Three-Quark Potential in SU(3) Lattice QCD

Abstract

The static three-quark (3Q) potential is measured in the SU(3) lattice QCD with $12^3\times 24$ and $\beta =5.7$ at the quenched level. From the 3Q Wilson loop, the 3Q ground-state potential $V_{3Q}$ is extracted using the smearing technique for the ground-state enhancement. With accuracy better than a few %, $V_{3Q}$ is well described by a sum of a constant, the two-body Coulomb term and the three-body linear confinement term ${\sigma }_{3Q}{L}_{\min }$, where $L_{\min }$ denotes the minimal length of the color flux tube linking the three quarks. By comparing with the Q-$\bar{\mathrm{Q}}$ potential, we find a universal feature of the string tension, ${\sigma }_{3Q}\simeq {\sigma }_{\mathrm{Q}\bar{\mathrm{Q}}}$, as well as the one-gluon-exchange result for the Coulomb coefficient, $A_{3Q}\simeq \frac{1}{2}{A}_{\mathrm{Q}\bar{\mathrm{Q}}}$.

Comments: 7 pages, 3 figure