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 123x24 at β=5.7 and 163x32 at β=5.8, 6.0 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-Q potential, we find a universality of the string tension as σ3Q≅σQQ and the one-gluon-exchange result for the Coulomb coefficients as A3Q≅(1/2)AQQ. We investigate also the several fit analyses with the various Ansaetze: the Y Ansatz with the Yukawa potential, the Δ Ansatz and a more general Ansatz including the Y and the Δ Ansaetze 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 σΔ≅0.53σ