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

TL;DR

This study explores how low-lying eigenmodes of the Faddeev-Popov operator influence hadron masses in lattice QCD, shedding light on the connection between QCD and the quark model through gauge configuration projections.

Contribution

It introduces a novel projection method based on Faddeev-Popov eigenmodes to analyze gauge configurations, revealing the role of low-lying modes in hadron mass splittings and the QCD-quark model relation.

Findings

Low-lying eigenmodes significantly affect hadron mass splittings.

The static quark-antiquark potential is independent of spatial gauge fields.

A small number of low-lying eigenmodes can approximately reproduce hadron masses.

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.