Lattice QCD study of color correlations between quarks in static multiquark 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 $ρ$ 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 $β= 5.8$, 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 $ρ$ 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.

Figures (23)

• Figure 1: The paths $\Gamma_i$ that define the path-ordered products $U(\Gamma_i,t)\in {\rm SU(3)}$ are shown for 3Q and 4Q cases.
• Figure 2: Three quarks are located at $(+d,0,0)$, $(-d,0,0)$, $(0,+h,0)$ with integers $d$ and $h$ on the lattice. When the correlation between 1- and 2-quarks (1- and 3-quarks) is measured, it is on-axis (off-axis) correlation.
• Figure 3: Shematic pictures which express the definition of $L$ in $Q\bar{Q}$ and 3Q systems. Two (anti)quarks of which we measure the color correlation are enclosed in dotted circles.
• Figure 4: Antitriplet and sextet components ($\rho_{\bar{\bm 3}}$ and $\rho_{ {\bm 6}}$) for 3Q systems plotted as a function of $L$. The dashed and dotted lines indicate the values $\frac{3}{9}$ and $\frac{6}{9}$ for $\rho_{\bar{\bm 3}}$ and $\rho_{ {\bm 6}}$ in the random-limit color configuration, respectively.
• Figure 5: ${F^{\rm 3Q}_{\bar{\bm 3}}}({\cal R})$ is plotted as a function of $L$. The square symbols denote ${F^{\rm 2Q}_{\bm 1}}({\cal R})$ obtained in a $Q\bar{Q}$ system.