Shin Nan Yang National Taiwan University

1. Shin Nan YangNational Taiwan University Collaborators: Guan Yeu Chen (Taipei) Sabit S. Kamalov (Dubna) D. Drechsel, L. Tiator (Mainz) DMT dynamical model 10th International Workshop on “Meson-Nucleon Scatterings and Nucleon Structure”, Aug. 29 – September 4, 2004, Beijing, China.

2. Outline • Motivation • Meson-exchange model below 400 MeV • Extension to higher energies • Dynamical model for pion photoproduction • Results • Conclusion

3. Motivation Aim: To extract baryon resonance parameters from N scattering and pion photoproduction Test of Theoretical Predictions (Quark Models, Lattice QCD) ) Need a coupled-channel dynamical model This talk: S11 channel only

4. There are 44 nonstrange baryonstates listed in PDG2002 T = 1/2, 22 states = 3/2, 22 states Large uncertainties still exist in the extracted properties, even for 4-star states. E.g., for S11(1535) • = 60, 120(20), 151(27), 151-198, 270(50) MeV Ap1/2= 60 (), 100 () x 10-3 GeV-1/2

5. Meson-exchange  N model below 400 MeV

6. Three-dimensional reduction Cooper-Jennings reduction scheme

7. Choose to be given by

8. C.T. Hung, S.N. Yang, and T.-S.H. Lee, Phys. Rev. C64, 034309 (2001)

9. Extension to higher energies • coupled , , 2 channels • Include resonances R’s with couplings to , , 2 channels

12. 2R 3R 4R

13. ---------- 1R 2R 3R No evidence for the 4th S11 resonance in N !  N

14. Extraction of resonance parameters

15. BES: (R1)=95(25) MeV

16. Dynamical model for  N ! N To order e, the t-matrix for  N ! N is written as t(E) = v+ kvk gk(E) tk N (E), (1) where, vk= transition potential, two ingredients tkN (E) = k N t-matrix, gk (E) = . v and t N Multipole decomposition of (1) gives the physical amplitude in channel =( , l , j), (with  N intermediate states neglected) where (), R() :  N scattering phase shift and reaction matrix in channel  k=|k|, qE : photon and pion on-shell momentum vk , tkN

17. Both on- & off-shell

19. DMT Model

21. In DMT, we approximate the resonance contributionAR(W,Q2) by the following Breit-Winger form • with • f R = Breit-Winger factor describing the decay of the resonance R • R (W) = total width • MR = physical mass • (W) = to adjust the phase of the total multipole to be equal to the corresponding  N phase shift  (). Note that

25. Pion cloud

26. 2=64 full Need 4 S11 Resonances 2=3.5

27. Extraction of helicity amplitudes

31. Summary • The DMT coupled-channel dynamical model gives excellent description of the pion scattering and pion photoproduction data in S11 channel from threshold to 2 GeV • Background contributions become large and negative in the region of S11(1535) much larger resonance contribution required

32. As in the  channel, pion cloud effects is very important in S11 channel in both threshold and resonances region • For the first S11(1535) resonance, we obtain

33. Our analysis at energies higher than 1750 MeV yields considerable strength, which can be • described by a third and a fourth S11 • resonance with masses • 1846(47) and 2113(70) MeV, • in good agreement with the prediction of • HCQM • Extension to other channels is underway

34. The End

36. In CM frame,

37. Cooper-Jennings reduction scheme