Remnants of quark model in lattice QCD simulation in the Coulomb gauge

Abstract: Aiming at the relation between QCD and the quark model, we consider projections of gauge configurations generated in quenched lattice QCD simulations in the Coulomb gauge on a 16$^{\rm 3}$ $\rm \times$ 32, $\rm \beta$ = 6.0 lattice. First, we focus on a fact that the static quark-antiquark potential is independent of spatial gauge fields. We explicitly confirm this by performing $\vec{A}$ = 0 projection, where spatial gauge fields are all set to zero. We also apply the $\vec{A}$ = 0 projection to light hadron masses and find that nucleon and delta baryon masses are almost degenerate, suggesting vanishing of the color-magnetic interactions. After considering the physical meaning of the $\vec{A}$ = 0 projection, we next propose a generalized projection, where spatial gauge fields are expanded in terms of Faddeev-Popov eigenmodes and only some eigenmodes are left. We apply the proposed projection to light hadron and glueball masses and find that the N-$\rm \Delta$ and 0$^{\rm ++}$-2$^{\rm ++}$ mass splittings become evident when projected with more than 33 (0.10 \%) low-lying eigenmodes, suggesting emergence of the color-magnetic interactions. We also find that the original hadron masses are approximately reproduced with just 328 (1.00 \%) low-lying eigenmodes. These findings indicate an important role of low-lying eigenmodes on hadron masses and would be useful in clarifying the relation between QCD and the quark model.