Chung-Wen Kao Chung-Yuan Christian University, Taiwan

1. Two is too many: A personal review of Two-Photon Physics Chung-Wen Kao Chung-Yuan Christian University, Taiwan In Collaboration with Hai-Qing Zhou, Yu-Chun Chen, Shin-Nan Yang 23.5.2008 National Taiwan University, Lattice QCD Journal Club

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

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

4. 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 !

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

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

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

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

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

10. 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)

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

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

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

14. Partonic ModelCalculation GPDs Y.C.Chen, Afanasev,Brodsky, Carlson, Vanderhaeghen (2004)

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

16. 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)

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

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

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

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

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

22. Fit (A) Fit (B)

23. 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

24. 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)

25. 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

26. 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

27. 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

28. 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

29. 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

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

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

32. Electroweak radiative corrections

33. Zero Transfer Momentum Approximations Q2=(p-q)^2 Approximation made in previous analysis: p=q=k p q Marciano, Sirlin (1984)

34. One-loop-diagrams

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

36. Impact of our results Avoid double counting Old New

37. Change of the results of Strange form factors -14.6 -45.05

38. 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 !!!

39. 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!

40. Thank you for listening Two photons may be too many, but two cups of Italian ice cream are not………