Shin Nan Yang National 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.

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

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: S 11 channel only

There are 44 nonstrange baryon states 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 S 11 (1535)  eV  p 1/2 = 60 (  ), 100 (  ) x GeV -1/2

Meson-exchange  N model below 400 MeV

Three-dimensional reduction Cooper-Jennings reduction scheme

Choose to be given by

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

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

2R 3R 4R

R 2R 3R No evidence for the 4th S 11 resonance in  N !  N

Extraction of resonance parameters

BES:  (R 1 )=95(25) MeV

To order e, the t-matrix for  N !  N is written as t  (E) = v  +   v  k g k (E) t k N (E), (1) where, v  k = transition potential, two ingredients t kN (E) = k N t-matrix, g k (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|, q E : photon and pion on-shell momentum Dynamical model for  N !  N v , t  N

Both on- & off-shell

DMT Model

In DMT, we approximate the resonance contribution A R  (W,Q 2 ) by the following Breit-Winger form with f  R = Breit-Winger 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

Pion cloud

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

Extraction of helicity amplitudes

Summary  The DMT coupled-channel dynamical model gives excellent description of the pion scattering and pion photoproduction data in S 11 channel from threshold to 2 GeV  Background contributions become large and negative in the region of S 11 (1535) much larger resonance contribution required

 As in the  channel, pion cloud effects is very important in S 11 channel in both threshold and resonances region  For the first S 11 (1535) resonance, we obtain

 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

The End

In CM frame,

Cooper-Jennings reduction scheme