Deeply Virtual Compton Deeply Virtual Compton Scattering and Pseudoscalar Scattering and Pseudoscalar

Meson Electroproduction with Meson Electroproduction with CLASCLAS

Valery KubarovskyValery KubarovskyJefferson LabJefferson Lab

XII Workshop on High Energy Spin PhysicsSeptember 5, 2007, Dubna

OutlineOutline

Physics MotivationPhysics Motivation DVCS results (CLAS/Jlab)DVCS results (CLAS/Jlab)

- Beam-spin asymmetry- Beam-spin asymmetry- Comparison with theoretical models- Comparison with theoretical models

electroproductionelectroproduction– Cross sectionCross section– Beam spin asymmetryBeam spin asymmetry– Cross section ratioCross section ratio

ConclusionConclusion

Electron ScatteringElectron Scattering, a clean , a clean probe of the Proton probe of the Proton StructureStructure

Q2 = -(e-e’)2

ν = Ee – Ee’

xB = Q2/2M t = (p-p’)2

1/Q2 is the space-time resolution of the virtual

e’

p

eQ

p’

elastic

ve’

p

eQ

X

inclusive

ve’

p

eQ

p’

exclusive

v

Interaction described by:

Reveal different aspects of the proton’s internal structure

Proton form factors, transverse charge & current densities

D. Mueller, X. Ji, A. Radyushkin, …1994 -1997M. Burkardt, A. Belitsky… Interpretation in impact parameter space

Structure functions,quark longitudinalmomentum & spin distributions

How are the proton’s charge densities related to its quark momentum distribution?

?

Correlated quark momentum and helicity distributions in transverse space - GPDs

Basic Process – Handbag Mechanism

xB

2-xB

=GPDs depend on 3 variables, e.g. H(x, , t). They probe the quark structure at the amplitude level.

Deeply Virtual Compton Scattering (DVCS)

x – longitudinal quark momentum fraction

–t – Fourier conjugateto transverse impact parameter

– longitudinal momentum transfer

Proton’s gravitational form factors

GPDs Quark angular momentum

Quark-quark correlations

3D Imaging of quark distributions

Universality of GPDs

Forces on quarks

Universality of GPDs

Single Spin Asymmetries

Deeply Virtual Meson production

Real Compton Scattering

Elastic Form Factors

Parton Momentum Distributions

Deeply Virtual Compton Scattering

GPDs

∫H(x,t)dx

∫H(x,ξ,t)dxH(x=ξ,ξ,t)

∫H(x,t)x-1dx

∫H(x,ξ,t)dx

Experimental measurements of the exclusive processes is a challenge, requiring high luminosity to compensate for the small cross section and detectors capable of ensuring the exclusivity of the final state.

H(x,ξ=0,t=0)=q(x)H(x,ξ=0,t=0)=q(x)~

A =

=

Measuring GPDs through polarization

Unpolarized beam, transverse target:

UT~ sin{k(F2H – F1E) + …. }d

Kinematically suppressed

H(t), E(t)

LU~ sin{F1H + ξ(F1+F2)H +kF2E}d~

Polarized beam, unpolarized target:

H(,t)

Kinematically suppressed

ξ ~ xB/(2-xB)

Unpolarized beam, longitudinal target:

UL~ sin{F1H+ξ(F1+F2)(H +ξ/(1+ξ)E) -.. }d~

Kinematically suppressed

H(,t)~

k = t/4M2 ~

AUL=sin+sin2

Pioneering measurements in 2001Pioneering measurements in 2001

Evidence for twist-2 dominance in asymmetry.

DVCS first observed in non-dedicated experiments at HERA and JLab.

First DVCS measurement with spin-aligned target

Unpolarized beam, longitudinally spin-aligned target:

UL~ sinIm{F1H+ξ(F1+F2)H +… }d~

= 0.252 ± 0.042 = -0.022 ± 0.045

Planned experiment in 2009 will improve accuracy dramatically.

CLAS preliminary

H=0~

H=0~

AUL sensitive to GPD H ~

fitmodelmodel (H=0)

~

S. Chen, et al., Phys. Rev. Lett 97, 072002 (2006)

Deeply Virtual Meson Electroproduction

High Q 2 - Low -tComplement DVCS experiment.

Unique access to spin dependent GPDs

Low Q 2 - High -t New form factors related to 1/x moments of GPDs

High Q 2 - High -tRegion never accessed.

Q2

-t

p p’

L

(z)

x-

z

x+

p p’

L

(z)

x-

z

x+

+ t.c.

