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${}^3$ $\times$ 32, $\beta$ = 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-$\mathrm{\Delta }$ and 0${}^{++}$-2${}^{++}$ 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.

arXiv comment22 pages, 9 figures, and 2 tables, to appear in EPJA

References in corpus (28)

• The $XYZ$ states: experimental and theoretical status and perspectives
• Pentaquark and Tetraquark states
• Non-perturbative O(a) improvement of lattice QCD
• Constituent quark model study of the meson spectra
• Center Dominance and Z2 Vortices in SU(2) Lattice Gauge Theory
• Coulomb Gauge QCD, Confinement, and the Constituent Representation
• The light baryon spectrum in a relativistic quark model with instanton-induced quark forces I. The non-strange baryon spectrum and ground-states
• Mass spectra and Regge trajectories of light mesons in the relativistic quark model
• Masses of excited heavy baryons in the relativistic quark-diquark picture
• Quark-model study of few-baryon systems
• Detection of Center Vortices in the Lattice Yang-Mills Vacuum
• No confinement without Coulomb confinement
• Unquenched Gluon Propagator in Landau Gauge
• Light hadron spectroscopy with two flavors of $O(a)$-improved dynamical quarks
• Exotic meson-meson molecules and compact four--quark states
• Lattice quark propagator with staggered quarks in Landau and Laplacian gauges
• Nonperturbative improvement and tree-level correction of the quark propagator
• Quark propagator in the Landau gauge
• Lattice Coulomb Hamiltonian and Static Color-Coulomb Field
• Gluon Chain Model of the Confining Force
• Overlap Quark Propagator in Landau Gauge
• Perturbative Confinement
• Scaling behavior of the overlap quark propagator in Landau gauge
• Relevant energy scale of color confinement from lattice QCD
• Lattice analysis for the energy scale of QCD phenomena
• Instantaneous Interquark Potential in Generalized Landau Gauge in SU(3) Lattice QCD: A Linkage between the Landau and the Coulomb Gauges
• Instantaneous interquark potential in generalized Landau gauge in SU(3) lattice QCD: a possible gauge for the quark potential model
• Lattice QCD analysis for Faddeev-Popov eigenmodes in terms of gluonic momentum components in the Coulomb gauge