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

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

Hofstadter determined the precise size of the proton and neutron by measuring their form factor. Nucleon Form Factors

Why bother to go beyond One-photon- exchange framework? Since α EM =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 !

Rosenbluth Separation Method Within one-photon-exchange framework:

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

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

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

Two-Photon-Exchange Effects on two techniques large small

Possible explanation 2-photon-exchange effect can be large on Rosenbluth method when Q 2 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)

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-exchangeTwo-photon-exchange

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

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

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

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

Our Choice of F(Q 2, ε ) Fit (A) Fit (B) ε→ 1, y→0, F→0ε→0, y→1, F≠0 YC Chen, CWK,SN Yang, PLB B652 (2007)

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

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

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

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

Dashed Line : Fit (B)Solid line: Fit (A) TPE contribution to slope SLOPE(TPE)/SLOPE(OPE) =C 1 /(G E /τ)

Fit (A) Fit (B)

Common features of Two fits G M increase few percents compared with Rosenbluth results G E are much smaller than Rosenbluth Result at high Q 2 OPE-TPE interference effects are always destructive TPE play important role in the slope TPE give very small curvature

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) Amp(e + p )= Amp(1γ)-Amp(2γ) Due to Charge conjugation

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

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

Parity Violating Electron 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

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

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

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

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

Electroweak radiative corrections

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

One-loop-diagrams

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

Old New Impact of our results Avoid double counting

Change of the results of Strange form factors

Preliminary G M s = / G E s = / ~3% +/- 2.3% of proton magnetic moment ~20% +/- 15% of isoscalar magnetic moment ~0.2 +/- 0.5% of Electric distribution This above plot should be modified !!!

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!

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