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Chung-Wen Kao Chung-Yuan Christian University Taiwan

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. Collaboration and Reference.

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Chung-Wen Kao Chung-Yuan Christian University Taiwan

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  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 onthe 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

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

  5. Nucleon E.M form factors • Hofstadterdetermined 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 GE and GM 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 P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003). New Structure

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

  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-exchange Two-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. DVCSDeeply Virtual Compton Scattering DVMPDeeply Virtual Meson Production DA Hard gluon GPDs GPDs GPDs can be accessed via exclusive reactionsin the Bjorken kinematic regime. Longitudinal response only • 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. . 5/6

  16. QCD factorization approach 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 N.Kivel and M.Vanderhaeghen, Phys. Rev. Lett.103 (2009) 092004 1γ 1γ+2 γ(BLW) 1γ+2 γ(COZ)

  17. Comparison with data arXiv:1012.0339 JLab Hall C

  18. Empirical extraction of TPE

  19. Upcoming TPE experiments 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. J.Guttmann, N. Kivel, M. Meziane,and M. Vanderhaeghen, arXiv1012.0564

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

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

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

  23. OPE vs OZE

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

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

  26. Gg,pE,M GuE,M GpE,M Well Measured Charge symmetry Gg,nE,M GdE,M Shuffle GnE,M GsE,M GZ,pE,M GsE,M <N| sγμs |N> Apply Charge Symmetry

  27. 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…..

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

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

  30. 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 Q2 and ε dependence So how one can squeeze the box diagrams?

  31. Zero Transfer Momentum Approximations for Box diagrams Approximation made in previous analysis: Pe p=q=k Pe=Pe’=0 Q2=t=(p-q)2 =0 p q Pe’ Marciano, Sirlin (1983)

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

  33. 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: • Q2=0. • Elab=0 • Coulomb force is taken away

  34. Indeed MS is not good enough !

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

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

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

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

  39. Result of Partonic calculation

  40. Comparison with Marciano and Sirlin’s approximation

  41. Qweak experiment δQw / Qw = 4% δsin2θW / sin2θW = 0.3%

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

  43. Dispersion calculation

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

  45. 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.

  46. Personal comment….

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

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