1. A unified description of hadronic form factors Preliminary Results Qian Wan Center for Theoretical Physics, Yale University August 20, 2004

2. Introduction N’ N  Electromagnetic form factors (helicity amplitudes) are closely related to the structure of hadrons Related Processes: Elastic Electron-Nucleon Scattering, Meson Electroproduction, Photoproduction, … High Q 2 region: pQCD gives out asymptotic behavior Low Q 2 region: Only phenomenological models Any consistent theory for all hadrons in low Q 2 region?

3. Two component Model Intrinsic structure (algebraic model of baryons) Meson cloud (vector meson dominance) N’ N  N  N ,,,, += (A)(B)

4. Algebraic Structure of Baryons 1 2 3

6. Nucleon EM Form Factors

8. Spacelike Region

9. Timelike Region

10. Nucleon EM Form Factors The model’s asymptotic behavior agrees with p-QCD. The coupling constants determined by a 1973 calculation indicate significant contributions from meson cloud. Results agree perfectly with the experiments using the recoil polarization technique. Calculations are in perfect agreement with spacelike proton data, but deviate drastically from spacelike neutron data at An analytic continuation of the original model is in excellent agreement with timelike data for both proton and neutron. There might be a discrepancy between spacelike data and timelike data of neutron according to the properties of analytic functions.

11.  EM Form Factors Helicity Amplitudes:

12.  EM Form Factors Observables:

13.  EM Form Factors Data: Frolov (TJNAF 1999) Stein (SLAC 1975) Alder (DESY 1972) Batzner (BONN 1972) Bartel (DESY 1968) PDG 2002 Joo (TJNAF CLAS 2001) Pospischil (MAMI 2000) Mertz (MIT BATES 1998) Kamalov (TJNAF 1999) Frolov (TJNAF 1999) Beck (DAPHNE 1997) Blanpied (LEGS 1997) Burkert (DESY 1979) Alder (DESY 1972) Siddle (DNPL 1971) Haidan (DESY 1979) E133 (SLAC 1992) E89 (SLAC) E19 (SLAC) Brasse 1976

14. G Ash M (Q 2 )

15. R EM (Q 2 )

16. R SM (Q 2 )

17. A T (Q 2 )

18. Parameters for  There is significant contribution from meson cloud b 1 =b 2 confirms the SU(6) symmetry of the intrinsic part of form factors

19.  EM Form Factors Fitting results can perfectly describe experimental data. The importance of meson cloud is further confirmed by the fitted parameters. Results show a slightly larger quark core with size parameter  = 0.350 (GeV) -1 than the results for nucleon. At high Q 2, the model predicts R EM →Const., R SM →0, although current parameters doesn’t give R EM →1.

20. Future direction Understand MBB’ vertex better Explore the choice of other mesons Use algebraic methods to minimize the number of parameters in the coupling constants A unified description of EM form factors of all hadrons

21. Conclusion EM form factors of baryons may be described by a two component model in terms of an intrinsic q 3 structure and a meson cloud. If the Distributed String Model is used for the intrinsic part and vector mesons are included as the meson cloud, results on N and  agree with experimental data respectively. It is very likely that a unified description of all EM form factors of hadrons can be obtained based on this two component model.

22. Thank You!