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| Main Authors: | , , , , , , |
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| Format: | Preprint |
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2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.07095 |
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| _version_ | 1866914542917779456 |
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| author | Kaur, Satvir Nair, Sreeraj Mondal, Chandan Lan, Jiangshan Zhao, Xingbo de Melo, J. P. B. C. Frederico, Tobias |
| author_facet | Kaur, Satvir Nair, Sreeraj Mondal, Chandan Lan, Jiangshan Zhao, Xingbo de Melo, J. P. B. C. Frederico, Tobias |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_07095 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Baryon Bethe-Salpeter Equation in Minkowski-Space QCD$_2$ Kaur, Satvir Nair, Sreeraj Mondal, Chandan Lan, Jiangshan Zhao, Xingbo de Melo, J. P. B. C. Frederico, Tobias High Energy Physics - Phenomenology 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. |
| title | Baryon Bethe-Salpeter Equation in Minkowski-Space QCD$_2$ |
| topic | High Energy Physics - Phenomenology |
| url | https://arxiv.org/abs/2605.07095 |