• Factorization theorem states that in the limit Q2∞ exclusive electroproduction of mesons is described by hard rescattering amplitude, generalized parton distributions (GPDs), and the distribution amplitude (z) of the outgoing meson. • The prove applies only to the case when the virtual photon has longitudinal polarization• Q2∞ L~1/Q6 , T/L~1/Q2

• The full realization of this program is one of the major objectives of the 12 GeV upgrade

Collins,Frankfurt,Strikman -1997

High QHigh Q22 Low t Region Low t Region

Pseudoscalar Mesons Pseudoscalar Mesons

In the case of pseudoscalar meson In the case of pseudoscalar meson production the amplitude involves the production the amplitude involves the axial axial vector-type GPDsvector-type GPDs

These GPDs are closely related to the These GPDs are closely related to the distributions of quark spin in the proton. The distributions of quark spin in the proton. The function reduces to the function reduces to the polarized polarized quark/antiquark densitiesquark/antiquark densities in the limit of zero in the limit of zero momentum transfermomentum transfer

The Fourier transform with respect to pThe Fourier transform with respect to pTT, the , the so-called so-called impact parameter distributionsimpact parameter distributions, , describes the transverse spatial distribution describes the transverse spatial distribution of quark spin in the proton.of quark spin in the proton.

H~

Flavor Separation and Flavor Separation and Helicity-Dependent GPDsHelicity-Dependent GPDs

DVCS is the cleanest way of accessing GPDs. However, DVCS is the cleanest way of accessing GPDs. However, it is difficult to perform a it is difficult to perform a flavor separationflavor separation..

Vector and pseudoscalar meson production allows one Vector and pseudoscalar meson production allows one to separate flavor and isolate the to separate flavor and isolate the helicity-dependent helicity-dependent GPDsGPDs. .

EH~

,~

EH ,

““Precocious Precocious Factorization”Factorization” Precocious factorization could be valid Precocious factorization could be valid

already at relatively low Qalready at relatively low Q22 especially especially for ratios of cross sections as a for ratios of cross sections as a function of xfunction of xBB

For example For example 00 and and ratio on the ratio on the protonproton

220

3

2

3

1

3

2

6

1:

3

1

3

2

2

1:

ududu

Eides,Frankfurt,Strikman -1997

Cross Section Ratios Cross Section Ratios as a function of xas a function of xBB

)(

)(

epep

enen

)(

)(0

0

epep

enen

All data are available. 0 ratio from proton data will be released very soon

Eides,Frankfurt,Strikman -1997

)(

)(0

enen

enen

)(

)(0

epep

epep

CLAS

JLab Site: The 6 GeV Electron Accelerator

3 independent beams with energies up to 6 GeV Dynamic range in beam current: 106

Electron polarization: 85%

CCEBAF EBAF LLarge arge AAcceptance cceptance SSpectrometerpectrometer CLASCLAS

TOF counters

Drift chambers

Beam line and the target

Electromagnetic calorimeters

6 Superconducting coils

Cherenkov counters

CLAS (forward carriage and side clamshells retracted)

Region 3 drift chamber

Panel 4 TOF

Panel 1 TOF

Panel 2 & 3TOF

Cerenkov & Forward angle EC

Large angle EC

CLAS Lead Tungstate CLAS Lead Tungstate Electromagnetic CalorimeterElectromagnetic Calorimeter

/E~3%

424 crystals,18 RL, pointing geometry, APD readout

Fit: ALU = sincos

Fully integrated asymmetry and one of 65 bins in Q2, x, t .

First results in wide First results in wide kinematicskinematics

A =

=

t-dependence of leadingtwist term (sinΦ).

GPD model predictionsGPD model predictions

VGG parameterization reproduces –t > 0.5GeV2 behavior, and overshoots asymmetry at small t.

The latter could indicate that VGG misses some important contributions to the DVCS cross section.

VGG Model (Vanderhaeghen, Guichon, Guidal)

Fit: ALU = sincos

Regge model Regge model predictionprediction

While there are good indications that Compton scattering does occur at the quark level a description of the process by Regge model (J-M Laget) is in fair agreement in some kinematic bins with our results.

The full significance of this dual description remains to be investigated

DVMP: Kinematic DVMP: Kinematic CoverageCoverage

4 dimensional grid in Q4 dimensional grid in Q22, x, xBB, t, and , t, and

00 ,epep

,epep

t

Q2 xB

W

KinematicsKinematics 4 dimensional grid4 dimensional grid

BinsBins FromFrom ToTo UnitsUnits

77 1.01.0 4.64.6 GeVGeV22

77 0.10.1 0.580.58

66 0.090.09 2.02.0 GeVGeV22

1212 00 360360 degreesdegrees

22 )'( eeQ

m

QxB 2

2

2)'( ppt

Remarks on the Remarks on the following slidesfollowing slides CLAS data CLAS data All data are All data are preliminarypreliminary No radiative correction were appliedNo radiative correction were applied Cross sections are in arbitrary units Cross sections are in arbitrary units No No LL//TT separation separation 12 GeV: 12 GeV: Rosenbluth L/T separation

