Lattice QCD study of color correlations between static quarks with gluonic excitations

We study the color correlation between static quark and antiquark ($q\bar q$) that is accompanied by gluonic excitations in the confined phase at $T=0$ by constructing reduced 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 color density matrix $\rho$ of static $q\bar q$ pairs in 6 channels (${\Sigma_g^+}$, ${{\Sigma_g^+}'}$, ${\Pi_u}$, ${\Pi_u'}$, ${\Delta_g}$, ${\Delta_g'}$), and investigate the interquark-distance dependence of color correlations. We find that as the interquark distance increases, the color correlation quenches because of color leak into the gluon field and finally approaches the random color configuration in the $q\bar q$ systems with and without gluonic excitations. For this color screening effect, we evaluate the "screening mass" to discuss its dependence on channels, the quantum number of the gluonic excitations.