1. Chung-Wen Kao Chung-Yuan Christian University Taiwan TBE effects for both parity-conserving and parity-violating ep elastic scattering 12th International Conference on the Structure of the Baryon, Dec 7-11, RCNP, Osaka University, Japan

2. Collaboration and Reference In Collaboration with Hai-Qing Zhou(SouthEast U, China), Keitaro Nagata(CYCU, Taiwan), Yu-Chun Chen(AS, Taiwan), M. Vanderhaeghen(Mainz, Germany), Shin-Nan Yang (NTU,Taiwan) This talk is based on the following works: (1) H-Q Zhou, CWK, S-N. Yang: Phys.Rev.Lett.99:262001,2007 (2) K.Nagata, H-Q Zhou, CWK, S-NYang: Phys.Rev.C79:062501,2009. (3) H-Q Zhou, CWK,S-N Yang, K. Nagata: Phys.Rev.C81:035208,2010 (4) Y.C. Chen, CWK, M. Vanderhaeghen: arXiv: 0903.1098

3. Part 1: TPE in parity-conserving ep elastic scattering 3

4. Form factor in quantum mechanics Atomic form factor: is the Fourier transform of the charge density. The cross section: E.g., the hydrogen atom in the ground state: charge density with Bohr radius

5. Nucleon E.M form factors Hofstadter determined the precise size of the proton and neutron by measuring their form factor. "for his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons

6. Rosenbluth Separation Method Within one-photon-exchange framework:

7. Polarization Transfer Method Polarization transfer cannot determine the values of G E and G M but can determine their ratio R.

8. Inconsistency between two methods SLAC, JLab Rosenbluth data JLab/HallA Polarization data Jones et al. (2000) Gayou et al (2002)

9. Go beyond One-Photon exchange New Structure P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).

10. Two-Photon-Exchange Effects on two techniques large small P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).

11. One way or another ……. There are two ways to estimate the TPE effect: Use models to calculate Two-Photon-Exchange diagrams: Like parton model, hadronic model and so on….. Direct analyze the cross section and polarization data by including the TPE effects: One-Photon-exchangeTwo-photon-exchange

12. Results of hadronic model Insert the on-shell form factors P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 91 (2003) 142304

13. Inclusion of resonance Insert the on-shell form factors S.Kondratyuk, P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 95 (2005) 172503

14. Partonic Model Calculation GPDs A. V. Afanasev, S. J. Brodsky, C. E. Carlson, Y.-C. Chen, and M. Vanderhaeghen, Phys. Rev. D 72, 013008 (2005).

15. 5/6 GPDs DVCS Deeply Virtual Compton Scattering Longitudinal response only GPDs can be accessed via exclusive reactions in the Bjorken kinematic regime.  The DVCS process is identified via double (eg) or triple (egN) coincidences, allowing for small scale detectors and large luminosities. Factorisation applies only to longitudinally polarized virtual photons whose contribution to the electroproduction cross section must be isolated.. GPDs DA DVMP Deeply Virtual Meson Production Hard gluon

16. QCD factorization approach 1γ1γ 1 γ+2 γ(BLW) 1 γ+2 γ(COZ) N.Kivel and M.Vanderhaeghen, Phys. Rev. Lett.103 (2009) 092004 The leading perturbative QCD (pQCD) contribution to the 2 γ exchange correction to the elastic ep amplitude is given by a convolution integral of the proton distribution amplitudes (DAs) with the hard coefficient function

17. Comparison with data arXiv:1012.0339 JLab Hall C

18. Empirical extraction of TPE

19. Upcoming TPE experiments J.Guttmann, N. Kivel, M. Meziane,and M. Vanderhaeghen, arXiv1012.0564 Olympus@DESY experiment are underway. Over the measured range of this experiment, the 2TPE corrections to the e + p/e − p elastic cross section ratio are predicted to vary in the 1 - 6 % range.

