Two is Too Many: A Review of Two-Photon Physics in Nucleon Structure

1. Two is too many: A personal review of Two-Photon Physics Chung-Wen Kao Chung-Yuan Christian University, Taiwan 2007,12.24. National Taiwan Normal University

2. Nucleon structure • Nucleons are the basic building blocks of atomic nuclei. • Their internal structure, arising from the underlying quark and gluon constituents, determines their mass, spin, and interactions. • These, in turn, determine the fundamental properties of the nuclei and atoms. • Nucleon physics represents one of the most important frontiers in modern nuclear physics.

3. electron virtuality ( ) * g Q How to explore the proton? • Experiments with highly energetic electromagnetic probe acting as a micro-scope • Virtual photon resolves the proton on the distance:

4. 2 PD hadronization One-Photon Physics: From Low to High High Q2, deeply inelastic, inclusive Low Q2, elastic, exclusive Parton distribution Form factors

5. 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

6. Nucleon Form Factors • Hofstadterdetermined the precise size of the proton and neutron by measuring their form factor.

7. Why bother to go beyond One-photon-exchange framework? • Since αEM=1/137, the two-photon-exchange effect is just few percent. • However, few percent may be crucial for high precision electroweak experiments. • Surprisingly, two-photon-exchange effect is more important than we thought sometimes.

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

9. Polarization Transfer Method Polarization transfer cannot determine the values of GE and GM but can determine their ratio R.

10. Two methods, Two Results! SLAC, JLab Rosenbluth data JLab/HallA Polarization data Jones et al. (2000) Gayou et al (2002)

11. How to explain it? Go beyond One-Photon Exchange…. New Structure

12. Two-Photon-Exchange Effects on two techniques small large

13. Possible explanation • 2-photon-exchange effect can be large on Rosenbluth method when Q2 is large. • 2-Photon-exchange effect is much smaller on polarization transfer method. • Therefore 2-photon-exchange may explain the difference between two results. Guichon, Vanderhaeghen, PRL 91 (2003)

14. 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 data by including the TPE effects: One-Photon-exchange Two-photon-exchange

15. Hadronic Model Result + Cross diagram Insert on-shell form factors Blunden, Tjon, Melnitchouk (2003, 2005)

16. Results of hadronic model Blunden, Tjon, Melnitchouk (2003, 2005)

17. Partonic Model Calculation GPDs Y.C.Chen, Afanasev,Brodsky, Carlson, Vanderhaeghen (2004)

18. Model-independent analysis Determined from polarization transfer data TPE effects Inputs From crossing symmetry and charge conjugation:

19. YC Chen, CWK ,SN Yang, PLB B652 (2007) Our Choice of F(Q2, ε) ε→ 1, y→0, F→0 ε→0, y→1, F≠0 Fit (A) Fit (B)

20. Result of fits Dashed Line: Rosenbluth Solid line: Fit (A) Dotted line: Fit (B)

21. Result of fits Dashed Line: Rosenbluth Solid line: Fit (A) Dotted line: Fit (B)

22. Puzzle about nonlinearity V.Tvaskis et al, PRC 73, 2005 Purely due to TPE

23. TPE vs OPE Fit (A) : Fit (B):

24. TPE contribution to slope Dashed Line : Fit (B) Solid line: Fit (A) SLOPE(TPE)/SLOPE(OPE) =C1/(GE/τ)

25. Fit (A) Fit (B)

26. Common features of Two fits • GM increase few percents compared with Rosenbluth results • GE are much smaller than Rosenbluth • Result at high Q2 • OPE-TPE interference effects are always destructive • TPE play important role in the slope • TPE give very small curvature

27. Any other places for TPE? Normal spin asymmetries in elastic eN scattering directly proportional to the imaginary part of 2-photon exchange amplitudes spin of beam OR target NORMAL to scattering plane Comparison of e-p/e+p : Amp(e-p)=Amp(1γ)+Amp(2γ) Due to Charge conjugation Amp(e+p)=Amp(1γ)-Amp(2γ)

28. R=σ(e+p) / σ(e-p) Fit (B) Fit (A) Q^2=5 GeV^2 Q^2=5 GeV^2 Q^2=3.25 GeV^2 Q^2=3.25 GeV^2 Q^2=1.75 GeV^2 Q^2=1.75 GeV^2

29. Strangeness in the nucleon « sea » • s quark: cleanest candidate to study the sea 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

30. Parity Violating Electron 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

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

32. 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| sgm s |N> Charge Symmetry

33. Backward angle Forward angle Isolating the form factors: vary the kinematics or target For a proton: ~ few parts per million

34. Extraction of strange form factors Strange form factors ρand κare from electroweak radiative corrections

35. Electroweak radiative corrections

36. Approximations Q2=(p-q)^2 Approximation made in previous analysis: p=q=k p q

37. One-loop-diagrams

38. HQ. Zhou, CWK and SN Yang, accepted by PRL, 0708.4297

39. Impact of our results Avoid double counting Old New

40. Change of the results of Strange form factors

41. Overestimate of previous analysis

42. GMs = 0.28 +/- 0.20 GEs = -0.006 +/- 0.016 ~3% +/- 2.3% of proton magnetic moment ~20% +/- 15% of isoscalar magnetic moment ~0.2 +/- 0.5% of Electric distribution Preliminary This above plot should be modified !!!

43. Summary and Outlook • Two-Photon physics is important to obtain the information of nucleon structure even it is small! • Two-photon-exchange effect is crucial to extract electric and magnetic form factors. • Two-boson exchange effect is also crucial to extract the strange form factors! • More TPE-related research is going: N→ Δ transition form factor, normal beam asymmetry and so on… • In particular, low energy precision measurement of electroweak experiments which is sensitive to NEW PHYSICS rely on the good theoretical understand of Two-photon physics!

44. Thank you for your attention And Merry Christmas!!!