Detailed Analysis of the Three Quark Potential in SU(3) Lattice QCD

Abstract

The static three-quark (3Q) potential is studied in detail using SU(3) lattice QCD with $12^3\times 24$ at $\beta =5.7$ and $16^3\times 32$ at $\beta =5.8$, 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 $V_{3Q}$. We perform the detailed fit analysis on $V_{3Q}$ 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 $V_{3Q}$ are well reproduced within a few % deviation by the sum of a constant, the two-body Coulomb term and the three-body linear confinement term ${\sigma }_{3Q}{L}_{\min }$, with $L_{\min }$ the minimal value of the total length of color flux tubes linking the three quarks. From the comparison with the Q-$\bar{\mathrm{Q}}$ potential, we find a universality of the string tension as ${\sigma }_{3Q}\simeq {\sigma }_{\mathrm{Q}\bar{\mathrm{Q}}}$ and the one-gluon-exchange result for the Coulomb coefficients as $A_{3Q}\simeq \frac{1}{2}{A}_{\mathrm{Q}\bar{\mathrm{Q}}}$. 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 $V_{3Q}$, although $V_{3Q}$ seems to be approximated by the $\Delta$-ansatz with ${\sigma }_{\Delta }\simeq 0.53\sigma$.

Comments: 30 pages, 14 figures and 13 tables submitted to Phys.Rev.D