1. Chung-Wen Kao Chung-Yuan Christian University, Taiwan
Two is too many:
A personal review of Two-Photon Physics
Chung-Wen Kao
Chung-Yuan Christian University,
Taiwan
2007, 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. How to explore the proton?
Experiments with highly energetic electromagnetic probe acting as a micro-scope
Virtual photon resolves the proton on the distance:
virtuality
electron ( ) Q * g

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

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 Bohr radius

6. Nucleon Form Factors
Hofstadter determined 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. Blunden, Tjon, Melnitchouk (2003, 2005)
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. Our Choice of F(Q2, ε) ε→ 1, y→0, F→0 ε→0, y→1, F≠0 Fit (A) Fit (B)
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 (A) Fit (B) Q^2=5 GeV^2 Q^2=5 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. Charge Symmetry Gg,pE,M GsE,M GuE,M GdE,M Gg,nE,M GZ,pE,M GnE,M GpE,M
<N| sgm s |N>
GnE,M
GpE,M
Shuffle
Well Measured

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

34. Extraction of 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. This above plot should be modified !!!
GMs = /- 0.20
GEs = /
~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!!!