Meson-isospectral pair interactions and the residual three-quark force
Abstract
Meson-isospectral pair rotations can closely reproduce low-lying baryon energies while producing a substantial connected action under their consistent three-body embedding. Starting from an independently calibrated S-wave meson model, we compare ground-mass fits, joint ground-level and gap fits, and direct minimization of the connected remainder. With eighteen shared coefficients, a four-packet joint fit reproduces the nine calibration ground masses and first gaps with RMS errors of JointGroundTrain and JointGapTrain MeV, respectively. The excluded ground masses and gaps have RMS errors of $10.7$ and $8.1$ MeV in the same enlarged radial space. Its connected action on the eighteen calibrated inputs is JointActionCal times the unrotated source action. Eigenvalue agreement and removal of the connected interaction thus impose different tests. Separately optimizing the action with five packets gives a normalized residual of ShortActionAll for an intermediate-distance fifth packet; a long-distance extension also leaves a substantial remainder. An eliminated-state construction realizes the central color--color structure of an intermediate-configuration mechanism together with correlated pair dressing. These results favor a connected operator basis with three fitted strengths as an economical description within the tested pair family, and quantify its relation to the representation freedom of equivalent few-body Hamiltonians.
Related
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BibTeX
@misc{baek2026mesonisospectral,
title = {{Meson-isospectral pair interactions and the residual three-quark force}},
author = {Jongheon Baek and Gihwan Nam and Gyucheol Sim},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.30190},
eprint = {2610.30190},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.30190},
}
RIS
TY - UNPB
TI - Meson-isospectral pair interactions and the residual three-quark force
AU - Jongheon Baek
AU - Gihwan Nam
AU - Gyucheol Sim
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.30190
UR - https://arxiv.org/abs/2610.30190
AB - Meson-isospectral pair rotations can closely reproduce low-lying baryon energies while producing a substantial connected action under their consistent three-body embedding. Starting from an independently calibrated S-wave meson model, we compare ground-mass fits, joint ground-level and gap fits, and direct minimization of the connected remainder. With eighteen shared coefficients, a four-packet joint fit reproduces the nine calibration ground masses and first gaps with RMS errors of JointGroundTrain and JointGapTrain MeV, respectively. The excluded ground masses and gaps have RMS errors of $10.7$ and $8.1$ MeV in the same enlarged radial space. Its connected action on the eighteen calibrated inputs is JointActionCal times the unrotated source action. Eigenvalue agreement and removal of the connected interaction thus impose different tests. Separately optimizing the action with five packets gives a normalized residual of ShortActionAll for an intermediate-distance fifth packet; a long-distance extension also leaves a substantial remainder. An eliminated-state construction realizes the central color--color structure of an intermediate-configuration mechanism together with correlated pair dressing. These results favor a connected operator basis with three fitted strengths as an economical description within the tested pair family, and quantify its relation to the representation freedom of equivalent few-body Hamiltonians.
ER -