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

TL;DR

This study uses SU(3) lattice QCD simulations to analyze the static three-quark potential, confirming the Y-shaped flux tube model and demonstrating universality of string tension and Coulomb coefficients.

Contribution

First lattice QCD calculation of the three-quark potential supporting the Y-type flux tube model with detailed potential parametrization.

Findings

The 3Q potential fits a Coulomb plus linear form with minimal flux-tube length.

Results support the Y-type flux picture over the Δ-type.

String tension and Coulomb coefficient relations are consistent with Q-Qbar potential.

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 $\beta =5.7 (a\simeq 0.2{\rm fm})$ and $12^3\times 24$. With the 3Q Wilson loop, the ground-state 3Q potential $V_{\rm 3Q}$ 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 $V_{\rm 3Q}$ are well described by a sum of the Coulomb term, a constant and the linear term which is proportional to the minimal length $L_{\rm min}$ 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 $V_{\rm 3Q}$ with the ${\rm Q}$-${\rm \bar{Q}}$ potential, we find the universality of the string tension, $\sigma_{\rm 3Q}\simeq \sigma_{\rm Q\bar{Q}}$ as well as the OGE relation on the Coulomb coefficient, $A_{\rm 3Q}\simeq {1/2}A_{\rm Q\bar{Q}}$.