dorsal/arxiv
View SchemaGhost poles in the nucleon propagator in the linear-sigma model approach and its role in pion-nucleon low-energy theorems
| Authors | C. A. da Rocha, G. Krein, L. Wilets |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9701017 |
| URL | https://arxiv.org/abs/nucl-th/9701017 |
| DOI | 10.1016/S0375-9474(96)00480-0 |
| Journal | Nucl.Phys. A616 (1997) 625-647 |
Abstract
Complex mass poles, or ghost poles, are present in the Hartree-Fock solution of the Schwinger-Dyson equation for the nucleon propagator in renormalizable models with Yukawa-type meson-nucleon couplings, as shown many years ago by Brown, Puff, and Wilets (BPW). These ghosts violate basic theorems of quantum field theory and their origin is related to the ultraviolet behavior of the model interactions. Recently, Krein et.al, proved that the ghosts disappear when vertex corrections are included in a self-consistent way, softening the interaction sufficiently in the ultraviolet region. In previous studies of pion-nucleon scattering using "dressed" nucleon propagator and bare vertices, did by Nutt and Wilets in the 70's (NW), it was found that if these poles are explicitly included, the value of the isospin-even amplitude A+ is satisfied within 20% at threshold. The absence of a theoretical explanation for the ghosts and the lack of chiral symmetry in these previous studies led us to re-investigate the subject using the approach of the linear-sigma model and study the interplay of low-energy theorems for pion-nucleon scattering and ghost poles. For bare interaction vertices we find that ghosts are present in this model as well and that the A+ value is badly described. As a first approach to remove these complex poles, we dress the vertices with phenomenological form factors and a reasonable agreement with experiment is achieved. In order to fix the two cutoff parameters, we use the A+ value for the chiral limit (m_pion -> 0) and the experimental value of the isoscalar scattering length. Finally, we test our model by calculating the phase shifts for the S waves and we find a good agreement at threshold.
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"abstract": "Complex mass poles, or ghost poles, are present in the Hartree-Fock solution\nof the Schwinger-Dyson equation for the nucleon propagator in renormalizable\nmodels with Yukawa-type meson-nucleon couplings, as shown many years ago by\nBrown, Puff, and Wilets (BPW). These ghosts violate basic theorems of quantum\nfield theory and their origin is related to the ultraviolet behavior of the\nmodel interactions. Recently, Krein et.al, proved that the ghosts disappear\nwhen vertex corrections are included in a self-consistent way, softening the\ninteraction sufficiently in the ultraviolet region. In previous studies of\npion-nucleon scattering using \"dressed\" nucleon propagator and bare vertices,\ndid by Nutt and Wilets in the 70\u0027s (NW), it was found that if these poles are\nexplicitly included, the value of the isospin-even amplitude A+ is satisfied\nwithin 20% at threshold. The absence of a theoretical explanation for the\nghosts and the lack of chiral symmetry in these previous studies led us to\nre-investigate the subject using the approach of the linear-sigma model and\nstudy the interplay of low-energy theorems for pion-nucleon scattering and\nghost poles. For bare interaction vertices we find that ghosts are present in\nthis model as well and that the A+ value is badly described. As a first\napproach to remove these complex poles, we dress the vertices with\nphenomenological form factors and a reasonable agreement with experiment is\nachieved. In order to fix the two cutoff parameters, we use the A+ value for\nthe chiral limit (m_pion -\u003e 0) and the experimental value of the isoscalar\nscattering length. Finally, we test our model by calculating the phase shifts\nfor the S waves and we find a good agreement at threshold.",
"arxiv_id": "nucl-th/9701017",
"authors": [
"C. A. da Rocha",
"G. Krein",
"L. Wilets"
],
"categories": [
"nucl-th",
"hep-ph"
],
"doi": "10.1016/S0375-9474(96)00480-0",
"journal_ref": "Nucl.Phys. A616 (1997) 625-647",
"title": "Ghost poles in the nucleon propagator in the linear-sigma model approach and its role in pion-nucleon low-energy theorems",
"url": "https://arxiv.org/abs/nucl-th/9701017"
},
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