SU(3) Lattice QCD Study for Static Three-Quark Potential

TL;DR

This study uses SU(3) lattice QCD to accurately determine the static three-quark potential, confirming the universality of string tension and Coulomb coefficients across different quark systems.

Contribution

It provides the first detailed numerical analysis of the three-quark potential using lattice QCD, demonstrating the potential's form and universal properties.

Findings

The three-quark potential is well described by a sum of Coulomb and linear confinement terms.

The string tension in three-quark systems matches that in quark-antiquark systems.

The Coulomb coefficient in three-quark systems is approximately half of that in quark-antiquark systems.

Abstract

We study the static three-quark (3Q) potential 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 200 patterns of the 3Q systems, we numerically derive 3Q ground-state potential $V_{3Q}$ from the 3Q Wilson loop with the smearing technique, which reduces excited-state contaminations. The lattice QCD data of $V_{3Q}$ are well reproduced within a few % deviation by a 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 total length of color flux tubes linking the three quarks. From the comparison with the Q-$\bar {Q}$ potential, we find a universality of the string tension as $\sigma_{3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange result for Coulomb coefficients, $A_{3Q} \simeq \frac12 A_{\rm Q \bar Q}$.