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

¹ Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto 606-8502, Japan
² Department of Physics, Kyoto University, Kitashirakawa-oiwake, Sakyo, Kyoto 606-8502, Japan

^* e-mail: hiroki.ohata@yukawa.kyoto-u.ac.jp
^** e-mail: suganuma@scphys.kyoto-u.ac.jp

Published online: 22 December 2022

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 16³ × 32 lattice at β = 6.0, we consider the A⃗ = 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-Δ 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 N – Δ 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.