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

TL;DR

This study numerically extracts the three-quark ground-state potential in SU(3) lattice QCD, confirming a universal string tension and Coulomb coefficient, and providing a detailed description of the potential's components.

Contribution

The paper provides the first precise numerical analysis of the three-quark potential in SU(3) lattice QCD, confirming the flux tube picture and universal string tension.

Findings

The three-quark potential is well described by Coulomb plus linear confinement terms.

The string tension in the three-quark system matches that of the quark-antiquark system.

The Coulomb coefficient is approximately half of that in the quark-antiquark potential.

Abstract

With the smearing technique, the three-quark (3Q) ground-state potential $V_{\rm 3Q}$ 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 %, $V_{\rm 3Q}$ is well described by a sum of a constant $C_{\rm 3Q}$, the two-body Coulomb part $-A_{\rm 3Q}\sum_{i<j} \frac1{|{\bf r}_i-{\bf r}_j|}$ and the three-body linear confinement part $\sigma_{\rm 3Q} L_{\rm min}$, where $L_{\rm min}$ denotes the minimal length of the color flux tube linking the three quarks. By comparing with the Q-$\bar {\rm Q}$ potential, we find a universal feature of the string tension as $\sigma_{\rm 3Q} \simeq \sigma_{\rm Q \bar Q}$ and the one-gluon-exchange result for the Coulomb coefficient as $A_{\rm 3Q} \simeq \frac12 A_{\rm Q \bar Q}$. All our results including the constant term are consistent with the requirement on the diquark limit in the lattice regularization.