Chung-Wen KaoChung-Yuan Christian University,

Taiwan

2007,12.24. National Taiwan Normal University

Two is too many: A personal review of Two-Photon Physics

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.

How to explore the proton?

• Experiments with highly energetic electromagnetic probe acting as a micro-scope

• Virtual photon resolves the proton on the distance:

11 ~ Qhcr

e

21 QQ

e

m10~ 15pd

22 ~ Qhcr

rQ /1~

virtuality 22 )'( kkQ

electron

k

k '

p Q

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 factorsParton distribution

Form factor in quantum mechanics

2)(e)( rrdqF rqi

Atomic form factor:

( ) ~ ( ) q F q2

is the Fourier transform of the charge density.

The cross section:

E.g., the hydrogen atom in the ground state:

2

2

2201)(

qaqF

30

2/

8

e)(

0

ar

ar

2)()( rr

charge density

m105.04 10

20

ecma

with Bohr radius

ei k r

rki 'e

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 sometimes.

Rosenbluth Separation Method

Within 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)

Partonic Model CalculationPartonic 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(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 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)=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

lQ2

4 NC

VNC

AFNC

PV JgJgG

M 55

22

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

22

~~Z

EM

NCPV

LR

LRPV

M

Q

M

MA

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

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

sME

dME

uMEME GGGG //// 3

1

3

1

3

2

sMEW

dMEW

uMEW

ZME GGGG /

2/

2/

2/ sin

3

41sin

3

41sin

3

81

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

M

qiFNNuuNJ

Nqq

qq

EM

21 2

Q

Flavour decomposition

Charge Symmetry

snME

spME

unME

dpME

dnME

upME GGGGGG ,

/,/

,/

,/

,/

,/ ,,

GpE,M

GsE,M

GuE,M

GdE,MGn

E,MCharge

symmetry

GpE,M

<N| ss |N>Gn

E,M

GpE,M

GsE,M

Shuffle

Well Measured

As

MEn

MEp

MEFZ

LR

LRPV GGGG

QG

M

MMA ,,,F

2///

2

2

sME

dME

uME

pME GGGG ///

,/ 3

1

3

1

3

2

sME

uME

dME

nME GGGG ///

,/ 3

1

3

1

3

2

Isolating the form factors: vary the kinematics or target

p

AMEF AAAQGA

24

2

~ few parts per million

For 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

Approximations

p

q

Q2=(p-q)^2

Approximation made in previous analysis:

p=q=k

One-loop-diagrams

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

Old

New

Impact of our results

Avoid double counting

Change of the results of Strange form factors

Overestimate of previous analysis

Preliminary

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

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 your attention And Merry Christmas!!!