Chung-Wen KaoChung-Yuan

Christian University Taiwan

TBE effects for both parity-conserving and parity-violating ep elastic scattering

12th International Conference on the Structure of the Baryon , Dec 7-11, RCNP, Osaka University, Japan

Collaboration and Reference

In Collaboration with Hai-Qing Zhou(SouthEast U, China), Keitaro Nagata(CYCU, Taiwan), Yu-Chun Chen(AS, Taiwan), M. Vanderhaeghen(Mainz, Germany), Shin-Nan Yang (NTU,Taiwan)

This talk is based on the following works:(1) H-Q Zhou, CWK, S-N. Yang: Phys.Rev.Lett.99:262001,2007(2) K.Nagata, H-Q Zhou, CWK, S-NYang: Phys.Rev.C79:062501,2009.(3) H-Q Zhou, CWK,S-N Yang, K. Nagata: Phys.Rev.C81:035208,2010(4) Y.C. Chen, CWK, M. Vanderhaeghen: arXiv: 0903.1098

Part 1: TPE in parity-conserving ep elastic scattering

3

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/

8e)(

0

ar

ar

2)()( rr

charge density

m105.04 1020

ecm

a with Bohr radius

ei k r

rki 'e

Nucleon E.M form factors

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

"for his pioneering studies of electron scattering in atomic nuclei and for his thereby achieved discoveries concerning the structure of the nucleons

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.

Inconsistency between two methods

SLAC, JLab Rosenbluth data

JLab/HallA Polarization data

Jones et al. (2000)Gayou et al (2002)

Go beyond One-Photon exchange

New Structure

P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (2003).

Two-Photon-Exchange Effects on two techniques

large

small

P. A. M. Guichon and M. Vanderhaeghen, Phys. Rev. Lett. 91, 142303 (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 and polarization data by including the TPE effects:

One-Photon-exchange Two-photon-exchange

Results of hadronic model

Insert the on-shell form factors

P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 91 (2003) 142304

Inclusion of resonance

Insert the on-shell form factors

S.Kondratyuk, P.G.Blunden, W.Melnitchouk and J.A.Tjon, Phys.Rev.Lett. 95 (2005) 172503

Partonic Model Calculation

GPDs

A. V. Afanasev, S. J. Brodsky, C. E. Carlson, Y.-C. Chen, and M. Vanderhaeghen, Phys. Rev. D 72, 013008 (2005).

5/6

GPDsx x

t

DVCSDeeply Virtual Compton

Scattering Longitudinal response only

GPDs can be accessed via exclusive reactions in the Bjorken kinematic regime.

The DVCS process is identified via double (eg) or triple (egN) coincidences, allowing for small scale detectors and large luminosities.

Factorisation applies only to longitudinally polarized virtual photons whose contribution to the electroproduction cross section must be isolated..

GPDsx

x

DA

L

DVMPDeeply Virtual

Meson Production),(

),(

t

Hard gluon

QCD factorization approach

1γ

1γ+2 γ(BLW)

1γ+2 γ(COZ)

N.Kivel and M.Vanderhaeghen, Phys. Rev. Lett.103 (2009) 092004

The leading perturbative QCD (pQCD) contribution to the 2 γ exchange correction to the elastic ep amplitude is given by a convolution integral of the proton distribution amplitudes (DAs) with the hard coefficient function

Comparison with data

arXiv:1012.0339 JLab Hall C

Empirical extraction of TPE

Upcoming TPE experiments

J.Guttmann, N. Kivel, M. Meziane,and M. Vanderhaeghen, arXiv1012.0564

Olympus@DESY experimentare underway. Over the measured range of this experiment, the 2TPE corrections to the e+p/e−p elastic cross section ratio are predicted to vary in the 1 - 6 % range.

Part 2: TPE effect in parity-violating ep elastic scattering

20

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 quarks

Parity Violating ep Elastic Scattering

EMEM JQ

M lQ2

4 NC

VNC

AFNC

PV JgJgGM 55

22

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

22

~~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

OPE vs OZE

Isolating the neutral weak form factors: vary the kinematics or the targets

p

AMEF AAAQGA

24

2

~ few parts per millionFor a proton:

Forward angle Backward angle

eA

pMWA

ZM

pMM

ZE

pEE GGAGGAGGA '2sin41 , ,

sME

dME

uMEME GGGG //// 3

131

32

sMEW

dMEW

uMEW

ZME GGGG /

2/

2/

2/ sin

341sin

341sin

381

NC probes same hadronic flavour 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

Apply Charge Symmetry

snME

spME

unME

dpME

dnME

upME GGGGGG ,

/,/

,/

,/

,/

,/ ,,

GpE,M

GsE,M

GuE,M

GdE,MGn

E,MCharge

symmetryGp

E,M<N| sγμ s |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

Tree Level is not enough! The strange form factors are found to

be very small, just few percents. To make sure the extracted values

are accurate, it is necessary to take the radiative correction into consideration!

So one has to draw many diagrams as follows…..

Electroweak radiative corrections

Squeeze eq→eq amplitudes into 4-Fermion contact interactions

Extraction of strange form factors with radiative corrections

ρ and κ are from electroweak radiative corrections

Strange form factors

Be aware of the Box! Box diagram is intricate because it is

related with nucleon intermediate states. Box diagram is special because of its complicated Q2 and ε

dependence

So how one can squeeze the box diagrams?

Zero Transfer Momentum Approximations for Box diagrams

p

q

Q2=t=(p-q)2 =0

Approximation made in previous analysis:

p=q=k

Marciano, Sirlin (1983)

Pe=Pe’=0Pe

Pe’

High and Low Momentum Integration

N

Low Loop momentum Integration:Only include N intermediate state.Insert the on-shell form factors

High Loop momentum Integration:Lepton and a single quark exchange bosons.Convoluation with PDF

N

=l l

MS approximation Initially it is for atomic parity violation. Two exchanged boson carry the same 4-

momentum and lepton momenta are set to be zero. In other words MS approximation is three-fold approximation:

Q2=0. Elab=0 Coulomb force is taken away

Indeed MS is not good enough !

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

Adding resonances….

Δ(1232) plays an important role in the low energy regime due to its light mass and its strong coupling to πN systeam.

arXiv:0811.3539  PRC79:062501 2009

Keitaro Nagata, Hai Qing Zhou, CWK and SN Yang

Nagata et al, arXiv:0811.3539  PRC79:062501 2009

Partonic calculation of Box diagrams

=

Yu-Chun Chen, C-W K, M. Vanderhaeghen, arXiv 0903.1098

Result of Partonic calculation

Comparison with Marciano and Sirlin’s approximation

Qweak experiment

δQw / Qw = 4% δsin2θW / sin2θW = 0.3%

Dispersion relation approach

M.Gorchtein and C.J.Horowitz, Phys.Rev.Lett. 102} (2009) 091806

Dispersion calculation

The result of hadronic model is quite different

δN=0.6%δΔ=-0.1%

H.Q. Zhou, CWK and S. N.Yang, in progress.

Conclusion and Outlook

TBE are crucial for the extraction of the EM form factors and strangeness inside the nucleon!

More delicate estimate of the TBE effect is needed badly! (including more resonances, consider quark-level contributions…….)

Upcoming positron-proton scattering will provide us the precious information of TPE effects.

Uncertainty of TBE may jeopardize the interpretation of QWEAK data and requests an answer.

Personal comment….

Two bosons are too many,But two cups of ice cream are just perfect!