Static Three-Quark Potential in SU(3) Lattice QCD Monte-Carlo Simulation

Abstract

The static three-quark(3Q) potential is investigated in the SU(3) lattice QCD at the quenched level, using the standard Wilson action with $\beta =5.7(a\simeq 0.2\mathrm{fm})$ and $12^3\times 24$. With the 3Q Wilson loop, the ground-state 3Q potential $V_{3Q}$ is calculated for 16 patterns of the 3Q configuration, using the smearing technique, which enhances the ground-state overlap of the 3Q operator. With the accuracy better than a few %, the lattice QCD data for $V_{3Q}$ are well described by a sum of the Coulomb term, a constant and the linear term which is proportional to the minimal length $L_{\min }$ of the flux-tube linking the 3 quarks. Our results seem to support the Y-type flux picture rather than $\Delta$-type one. From the comparison of $V_{3Q}$ with the $\mathrm{Q}$-$\bar{\mathrm{Q}}$ potential, we find the universality of the string tension, ${\sigma }_{3Q}\simeq {\sigma }_{\mathrm{Q}\bar{\mathrm{Q}}}$ as well as the OGE relation on the Coulomb coefficient, $A_{3Q}\simeq 1/2A_{\mathrm{Q}\bar{\mathrm{Q}}}$.

Proceeding of the TMU-Yale Symposium on ``Dynamics of Gauge Fields'' at Tokyo Metropolitan Univ., Tokyo, December 13-15, 1999. ;2pages, 1figure, 1table