DMT model for πN scattering and pion e.m. production Shin Nan Yang National Taiwan University

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

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

4. Three-dimensional reduction Cooper-Jennings reduction scheme

5. Choose to be given by

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

7. DMT πN model:extension of Taipei-Argonne model to energies ≦ 2 GeV • Inclusion of ηN channel in S11 • Introduce higher resonances as indicated by the data G.Y. Chen et al., Phys. Rev. C 76 (2007) 035206.

8. Inclusion of ηN channel in S11

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

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

13. Self-energyΣR(E)

14. Extension of SL’s method to n resonances

15. DMT’s decomposition of bkg and reson. With only one resoance, Note that both tB and tR have the same phase of

16. Extension of DMT’s method to n resonances

17. It can be shown, contains contribution of Ri excitation

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

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|, qE : photon and pion on-shell momentum

21. both tB and tR satisfy Fermi-Watson theorem, respectively.

22. DMT Model

23. Dubna-Mainz-Taipei (DMT)

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

25. In DMT, we approximate the resonance contributionAR(W,Q2) by the following Breit-Wigner form • with • f R = Breit-Wigner 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

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. Results of DMT model near threshold,

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

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

30. D. Hornidge (CB@MAMI) private communication PRELIMINARY

31. D. Hornidge (CB@MAMI) private communication PRELIMINARY

32. D. Hornidge (CB@MAMI) private communication PRELIMINARY