The Goldberger-Treiman relation and the chiral soliton model |
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| Affiliation: | 1. Centro de Fisica Teorica (INIC) and Departmento de Fisica, Universidade de Coimbra, P-3000 Coimbra, Portugal;2. Institut für Kernphysik, Kernforschungsanlage Jülich, D-5170 Jülich, Fed Rep. Germany;3. Institut für Theoretische Kernphysik, Universität Bonn, D-5300 Bonn, Fed. Rep. Germany;1. TRIUMF, Vancouver, BC V6T2A3, Canada;2. Department of Physics and Astronomy, Appalachian State University, Boone, NC 28608, USA;3. Department of Chemistry, Simon Fraser University, Burnaby, BC V5A1S6, Canada;4. Department of Physics and Astronomy, University of Calgary, Calgary, AB T2N 1N4, Canada;5. Physikalisches Institut, Justus-Liebig-Universiteät, Gießen 35392, Germany;6. Department of Physics, Mcgill University, Montreal, QC H3A0G4, Canada;7. Department of Physics and Astronomy, University of Manitoba, Winnipeg, MB R3T 2N2, Canada;8. University of Heidelberg, Philosophenweg 12, Heidelberg 69120, Germany;9. Department of Physics, University of York, York YO10 5DD, UK;10. Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z4, Canada;11. Université Paris-Saclay, IJCLab-IN2P3/CNRS, France;12. Technische Universität Darmstadt, Department of Physics, Darmstadt 64289, Germany;13. ExtreMe Matter Institute EMMI, GSI Helmholtzzentrum für Schwerionenforschung GmbH, Darmstadt 64291, Germany;14. CERN, 1211 Geneva 23, Switzerland;15. Max-Planck-Institut für Kernphysik, Heidelberg 69117, Germany;p. School of Physics and Astronomy, University of Edinburgh, Edinburgh EH8 9YL, UK;q. Department of Physics, Colorado School of Mines, Golden, CO 80401, USA;r. Department of Physics and Astronomy, University of Victoria, Victoria, BC V8P 5C2, Canada;1. Department of Physics, Duke University, Durham, NC 27708, USA;2. Department of Physics, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan;3. Physics Department, Brookhaven National Laboratory, Upton, NY 11973, USA |
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| Abstract: | The linear chiral soliton model with explicit quark fields and elementary pion- and sigma-fields is solved in order to describes nucleon and delta properties. Special emphasis is put on the axial vector coupling constant gA and on the Goldberger-Treiman relation. To this end baryon Fock states are constructed in a mean field approximation with hedgehog-like configurations from which the physical states are obtained by projection techniques. It is shown that the Goldberger-Treiman relation is only fulfilled if the quark- and pion-hedgehog is generalized and the variation is performed with projected states. Under this condition no parameter set is found which yields a proper gA and a proper pion-nucleon coupling constant gπNN, if the polarization of the Dirac sea is neglected. Other observables are reproduced within 20% limits or less. |
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