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

2. Motivation Susanna Wilms Hadrons@FAIR 25-27 June 2008 Introduction of N* for chiral realization of the nucleonic Lagrangian z chiral invariant mass term =/ m 0 Correct description of the axial coupling constant gA(N)=1.26 gA(N*)=? Generation of the nucleonic mass: how is m N generated? Quark condensate vs. m 0 Study of pion-nucleon scattering

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

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

5. The chiral partner of the nucleon in the mirror assignment Susanna Wilms Hadrons@FAIR 25-27 June 2008 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?

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

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

8. Pion-nucleon scattering Susanna Wilms Hadrons@FAIR 25-27 June 2008 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

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

10. Susanna Wilms Hadrons@FAIR 25-27 June 2008 emphasize 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

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

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

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

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

15. Mixing angle and mass m 0 Mixing angle: no mixing maximal mixing with

16. Susanna Wilms Hadrons@FAIR 25-27 June 2008 Mixing angle and mass m 0 [MeV]

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

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

19. Susanna Wilms Hadrons@FAIR 25-27 June 2008 Introducing the chiral partner Conclusions

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

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

22. Susanna Wilms Hadrons@FAIR 25-27 June 2008 Model with global symmetry We determine the free parameters of the model m 0, c 1, and c 2 from N*(1200): speculative candidate, decay width G N*zpN > 800 MeV N*(1500) : PDG, decay width G N*zpN = 67.5 MeV N*(1650): PDG, decay width G N*zpN =92.5+/-37.5 MeV

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

24. Susanna Wilms Hadrons@FAIR 25-27 June 2008 m 0 vs. the axial coupling constant of N*(1535) Global symmetry: Results 350 MeV < m 0 < 600 MeV [MeV]

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

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

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

28. Susanna Wilms Hadrons@FAIR 25-27 June 2008 Conclusions

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