20. Part 2: TPE effect in parity- violating ep elastic scattering 20

21. Strangeness in the nucleon Goal: Determine the contributions of the strange quark sea ( ) to the charge and current/spin distributions in the nucleon : “strange form factors” G s E and G s M « sea » s quark: cleanest candidate to study the sea quarks

22. Parity Violating ep Elastic Scattering Interference with EM amplitude makes Neutral Current (NC) amplitude accessible Tiny (~10 -6 ) cross section asymmetry isolates weak interaction Interference:  ~ |M EM | 2 + |M NC | 2 + 2Re(M EM* )M NC

23. OPE vs OZE

24. Isolating the neutral weak form factors: vary the kinematics or the targets ~ few parts per million For a proton: Forward angleBackward angle

25. NC probes same hadronic flavour structure, with different couplings: G Z E /M provide an important new benchmark for testing non-perturbative QCD structure of the nucleon Flavour decomposition

26. Apply Charge Symmetry G  p E,M G s E,M G u E,M G d E,M G  n E,M Charge symmetry G  p E,M G n E,M G p E,M G s E,M Shuffle Well Measured

28. Tree Level is not enough! The strange form factors are found to be very small, just few percents. To make sure the extracted values are accurate, it is necessary to take the radiative correction into consideration! So one has to draw many diagrams as follows…..

29. Electroweak radiative corrections Squeeze eq→eq amplitudes into 4-Fermion contact interactions

30. Extraction of strange form factors with radiative corrections ρ and κ are from electroweak radiative corrections Strange form factors

31. Be aware of the Box! Box diagram is intricate because it is related with nucleon intermediate states. Box diagram is special because of its complicated Q 2 and ε dependence So how one can squeeze the box diagrams?

32. Zero Transfer Momentum Approximations for Box diagrams p q Q 2 =t=(p-q) 2 =0 Approximation made in previous analysis: p=q=k Marciano, Sirlin (1983) P e =P e ’=0 PePe P e’

33. High and Low Momentum Integration N Low Loop momentum Integration: Only include N intermediate state. Insert the on-shell form factors High Loop momentum Integration: Lepton and a single quark exchange bosons. Convoluation with PDF N = ll

34. One-loop box diagrams ＝ ＝ + + N N Quark-level Contribution

35. MS approximation Initially it is for atomic parity violation. Two exchanged boson carry the same 4-momentum and lepton momenta are set to be zero. In other words MS approximation is three-fold approximation: Q 2 =0. E lab =0 Coulomb force is taken away

36. Indeed MS is not good enough !

37. HQ. Zhou, CWK and SN Yang, PRL, 99, 262001 (2007)

38. Adding resonances…. Δ(1232) plays an important role in the low energy regime due to its light mass and its strong coupling to πN systeam. arXiv:0811.3539 PRC79:062501 2009 Keitaro Nagata, Hai Qing Zhou, CWK and SN Yang

39. Nagata et al, arXiv:0811.3539 PRC79:062501 2009

40. Partonic calculation of Box diagrams = Yu-Chun Chen, C-W K, M. Vanderhaeghen, arXiv 0903.1098

41. Result of Partonic calculation

42. Comparison with Marciano and Sirlin’s approximation

43. Q weak experiment δQw / Qw = 4% δsin 2 θ W / sin 2 θ W = 0.3%

44. Dispersion relation approach M.Gorchtein and C.J.Horowitz, Phys.Rev.Lett. 102} (2009) 091806

45. Dispersion calculation

46. The result of hadronic model is quite different δ N =0.6% δ Δ =-0.1% H.Q. Zhou, CWK and S. N.Yang, in progress.

47. Conclusion and Outlook TBE are crucial for the extraction of the EM form factors and strangeness inside the nucleon! More delicate estimate of the TBE effect is needed badly! (including more resonances, consider quark-level contributions…….) Upcoming positron-proton scattering will provide us the precious information of TPE effects. Uncertainty of TBE may jeopardize the interpretation of QWEAK data and requests an answer.

48. Personal comment….

49. Two bosons are too many, But two cups of ice cream are just perfect!