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 ${12}^3\times 24$ at $\beta =5.7\mathrm{}$ and ${16}^3\times 32$ at $\beta =5.8,6.0\mathrm{}$ 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 $V_{3\mathrm{Q}}.$ We perform the detailed fit analysis on $V_{3\mathrm{Q}}$ 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 $V_{3\mathrm{Q}}$ 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 ${\sigma }_{3\mathrm{Q}}{L}_{\min },$ with $L_{\min }$ the minimal value of the total length of color flux tubes linking the three quarks. From the comparison with the $\mathrm{Q}-\overline{\mathrm{Q}}$ potential, we find a universality of the string tension as ${\sigma }_{3\mathrm{Q}}\simeq {\sigma }_{\mathrm{Q}\overline{\mathrm{Q}}}$ and the one-gluon-exchange result for the Coulomb coefficients as $A_{3\mathrm{Q}}\simeq \frac{1}{2}{A}_{\mathrm{Q}\overline{\mathrm{Q}}}.$ We investigate also the several fit analyses with the various Ansätze: the Y Ansatz with the Yukawa potential, the $\Delta$ Ansatz and a more general Ansatz including the Y and the $\Delta$ Ansätze in some limits. All these fit analyses support the Y Ansatz on the confinement part in the 3Q potential $V_{3\mathrm{Q}},$ although $V_{3\mathrm{Q}}$ seems to be approximated by the $\Delta$ Ansatz with ${\sigma }_{\Delta }\simeq 0.53\sigma .$