Three-body forces in the quark model
Abstract
We review the connection between constituent-quark Hamiltonians and QCD and investigate the long-standing difficulty of describing meson and baryon spectra with one common two-body interaction. A Hamiltonian calibrated to ground-state mesons leaves systematic baryon mass residuals, largest in the light-quark sector and decreasing toward heavier flavors. We show that a short-range, color-spin-dependent connected three-quark interaction substantially reduces this incompatibility. Mass-scaled finite-range profiles yield high-accuracy baryon spectra, whereas flavor-independent common-range profiles do not remove the residual flavor pattern. The result is tested on additional ground-state baryons outside the calibration set and through meson--baryon compatibility analyses across several alternative quark-model Hamiltonians. We also benchmark radial and orbital excitations to identify the regime in which a static compact valence Hamiltonian remains reliable, and provide explicit color-spin matrix elements for two- and three-body operators in baryons and multiquark configurations. Within the tested valence-space representations, the results indicate that a mass-dependent short-range connected three-quark interaction provides the missing contribution required for a consistent simultaneous description of meson and baryon ground-state spectra.
Related
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BibTeX
@misc{baek2026threebody,
title = {{Three-body forces in the quark model}},
author = {Jongheon Baek and Aaron Park and Emiko Hiyama and Sungsik Noh and Hyeongock Yun and Kyong Chol Han and Su Houng Lee},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2608.18949},
eprint = {2608.18949},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.18949},
}
RIS
TY - UNPB
TI - Three-body forces in the quark model
AU - Jongheon Baek
AU - Aaron Park
AU - Emiko Hiyama
AU - Sungsik Noh
AU - Hyeongock Yun
AU - Kyong Chol Han
AU - Su Houng Lee
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2608.18949
UR - https://arxiv.org/abs/2608.18949
AB - We review the connection between constituent-quark Hamiltonians and QCD and investigate the long-standing difficulty of describing meson and baryon spectra with one common two-body interaction. A Hamiltonian calibrated to ground-state mesons leaves systematic baryon mass residuals, largest in the light-quark sector and decreasing toward heavier flavors. We show that a short-range, color-spin-dependent connected three-quark interaction substantially reduces this incompatibility. Mass-scaled finite-range profiles yield high-accuracy baryon spectra, whereas flavor-independent common-range profiles do not remove the residual flavor pattern. The result is tested on additional ground-state baryons outside the calibration set and through meson--baryon compatibility analyses across several alternative quark-model Hamiltonians. We also benchmark radial and orbital excitations to identify the regime in which a static compact valence Hamiltonian remains reliable, and provide explicit color-spin matrix elements for two- and three-body operators in baryons and multiquark configurations. Within the tested valence-space representations, the results indicate that a mass-dependent short-range connected three-quark interaction provides the missing contribution required for a consistent simultaneous description of meson and baryon ground-state spectra.
ER -