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

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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\(^{\textrm{3}}\) \(\mathrm \times \) 32, \(\mathrm \beta \) = 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 \(\textbf{A}\) = 0 projection, where spatial gauge fields are all set to zero. We also apply the \(\textbf{A}\) = 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 \(\textbf{A}\) = 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\(^{\mathrm{++}}\)–2\(^{\mathrm{++}}\) 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.

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Data Availibility Statement

This manuscript has associated data in a data repository. [Author’s comment: Raw data were generated at Kyoto University. Derived data supporting the findings of this study are available from the authors [H. Ohata, H. Suganuma] on request.]

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Acknowledgements

H.O. was supported by a Grant-in-Aid for JSPS Fellows (Grant No.21J20089). H.S. was supported by a Grants-in-Aid for Scientific Research [19K03869] from Japan Society for the Promotion of Science. This work was in part based on Bridge++ code [54]. We have used SLEPc [50] to solve eigenvalue problems for the Faddeev–Popov operator. The numerical simulations have been carried out on Yukawa-21 at Yukawa Institute for Theoretical Physics, Kyoto University.

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  1. Hiroki Ohata and Hideo Suganum contributed equally to this work.

Authors and Affiliations

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

    Hiroki Ohata

  2. Department of Physics, Graduate School of Science, Kyoto University, Kitashirakawa oiwake, Sakyo, Kyoto, Kyoto, 606-8502, Japan

    Hideo Suganuma

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  1. Hiroki Ohata
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Correspondence to Hiroki Ohata.

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Communicated by Carsten Urbach.

hopping parameters

hopping parameters

The hopping parameters used in hadron mass measurements under the eigenmode projection remaining low/high-lying FP modes are listed in Tables 3 and 4, respectively. We roughly tuned them to cover the range of \(m_{\pi } / m_{\rho } = 0.80 - 0.60\). The resulting \(m_{\pi } / m_{\rho }\) are also listed.

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Ohata, H., Suganuma, H. Remnants of quark model in lattice QCD simulation in the Coulomb gauge. Eur. Phys. J. A 60, 97 (2024). https://doi.org/10.1140/epja/s10050-024-01327-1

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