dorsal/arxiv
View SchemaChiral Symmetry and Low Energy Pion-Nucleon Scattering
| Authors | Sidney A. Coon |
|---|---|
| Categories | |
| ArXiv ID | nucl-th/9906011 |
| URL | https://arxiv.org/abs/nucl-th/9906011 |
| DOI | 10.1023/A:1022868110424 |
| Journal | Czech.J.Phys.49:1235-1271,1999 |
Abstract
In these lectures, I examine the effect of the meson factory $\pi$N data on the current algebra/PCAC program which describes chiral symmetry breaking in this system. After historical remarks on the current algebra/PCAC versus chiral Lagrangians approaches to chiral symmetry, and description of the need for $\pi$N amplitudes with virtual (off-mass-shell) pions in nuclear force models and other nuclear physics problems, I begin with kinematics and isospin aspects of the invariant amplitudes. A detailed introduction to the hadronic vector and axial-vector currents and the hypothesis of partially conserved axial-vector currents (PCAC) follows. I review and test against contemporary data the PCAC predictions of the Goldberger-Treiman relation, and the Adler consistency condition for a $\pi$N amplitude. Then comes a detailed description of the current algebra Ward-Takahashi identities in the chiral limit and a brief account of the on-shell current algebra Ward-Takahashi identities. The latter identities form the basis of so-called current algebra models of $\pi$N scattering. I then test these models against the contemporary empirical $\pi$N amplitudes extrapolated into the subthreshold region via dispersion relations. The scale and the t dependence of the "sigma term" is determined by the recent data.
{
"annotation_id": "f2ceed96-0fcf-4785-8e39-04a22f715db6",
"date_created": "2026-03-02T18:00:25.377000Z",
"date_modified": "2026-03-02T18:00:25.377000Z",
"file_hash": "cc5cc9878ca216a833123c70a642a308bdd0b479cc1c8c95b39f4e83b3e046e8",
"private": false,
"record": {
"abstract": "In these lectures, I examine the effect of the meson factory $\\pi$N data on\nthe current algebra/PCAC program which describes chiral symmetry breaking in\nthis system. After historical remarks on the current algebra/PCAC versus chiral\nLagrangians approaches to chiral symmetry, and description of the need for\n$\\pi$N amplitudes with virtual (off-mass-shell) pions in nuclear force models\nand other nuclear physics problems, I begin with kinematics and isospin aspects\nof the invariant amplitudes. A detailed introduction to the hadronic vector and\naxial-vector currents and the hypothesis of partially conserved axial-vector\ncurrents (PCAC) follows. I review and test against contemporary data the PCAC\npredictions of the Goldberger-Treiman relation, and the Adler consistency\ncondition for a $\\pi$N amplitude. Then comes a detailed description of the\ncurrent algebra Ward-Takahashi identities in the chiral limit and a brief\naccount of the on-shell current algebra Ward-Takahashi identities. The latter\nidentities form the basis of so-called current algebra models of $\\pi$N\nscattering. I then test these models against the contemporary empirical $\\pi$N\namplitudes extrapolated into the subthreshold region via dispersion relations.\nThe scale and the t dependence of the \"sigma term\" is determined by the recent\ndata.",
"arxiv_id": "nucl-th/9906011",
"authors": [
"Sidney A. Coon"
],
"categories": [
"nucl-th"
],
"doi": "10.1023/A:1022868110424",
"journal_ref": "Czech.J.Phys.49:1235-1271,1999",
"title": "Chiral Symmetry and Low Energy Pion-Nucleon Scattering",
"url": "https://arxiv.org/abs/nucl-th/9906011"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "438fb6c3-b4ff-4307-b028-25cd549b0ab9",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}