Study of Hadron Masses with Faddeev-Popov Eigenmode Projection in the Coulomb Gauge

TL;DR

This study uses lattice QCD in the Coulomb gauge to explore how spatial gluons influence hadron masses, revealing that low-lying Faddeev-Popov eigenmodes predominantly determine mass splittings like N-Δ and glueball differences.

Contribution

It introduces a novel projection method based on Faddeev-Popov eigenmodes to analyze the role of spatial gluons in hadron mass generation.

Findings

Nucleon and delta masses are nearly degenerate in the A=0 gluon projection.

Low-lying Faddeev-Popov modes reproduce hadron mass splittings with only 1% of components.

Color-magnetic interactions from low-lying modes are key to hadron mass differences.

Abstract

Using SU(3) lattice QCD, we investigate role of spatial gluons for hadron masses in the Coulomb gauge, considering the relation between QCD and the quark model. From the Coulomb-gauge configurations at the quenched level on a $16^3 \times 32$ lattice at $\beta$ = 6.0, we consider the $\vec{A} = 0$ projection, where all the spatial gluon fields are set to zero. In this projection, the inter-quark potential is unchanged. We investigate light hadron masses and find that nucleon and delta baryon masses are almost degenerate. This result suggests that the N-$\Delta$ mass difference arises from the color-magnetic interactions, which is consistent with the quark model picture. Next, as a generalization of this projection, we expand spatial gluon fields in terms of Faddeev-Popov eigenmodes and leave only some partial components. We find that the ${\rm N}-\Delta$ and $0^{++}-2^{++}$ glueball mass splittings are almost reproduced only with 1 \% low-lying components. This suggests that low-lying color-magnetic interaction leads to the hadron mass splitting.