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The chiral partner of the nucleon in the mirror assignment

The chiral partner of the nucleon in the mirror assignment. Susanna Wilms in collaboration with: Francesco Giacosa and Dirk Rischke. Hadrons@FAIR University Frankfurt. Motivation. Introduction of N* for chiral realization of the nucleonic Lagrangian

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The chiral partner of the nucleon in the mirror assignment

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  1. The chiral partner of the nucleonin the mirror assignment Susanna Wilms in collaboration with: Francesco Giacosa and Dirk Rischke Hadrons@FAIR University Frankfurt

  2. Motivation Introduction of N* for chiral realization of the nucleonic Lagrangian zchiral invariant mass term =/ m0 Generation of the nucleonic mass: how is mN generated? Quark condensate vs. m0 Correct description of the axial coupling constant gA(N)=1.26 gA(N*)=? Study of pion-nucleon scattering Susanna WilmsHadrons@FAIR 25-27 June 2008

  3. The chiral partner: what is N*? Susanna WilmsHadrons@FAIR 25-27 June 2008

  4. The chiral partner of the nucleonin the mirror assignment Mirror assignment vs naive assignment: chiral transformation Mirror Naive No chiral invariant mass term 2 independent Linear Sigma models Nucleon mass not only dynamically generated Susanna WilmsHadrons@FAIR 25-27 June 2008

  5. The chiral partner of the nucleonin the mirror assignment Candidates with the correct quantum numbers from PDG: N*(1535) lowest nucleonic resonance N*(1650) Other possibility (speculative): N*(1200) (D. Zschiesche, L. Tolos, J. Schaffner-Bielich, R. Pisarski, Phys.Rev.C75:055202,2007) Very broad resonance? Not yet measured? Susanna WilmsHadrons@FAIR 25-27 June 2008

  6. A little bit of scattering theory Susanna WilmsHadrons@FAIR 25-27 June 2008

  7. A little bit of scattering theory General form of the Lorentz-invariant scattering amplitude: s-wave scattering lengths: Susanna WilmsHadrons@FAIR 25-27 June 2008

  8. Pion-nucleon scattering H. Schroder: Measured pion nucleon scattering lengths from pionic hydrogen and deuterium at PSI (Eur.Phys.J.C21:473-488,2001) T. Takahashi and T. Kunihiro: Axial charge of N(1535) in lattice QCD (e-Print: arXiv:0801.4707) L. Ya. Glozman: Phys.Rept.444:1-49,2007 Susanna WilmsHadrons@FAIR 25-27 June 2008

  9. The model Susanna WilmsHadrons@FAIR 25-27 June 2008

  10. The model Linear sigma model with vector and axial vector mesons, as well as the nucleonic fields in the mirror assignment local symmetric case Weinberg-Tomozawa-term local chiral symmetry Global chiral symmetry in agreement with mesonic decays Susanna WilmsHadrons@FAIR 25-27 June 2008 emphasize

  11. Linear sigma model with vector and axial vector mesons, as well as the nucleonic fields in the mirror assignment local symmetric case Susanna WilmsHadrons@FAIR 25-27 June 2008 emphasize

  12. Mesonic sector of the lagrangian Fields Field strength tensor Susanna WilmsHadrons@FAIR 25-27 June 2008

  13. Spontaneus symmetry breaking leads to mixing terms in the Lagrangian: we need to perform the shifts of the axial fields: and to renormalize the pseudovector fields: Susanna WilmsHadrons@FAIR 25-27 June 2008

  14. Introducing the chiral partner ? Susanna WilmsHadrons@FAIR 25-27 June 2008

  15. Mixing angle and mass m0 with Mixing angle: no mixing maximal mixing Susanna WilmsHadrons@FAIR 25-27 June 2008

  16. Mixing angle and mass m0 [MeV] Susanna WilmsHadrons@FAIR 25-27 June 2008

  17. Linear sigma model with vector and axial vector mesons, as well as the nucleonic fields in the mirror assignment local symmetric case: Results Susanna WilmsHadrons@FAIR 25-27 June 2008

  18. Introducing the chiral partner The s-wave scattering lengths Axial coupling constant of N*(1535) S.W., F. Giacosa, D.Rischke,e-Print: nucl-th/0702076 Susanna WilmsHadrons@FAIR 25-27 June 2008

  19. Introducing the chiralpartner Conclusions Susanna WilmsHadrons@FAIR 25-27 June 2008

  20. Global chiral symmetry in agreement with mesonic decays Susanna WilmsHadrons@FAIR 25-27 June 2008

  21. Model with global symmetry And in the mesonic sector: Susanna WilmsHadrons@FAIR 25-27 June 2008

  22. Model with global symmetry We determine the free parameters of the model m0, c1, and c2 from N*(1200):speculative candidate,decay width GN*zpN > 800 MeV N*(1500) : PDG , decay width GN*zpN = 67.5 MeV N*(1650): PDG, decay width GN*zpN =92.5+/-37.5 MeV Susanna WilmsHadrons@FAIR 25-27 June 2008

  23. Global chiral symmetry in agreement with mesonic decays Results Susanna WilmsHadrons@FAIR 25-27 June 2008

  24. Global symmetry: Results m0 vs. the axial coupling constant of N*(1535) [MeV] 350 MeV < m0 < 600 MeV Susanna WilmsHadrons@FAIR 25-27 June 2008

  25. Global symmetry: Results Susanna WilmsHadrons@FAIR 25-27 June 2008

  26. Global symmetry: Results s-wave scattering lengths Susanna WilmsHadrons@FAIR 25-27 June 2008

  27. Global symmetry: Results s-wave scattering lengths N*(1200) N*(1535) N*(1650) N*(1535) N*(1650) N*(1200) is off by over a factor 1000! Susanna WilmsHadrons@FAIR 25-27 June 2008

  28. Conclusions Susanna WilmsHadrons@FAIR 25-27 June 2008

  29. Thank you! Susanna WilmsHadrons@FAIR 25-27 June 2008

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