1. TPE Contributions to Proton EM Properties in TL Region Dian-Yong Chen Institute of High Energy Physics, Beijing 2009.04.19

2. Outline TPE in Space-Like Region General Analysis of TPE in Time-Like Region TPE Contributions in a Simple Baryon Model Summary

3. Rosenbluth separation method  R = d  /d  [  (1+  )/  Mott ] =  G M 2 +  G E 2 GM2GM2 GE2GE2 Reduced sensitivity to… G M if Q 2 << 1 G E if Q 2 >> 1 Form factor extraction is very sensitive to angle-dependent corrections in these cases Separation form factors from un-polarized elastic e-p scattering

4. polarization separation method Use polarized electron beam, un-polarized proton target, measure the polarization transferred to the struck proton Along final proton’s momentum Perpendicular final proton’s momentum G E /G M goes like ratio of two components. Insensitive to absolute polarization.

5. Experiment Results Rosenbluth separation method Polarization separation method This discrepancy is a serious problem as it generates confusion and doubt about the whole methodology of lepton scattering experiments.

6. Restudy of two-photon exchange contributions in a simple baryon model: 1. Recalculate the Infra-red divergent parts. 2. Include the finite part. 1:The intermediate state of two-photon exchange process are taken as on-shell nucleon 2:The proton current operator is taken as the form in OPE approximation The two-photon exchange contributions are calculated in a different way with the Standard M. T. correction:

7. After including two-photon exchange contributions, the cross section is still approximately linear in . Conclusions: 1:The effects of the additional terms in TPE are significant. 2:two-photon corrections have the proper sign and magnitude to resolve a large part of the discrepancy between the two experimental techniques.

8. TPE contributions to electromagnetic physical observables are obvious in space-like region. The TPE amplitudes have imaginary part. In this case, the interference terms are supposed to be more important in time-like region, as the form factors are complex. Motivation:

9. TPE in Space-Like Region General Analysis of TPE in Time-Like Region TPE Contributions in a Simple Baryon Model Summary

10. Model independent considerations for M. P. Rekalo, E. T-Gustafsson, and D. Prout, Phys. Rev. C 60, 042202(R) (1999). G. I. Gakh and E. T-Gustafsson, Nucl. Phys. A761, 120(2005). E. T-Gustafsson, E.A.Kuraev, S. Bakmaev and et al., Phys. Lett. B659, 197 (2008). Proton Current Operator: Recombination the Form Factors OPE TPE

11. TPE Contributions to unpolarized cross section OPE D 1  TPE D 2  C-Invariance Any odd number is allowed for and D 2  is odd function of 

12. TPE Contributions to polarized observables We consider the unpolarized incoming positron and longitudinally polarized incoming electron, and in the final state, the antiproton is polarized Double Spin Polarization Observable P x and P z Induces three new terms for P x and two terms for P z Odd function of cos  OPE TPE

13. TPE in Space-Like Region General Analysis of TPE in Time-Like Region TPE Contributions in a Simple Baryon Model Summary

14. TPE Contributions in a simple baryon model. TPE process with nucleon intermediate state TPE process with  (1232) intermediate state

15. Amplitudes of Two-Photon Exchange Process: N-Intermediate  -Intermediate N-Intermediate

16.  -Intermediate

17. Parameters Used in Our Calculations Form Factors Coupling Constants IR Divergence in the Calculation 1. Only exist in the nucleon-intermediate diagram. 2. The IR divergent part in the soft approximation is accurate. 3.Our final results are the full calculations minus the IR divergent part in the soft approximation. They are independent on.

18. Two-photon exchange contributions to cross section (1)

19. Conclusions: 1: Odd function of cos  2 : Contributions from N and  intermediate state are opposite. 3: TPE contributions are Small; 4 : Increases with q 2 5: Hard to be detected. Two-photon exchange contributions to cross section (2)

20. TPE contributions to P x Conclusions: 1: odd function of cos  2: Much larger. 3: it seems can be detected at cos  = +1(-1) 4: P x 1  proportional to sin , then the absolute contributions are small. 5: hard to be detected.

21. TPE contributions to P z Conclusions: 1: Odd function of cos  2: 3: Infinite at cos  =0 4: Deserves to be considered in the experiment.

22. Outline TPE in Space-Like Region General Analysis of TPE in Time-Like Region TPE Contributions in a Simple Baryon Model Summary

23. TPE Contributions to Cross section are small TPE Contributions to polarization observables are P z deserves to be considered in the experiment. relative large

24. The End Thanks !

25. Form Factors in TL region

26. Absolute TPE Contributions to P z

27. Absolute TPE Contributions to P x