Baryon Bethe-Salpeter Equation in Minkowski-Space QCD2
Abstract
We study the three-quark ladder Bethe--Salpeter equation in Minkowski-space QCD2 in the light-cone gauge. Using the quasi-potential expansion, we project the baryon equation onto the light front and show that, at leading order in the valence truncation, the resulting mass-squared eigenvalue equation is equivalent to the Bars--Durgut equation. We also derive the endpoint power-law behavior of the valence wave function in terms of the quark mass and coupling, closely paralleling the original 't Hooft analysis for mesons. The resulting three-quark equation is solved numerically for Nc=3, and the ground-state baryon mass is found to be in reasonable agreement with previous light-cone quantization results in QCD2, suggesting that the valence sector provides the dominant contribution to the ground state. The excited-state spectrum further yields a Regge trajectory that captures the overall trend of the experimental nucleon spectrum, and we compute selected structure observables, including parton distribution functions, double distribution amplitudes, and coordinate-space densities. This framework provides a useful confining test bed for Minkowski-space bound-state methods and for future developments toward confining formulations in 3+1 dimensions beyond the valence truncation.
Versions
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BibTeX
@misc{kaur2026baryon,
title = {{Baryon Bethe-Salpeter Equation in Minkowski-Space QCD$_2$}},
author = {Satvir Kaur and Sreeraj Nair and Chandan Mondal and Jiangshan Lan and Xingbo Zhao and J. P. B. C. de Melo and Tobias Frederico},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.07095},
eprint = {2605.07095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.07095},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Baryon Bethe-Salpeter Equation in Minkowski-Space QCD_2
AU - Satvir Kaur
AU - Sreeraj Nair
AU - Chandan Mondal
AU - Jiangshan Lan
AU - Xingbo Zhao
AU - J. P. B. C. de Melo
AU - Tobias Frederico
PY - 2026
DA - 2026/10/30
PB - arXiv
DO - 10.48550/arxiv.2605.07095
UR - https://arxiv.org/abs/2605.07095
AB - We study the three-quark ladder Bethe--Salpeter equation in Minkowski-space QCD_2 in the light-cone gauge. Using the quasi-potential expansion, we project the baryon equation onto the light front and show that, at leading order in the valence truncation, the resulting mass-squared eigenvalue equation is equivalent to the Bars--Durgut equation. We also derive the endpoint power-law behavior of the valence wave function in terms of the quark mass and coupling, closely paralleling the original 't Hooft analysis for mesons. The resulting three-quark equation is solved numerically for N_c=3, and the ground-state baryon mass is found to be in reasonable agreement with previous light-cone quantization results in QCD_2, suggesting that the valence sector provides the dominant contribution to the ground state. The excited-state spectrum further yields a Regge trajectory that captures the overall trend of the experimental nucleon spectrum, and we compute selected structure observables, including parton distribution functions, double distribution amplitudes, and coordinate-space densities. This framework provides a useful confining test bed for Minkowski-space bound-state methods and for future developments toward confining formulations in 3+1 dimensions beyond the valence truncation.
ER -