fit analysis on V3Q in terms of the Y Ansatz both with the continuum Coulomb potential and with the lattice Coulomb potential, and find that the lattice QCD data of the 3Q potential V3Q are well reproduced within a few percent deviation by the sum of a constant, the two-body Coulomb term and the three-body linear confinement term σ3QLₘᵢₙ, with Lₘᵢₙ the minimal value of the total length of color flux tubes linking the three quarks. From the comparison with the Q-Q̄ potential, we find a universality of the string tension as σ3QσQQ̄ and the one-gluon-exchange result for the Coulomb coefficients as A3Q1/2AQQ̄. We investigate also the several fit analyses with the various Ans\"atze: the Y Ansatz with the Yukawa potential, the Δ Ansatz and a more general Ansatz including the Y and the Δ Ans\"atze in some limits. All these fit analyses support the Y Ansatz on the confinement part in the 3Q potential V3Q, although V3Q seems to be approximated by the Δ Ansatz with σ_Δ0.53σ.