1. Shin Nan Yang National Taiwan University Collaborators: S. S. Kamalov (Dubna) Guan Yeu Chen (Taipei) 18th International Conference on “Few-body Problems in Physics” August 20 – 26, 2006, Santos, Brazil 1

2. Outline  Motivation  Previous works Meson-exchange  N model below 400 MeV Dubna-Mainz-Taipei (DMT) dynamical model for pion e.m. production  Extension to higher energies  Conclusion 2

3. Motivation low energies ─ ChPT high energies, high momentum transfer─ pQCD medium energies ․ LQCD ․ Phenomenology : hadron models, reaction theory QCD Hadronic phenomena 3

4. Aim: To construct a coupled-channel dynamical model to study  N scattering and pion electromagnetic production Aim: To construct a coupled-channel dynamical model to study  N scattering and pion electromagnetic production  low energies : e.m. threshold pion production, low energy theorems and compare with ChPT  medium energies : N-  transition form factors, resonance parameters  high energy and high momentum transfer: transition to pQCD region? 4

5. Meson-exchange  N model below 400 MeV 5

6. Three-dimensional reduction Cooper-Jennings reduction scheme 6

7. Choose to be given by 7

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

9. Both on- & off-shell Dynamical model for electromagnetic pion production 9

10. both t B and t R satisfy Fermi-Watson theorem, respectively. 10

11. DMT Model 11

12. 12

13. 13

14. 14

15. Frolov et al., PRL, 1999 15

16. 16

17. Extension to higher energies  coupled , , 2  channels  Include resonances R’s with couplings to , , 2  channels  coupled , , 2  channels  Include resonances R’s with couplings to , , 2  channels 17

18. 18

19. 19

20. 2R 3R 4R - - - - T B = V B + V B g 0 T B 20 S11

21. ---------- 1R 2R 3R No evidence for the 4th S 11 resonance in  N ->  N No evidence for the 4th S 11 resonance in  N ->  N 21 Consistent with data from ELSA

22. Extraction of resonance parameters 22

23. 23

24. full Need 4 S 11 Resonances  2 =64  2 =3.5 24

25. (3,3) 25 S13 (3,3), red PDG, blue DMT

26. (3,3) 26 P11

27. (2,3) 27 P31

28. (2,2) 28 D15

29. (2,2) 29 F15

30. 1st Resonance2nd Resonance3rd Resonance N*WpΓpΓp ΓpΓp ΓpΓp S 11 1499 (1505, 1501) 67 (170, 124) 1642 (1660, 1673) 97 (160, 82) 2065 (2150±70) 223 (350±100) S 31 1598 (1600, 1585) 136 (115, 104) 1775 (1870±40) 36 (1850±50) 2012 (2140±80) 148 (200±80) P 11 1366 (1365, 1346) 179 (210, 176) 1721 (1720, 1770) 185 (230, 378) 1869 (2120±40, 1810) 238 (240±80, 622) P 13 1683 (1700, 1717) 239 (250, 388) 1846 (not listed) 180 (not listed) P 31 1729 (1714) 70 (68) 1896 (1855, 1810) 130 (350, 494) 2065161 P 33 1218 (1210, 1211) 90 (100, 100) 1509 (1600, 1675) 236 (300, 386) 2149 (1900, 1900±80) 400 (300, 300±100) Pole Positions and Residues in [ MeV ] (preliminary) Red ： PDG04 Blue ： Arndt95 Green ： Cutkovsky80 Orange ： Vrana00 30

31. 1st Resonance2nd Resonance3rd Resonance N*WpΓpΓp ΓpΓp ΓpΓp D 13 (3,3) 1516 (1510, 1515) 123 (115, 110) not seen (1680, not seen) not seen (100, not seen) 1834 (1880±100) 210 (160±80) D 33 (2,2) 1609 (1660, 1655) 133 (200, 242) 2070 (1900±100) 267 (200±60) D 15 (2,2) 1657 (1660, 1663) 132 (140, 152) 2188 (2100±60) 238 (360±80) D 35 (2,1) 1992 (1890, 1913) 270 (250, 246) not seen ( 2400±60 ) not seen ( 400±150 ) F 15 (2,2) 1663 (1670, 1670) 115 (120, 120) 1931 (not listed) 62 (not listed) F 35 (2,2) 1771 (1830, 1832) 190 (280, 254) 2218 (2150±100, 1697) 219 (350±100, 112) F 37 (2,1) 1860 (1885, 1880) 201 (240, 236) 2207 (2350±100) 439 (260±100) Pole Positions and Residues in [ MeV ] (preliminary) Red ： PDG04 Blue ： Arndt95 Green ： Cutkovsky80 Orange ： Vrana00 31

32. Summary  The DMT coupled-channel dynamical model gives excellent description of the pion scattering and pion e.m. production data from threshold to first resonance region  The model has been extended up to c.m. energy 2 GeV in the sector and resonance parameters extracted 32

33.  Our analysis at W > 1750 GeV yields considerable strength, which can be explained by a third and a fourth S 11 resonance with masses 1846(47) and 2113(70) MeV 33 The End

34. (3,4), red PDG, blue DMT 25 S11

35. (2,2) 35

36. (3,3) 37

37. (3,3) 38

38. (2,2) 40

39. (2,1 ) 41

40. (2,2) 43

41. (2,1) 44