Shin Nan Yang National Taiwan University Collaborators: S. S. Kamalov (Dubna) Guan Yeu Chen (Taipei) 18th International Conference on “Few-body Problems.

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Presentation transcript:

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

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

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

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

Meson-exchange  N model below 400 MeV 5

Three-dimensional reduction Cooper-Jennings reduction scheme 6

Choose to be given by 7

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

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

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

DMT Model 11

12

13

14

Frolov et al., PRL,

16

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

19

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

R 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

Extraction of resonance parameters 22

23

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

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

(3,3) 26 P11

(2,3) 27 P31

(2,2) 28 D15

(2,2) 29 F15

1st Resonance2nd Resonance3rd Resonance N*WpΓpΓp ΓpΓp ΓpΓp S (1505, 1501) 67 (170, 124) 1642 (1660, 1673) 97 (160, 82) 2065 (2150±70) 223 (350±100) S (1600, 1585) 136 (115, 104) 1775 (1870±40) 36 (1850±50) 2012 (2140±80) 148 (200±80) P (1365, 1346) 179 (210, 176) 1721 (1720, 1770) 185 (230, 378) 1869 (2120±40, 1810) 238 (240±80, 622) P (1700, 1717) 239 (250, 388) 1846 (not listed) 180 (not listed) P (1714) 70 (68) 1896 (1855, 1810) 130 (350, 494) P (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

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

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

 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

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

(2,2) 35

(3,3) 37

(3,3) 38

(2,2) 40

(2,1 ) 41

(2,2) 43

(2,1) 44