Three-quark ground-state potential in the SU(3) lattice QCD

Abstract

With the smearing technique, the three-quark (3Q) ground-state potential $V_{3Q}$ is numerically extracted in the SU(3)${}_c$ lattice QCD Monte Carlo simulation with $12^3\times 24$ and $\beta =5.7$ at the quenched level. With accuracy better than a few %, $V_{3Q}$ is well described by a sum of a constant $C_{3Q}$, the two-body Coulomb part $-A_{3Q}{\sum }_{i<j}\frac{1}{|{\mathbf{r}}_i-{\mathbf{r}}_j|}$ and the three-body linear confinement part ${\sigma }_{3Q}{L}_{\min }$, 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 as ${\sigma }_{3Q}\simeq {\sigma }_{\mathrm{Q}\bar{\mathrm{Q}}}$ and the one-gluon-exchange result for the Coulomb coefficient as $A_{3Q}\simeq \frac{1}{2}{A}_{\mathrm{Q}\bar{\mathrm{Q}}}$. All our results including the constant term are consistent with the requirement on the diquark limit in the lattice regularization.

5 pages, 2 figures, 2 tables