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TPE Contributions to Proton EM Properties in TL Region

TPE Contributions to Proton EM Properties in TL Region. Dian-Yong Chen. Institute of High Energy Physics, Beijing. 2009.04.19. Outline. TPE in Space-Like Region. General Analysis of TPE in Time-Like Region. TPE Contributions in a Simple Baryon Model. Summary.

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TPE Contributions to Proton EM Properties in TL Region

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  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 Separation form factors from un-polarized elastic e-p scattering sR = ds/dW [e(1+t)/sMott] = tGM2+ eGE2 • Reduced sensitivity to… • GM if Q2 << 1 • GE if Q2 >> 1 • Form factor extraction is very sensitive to angle-dependent corrections in these cases GE2 tGM2

  4. polarization separation method Use polarized electron beam, un-polarized proton target, measure the polarization transferred to the struck proton Perpendicular final proton’s momentum Along final proton’s momentum GE/GM 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: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: 1. Recalculate the Infra-red divergent parts. 2. Include the finite part.

  7. After including two-photon exchange contributions, the cross section is still approximately linear in e. 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 amplitudeshave imaginary part. • In this case, the interference terms are supposed to be more important in time-like region, as the form factorsare 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 TPE OPE

  11. Any odd number is allowed for and D2g is odd function of q TPE Contributions to unpolarized cross section OPE D1g TPE D2g C-Invariance

  12. Induces three new terms for Px and two terms for Pz • Odd function of cosq 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 Px and Pz TPE OPE

  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 withD(1232) intermediate state

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

  16. D-Intermediate

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

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

  19. Two-photon exchange contributions to cross section (2) Conclusions: 1: Odd function of cosq 2: Contributions from N andD intermediate state are opposite. 3: TPE contributions are Small; 4: Increases with q2 5: Hard to be detected.

  20. TPE contributions to Px Conclusions: 1: odd function of cosq 2: Much larger. 3: it seems can be detected at cosq = +1(-1) 4: Px1g proportional tosinq, then the absolute contributions are small. 5: hard to be detected.

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

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

  23. Summary • TPE Contributions to Cross section are small • TPE Contributions to polarization observables are relative large • Pz deserves to be considered in the experiment.

  24. The End Thanks !

  25. Form Factors in TL region

  26. Absolute TPE Contributions to Pz

  27. Absolute TPE Contributions to Px

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