Faddeev description of baryons in two-dimensional QCD with Nc=3. I. Chiral spectrum, isospin, and strangeness
Abstract
We develop a light-front Faddeev description of baryons in two-dimensional QCD at Nc=3, in which an exact coupled-channel representation identifies the quark--diquark picture as a single-channel truncation, and solve it variationally with exact matrix elements. In the chiral limit we find an exactly massless lightest baryon, in agreement with the classic valence solutions, DLCQ, and bosonization; the excitation tower reproduces Webber's spectrum state by state and sets the valence gap 1.371 M∗mes. The channel content distinguishes these states: the massless baryon is single-channel, the gapped states are genuinely multi-channel, and all baryon Regge trajectories are of the meson class. The calculation is anchored at both ends of the coupling range: the meson-to-baryon mass ratio agrees with strong-coupling bosonization to $0.3−−4.3\%$, while the valence masses reproduce the full discretized light cone quantization (DLCQ) masses to 0.04% (meson) and 0.15% (baryon) at weak coupling. Extending to two degenerate flavors, we find the massless baryon to be the Δ-like quartet, while the N-like doublet at 0.977 M∗mes is an exact 50 : 50 superposition of good- and bad-diquark channels. Adding a massive strange quark, we obtain, to our knowledge for the first time at the valence three-quark level, the hyperon spectroscopy of QCD2: Σ-like states fall below Λ-like ones, inverting the four-dimensional ordering, the chiral thresholds count two kaon units per strange quark, and the Gell-Mann--Okubo relation is protected in mass squared. With all three quark masses non-degenerate, the proton-like state falls below the neutron-like one, Σ0--Λ mixing appears, and the Coleman--Glashow relation holds at the percent level.
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BibTeX
@misc{zahed2026faddeev,
title = {{Faddeev description of baryons in two-dimensional QCD with $N_c=3$. I. Chiral spectrum, isospin, and strangeness}},
author = {Ismail Zahed and Haocheng Zhang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.23435},
eprint = {2607.23435},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.23435},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Faddeev description of baryons in two-dimensional QCD with N_c=3. I. Chiral spectrum, isospin, and strangeness
AU - Ismail Zahed
AU - Haocheng Zhang
PY - 2026
DA - 2026/09/08
PB - arXiv
DO - 10.48550/arxiv.2607.23435
UR - https://arxiv.org/abs/2607.23435
AB - We develop a light-front Faddeev description of baryons in two-dimensional QCD at N_c=3, in which an exact coupled-channel representation identifies the quark--diquark picture as a single-channel truncation, and solve it variationally with exact matrix elements. In the chiral limit we find an exactly massless lightest baryon, in agreement with the classic valence solutions, DLCQ, and bosonization; the excitation tower reproduces Webber's spectrum state by state and sets the valence gap 1.371 M^∗_mes. The channel content distinguishes these states: the massless baryon is single-channel, the gapped states are genuinely multi-channel, and all baryon Regge trajectories are of the meson class. The calculation is anchored at both ends of the coupling range: the meson-to-baryon mass ratio agrees with strong-coupling bosonization to $0.3−−4.3\%$, while the valence masses reproduce the full discretized light cone quantization (DLCQ) masses to 0.04% (meson) and 0.15% (baryon) at weak coupling. Extending to two degenerate flavors, we find the massless baryon to be the Δ-like quartet, while the N-like doublet at 0.977 M^∗_mes is an exact 50 : 50 superposition of good- and bad-diquark channels. Adding a massive strange quark, we obtain, to our knowledge for the first time at the valence three-quark level, the hyperon spectroscopy of QCD_2: Σ-like states fall below Λ-like ones, inverting the four-dimensional ordering, the chiral thresholds count two kaon units per strange quark, and the Gell-Mann--Okubo relation is protected in mass squared. With all three quark masses non-degenerate, the proton-like state falls below the neutron-like one, Σ^0--Λ mixing appears, and the Coleman--Glashow relation holds at the percent level.
ER -