Chung-Wen KaoChung-Yuan Christian University,

Taiwan

23.5.2008 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

Q

e

p p p hadr

oniz

atio

n

( )Q

e

xp

p

)(Q

e

xp

2

X

Qx 2, mp p

xp

q q

PD

One-Photon Physics: From Low to High

Low Q2, 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 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 !

Rosenbluth Separation MethodWithin one-photon-exchange framework:

Polarization Transfer Method

Polarization transfer cannot determine the values of GE and GM 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 Two-Photon-Exchange Effects on two techniqueson two techniques

large

small

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)

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

Hadronic Model Result

Blunden, Tjon, Melnitchouk (2003, 2005)

Insert on-shell form factors

+ Cross diagram

Results of hadronic model

Blunden, Tjon, Melnitchouk (2003, 2005)

PPartonicartonic Model Model CCalculationalculation

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(Q2, ε)

Fit (A)

Fit (B)

ε→ 1, y→0, F→0 ε→0, y→1, F≠0

YC Chen, CWK ,SN Yang, PLB B652 (2007)

Result of fitsDashed Line: Rosenbluth

Solid line: Fit (A)

Dotted line: Fit (B)

Result of fitsDashed Line: Rosenbluth

Solid line: Fit (A)

Dotted line: Fit (B)

Puzzle about nonlinearityV.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)=C1/(GE/τ)

Fit (A)

Fit (B)

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

Any other places for TPE?

Normal spin asymmetries in elastic eN scatteringdirectly 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=1.75 GeV^2

Q^2=3.25 GeV^2

Q^2=5 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” GsE and Gs

M

ss

Puuduu dd ss g +.....•

« sea »

• s quark: cleanest candidate to study the sea

Parity Violating Electron Scattering

EMEM JQ

M

lQ24

NCV

NCA

FNCPV JgJgGM 5

5

22

Interference with EM amplitude makes Neutral Current (NC) amplitude accessible

2

2

~~Z

EM

NCPV

LR

LRPV M

QM

MA

Tiny (~10-6) cross section asymmetry isolates weak interaction

Interference: ~ |MEM |2 + |MNC |2 + 2Re(MEM*)MNC

sME

dME

uMEME GGGG //// 3

131

32

sMEW

dMEW

uMEW

ZME GGGG /

2/

2/

2/ sin

341sin

341sin

381

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

NF

Mqi

FNNuuNJN

qqq

qEM

21 2

Q

Flavour decomposition

Charge SymmetrysnME

spME

unME

dpME

dnME

upME GGGGGG ,

/,/

,/

,/

,/

,/ ,,

GpE,M

GsE,M

GuE,M

GdE,MGn

E,MCharge symmetry

GpE,M

<N| ss |N>GnE,M

GpE,M

GsE,M

ShuffleWell Measured

As

MEn

MEp

MEFZ

LR

LRPV GGGGQG

M

MMA ,,,F

2 ///

2

2

sME

dME

uME

pME GGGG ///

,/ 3

131

32

s

MEu

MEd

MEnME GGGG ///

,/ 3

131

32

Isolating the form factors: vary the kinematics or target

p

AMEF AAAQGA

24

2

~ few parts per millionFor a proton:

eAA

eA

sME

nME

nV

pME

pVW

ZME

RFsGG

GGRGRG

,,,2

, )1()1)(sin41(

Forward angle Backward angle

eA

pMWA

ZM

pMM

ZE

pEE GGAGGAGGA '2sin41 , ,

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, 262001 (2007)

Old

New

Impact of our results

Avoid double counting

Change of the results of Strange form factors

-14.6 -45.05

Preliminary

GMs = 0.28 +/- 0.20GEs = -0.006 +/- 0.016~3% +/- 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………