Lattice QCD study of color correlations between quarks in static multiquark systems

TL;DR

This study uses lattice QCD to analyze how color correlations between static quarks in multiquark systems depend on their spatial configuration and flux tube length, revealing a universal behavior in color leak dynamics.

Contribution

It provides the first detailed lattice QCD analysis of color correlations in 3Q and 4Q static systems, highlighting the flux tube path length dependence and universality of color leak.

Findings

Color correlations depend on flux tube minimal path length.

Color leak approaches random configuration at large distances.

Universal flux-tube path length dependence observed across systems.

Abstract

We study the color correlation between two static quarks in 3Q ($QQQ$) and 4Q ($QQ\bar Q\bar Q$) multiquark systems at $T=0$ based on the reduced two-body density matrices $\rho$ in color space. We perform quenched lattice QCD calculations with the Coulomb gauge adopting the standard Wilson gauge action, and the spatial volume is $L^3 = 32^3$ at $\beta = 5.8$, which corresponds to the lattice spacing $a=0.14$ fm and the system volume $L^3=4.5^3$ fm$^3$. We evaluate the two-body color density matrix $\rho$ of static quarks, and investigate the dependence of color correlations on the quarks' spatial configuration. As a result, we find that the color correlations depend on the minimal path length along a flux tube which connects two quarks under consideration. The color correlation between quarks quenches because of color leak into the gluon field (flux tube) and finally approaches the random color configuration in the large distance limit. We find a ``universality'' in the flux-tube path length dependence of the color leak for 2Q, 3Q, and 4Q ground-state systems.