1. 1 DMT model for πN scattering and pion e.m. production Shin Nan Yang National Taiwan University DMT model for πN scattering and pion e.m. production Shin Nan Yang National Taiwan University EBAC discussion meeting, Jlab, May 24-26, 2010. Dubna: Kamalov Mainz: Drechsel, Tiator Taipei: Guan Yeu Chen, SNY

2. 2 Motivation  To construct a meson-exchange model forπN scattering and e.m. production of pion so that a consistent extraction of the resonance properties like, mass, width, and form factors, from both reactions can be achieved.  Comparison with LQCD results requires reliable extraction. consistent extractions → minimize model dependence?  The resonances we study are always of the type which results from dressing of the quark core by meson cloud. → understand the underlying structure and dynamics

3. 3 Taipei-Argonne πN model: meson-exchange  N model below 400 MeV

4. 4 Three-dimensional reduction Cooper-Jennings reduction scheme

5. 5 Choose to be given by

6. 6 C.T. Hung, S.N. Yang, and T.-S.H. Lee, Phys. Rev. C64, 034309 (2001)

7. 7 DMT πN model: extension of Taipei-Argonne model to energies ≦ 2 GeV  Inclusion of ηN channel in S 11  Introduce higher resonances as indicated by the data G.Y. Chen et al., Phys. Rev. C 76 (2007) 035206.

8. 8 Inclusion of ηN channel in S 11

9. 9

10. 10 Introduction of higher resonances If there are n resonances, then How does one extract masses, widths et al. of the resonances? Coupled- channels equations can be solved

11. 11 How does one extract masses, widths et al. of the resonances?  Two schemes to separate the total t- matrix into background and resonance contribution 1.Afnan et al. and Sato-Lee 2.Dubna-Mainz-Taipei (DMT)

12. 12 Sato-Lee’s separation method Unitary with phase δ B Self-energy

13. 13 Self-energy Σ R (E)

14. 14 Extension of SL’s method to n resonances

15. 15 DMT’s decomposition of bkg and reson. Note that both t B and t R have the same phase of With only one resoance,

16. 16 Extension of DMT’s method to n resonances

17. 17 It can be shown, contains contribution of R i excitation

18. 18 Remark: the background in our separation, already does contain some resonance contributions and in the calculation of the residues, the full t-matrix has to be employed.

19. 19 To order e, the t-matrix for  N →  N is written as Dynamical model for  N →  N v , t  N two ingredients Both on- & off-shell

20. 20 Multipole decomposition of 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|, q E : photon and pion on-shell momentum

21. 21 both t B and t R satisfy Fermi-Watson theorem, respectively.

22. 22 DMT Model

23. 23 Dubna-Mainz-Taipei (DMT)

24. 24 SL’s decomposition of bkg and reson. dressed DMT, bare

25. 25 In DMT, we approximate the resonance contribution A R  (W,Q 2 ) by the following Breit-Wigner form with f  R = Breit-Wigner factor describing the decay of the resonance R  R (W) = total width M R = physical mass  ( W) = to adjust the phase of the total multipole to be equal to the corresponding  N phase shift  (  ). Note that

26. 26 Efforts are being undertaken to use the dressed propagators and vertices obtained in DMT πN model to achieve consistency in the analyses ofπN and π-production.

27. 27 Results of DMT model near threshold,

28. 28 M. Weis et al., Eur. Phys. J. A 38 (2008) 27

29. 29 Photon Beam Asymmetry near Threshold Data: A. Schmidt et al., PRL 87 (2001) @ MAMI DMT: S. Kamalov et al., PLB 522 (2001)

30. PRELIMINA RY D. Hornidge (CB@MAMI) private communication

31. PRELIMINA RY D. Hornidge (CB@MAMI) private communication

32. PRELIMINA RY D. Hornidge (CB@MAMI) private communication