DistributionDistribution

)cos)1(22cos(2

1),,,( 2

dt

d

dt

d

dt

d

dt

dtxQ

dtd

d LTTTLT

0* pp

Fit of the -distribution gives us three structure functions

dt

ddt

ddt

d

dt

d

LT

TT

LT

dd/d/d 0* pp

TTLLas a function as a function of tof t

0* epp

LTLTas a function of tas a function of t

0* epp

TTTT as a function t as a function t

0* epp

TTL L ) ) TTTT LTLT as a function of tas a function of t

t GeV2

Q2=2.3xB=0.4

cos)1(22cos)(),,,( 2LTTTLTtxQ

dtd

d

0* pp

Non-zero Non-zero TTTT andand LTLT imply imply

that both transverse that both transverse

and longitudinal amplitudesand longitudinal amplitudes

participate in the processparticipate in the process

TTL L ) ) TTTT LTLT in Regge Model (J-M in Regge Model (J-M Laget)Laget)

• The dashed lines correspond to the /b1 Regge poles and elastic rescattering

• The full lines include also charge pion nucleon and Delta intermediate states.

• Regge model qualitatively describes Regge model qualitatively describes the experimental datathe experimental data

/b1 elastic rescat. charge pion

0* pp

dd/dt/dt 0* pp

tQxB Bedt

d ),( 2

t-Slope Parameter as a t-Slope Parameter as a Function of xFunction of xBB and Q and Q22

xB

B(xB ,Q2)

•B(xB , Q2) is almost independent of Q2

•B(xB) is decreasing with increasing xB

0* pp

tQxB Bedt

d ),( 2

t-dependencet-dependence

xB

B(xB )

1.1'

)/1ln('2)(

),(

)/1ln('22'

')(

xxB

exdt

d

xxtxf

txt

ttq q

txBedt

d )(

This is not fit of data. This is GPD predictionswith Regge inspired t-dependence xt

Impact Parameter Impact Parameter Dependent PDFsDependent PDFs Fourier transform of GPDFourier transform of GPD

For impact parameter dependent For impact parameter dependent parton distributions the perp width parton distributions the perp width should go to zero for xshould go to zero for x11

In momentum space, this implies that t-In momentum space, this implies that t-slope should decrease with increasing slope should decrease with increasing x, what we observe experimentallyx, what we observe experimentally

),0,(~

)2(

1),,( 22

2

xHedbbxIPD biyx

Impact Parameter ProfileImpact Parameter Profileof axial current of axial current distributiondistribution

||91.022)2(

1)0,,(

xedbbxIPD biyx

X

xb

The curve is whatwe obtained from experimental data

The size of the The size of the proton decreases proton decreases with increasing xwith increasing x

From data fit

00 and and Beam Spin Beam Spin AsymmetryAsymmetry

)sin)1(2

cos)1(22cos(2

1),,,(

'

2

dt

dh

dt

d

dt

d

dt

d

dt

dtxQ

dtd

d

TL

LTTTLT

h is the beam helicity

sin44

44

VV

dd

ddA

Any observation of a non-zero BSA would be indicative of an L’T interference.If L dominatesLTand L’T go to zero

00 Beam Spin Asymmetry Beam Spin AsymmetryA()XB=0.25Q2=1.95 GeV2

t=-0.29 GeV2

Balck curve – A=sinRed curve – Regge model

A=sinas a function of t The red curves The red curves

correspond to the correspond to the Regge model Regge model (JML)(JML)

BSA are BSA are systematically of systematically of the order of 0.03-the order of 0.03-0.09 over wide 0.09 over wide kinematical range kinematical range in xin xBB and Q and Q22

Beam Spin Beam Spin AsymmetryAsymmetry

Conclusion

Beam-spin asymmetries were extracted in the valence quark region, as a function of all variables describing the reaction. Present GPD parameterization describe reasonably well the main features of our data. The measured kinematic dependencies will put stringent constraisins on any DVCS model.

Cross sections and beam-spin asymmetries for the 0

and exclusive electroproduction in a very wide kinematic range will be released soon

These data will help us to understand better the transition from soft to hard mechanisms

New experiments at 6 GeV with polarized and unpolarized target are coming

CLAS12 will continue the GPD study with broader kinematics at 12 GeV machine.

Questions to theoryQuestions to theory What will our data tell us?What will our data tell us?

What does t-slope B(QWhat does t-slope B(Q22,x,xBB) tell us ?) tell us ? What can we learn from the QWhat can we learn from the Q22 evolution of evolution of

cross section?cross section? Can Can LTLT and and TTTT help us to constrain R= help us to constrain R=LL//T T

?? Can we constrain the GPDs within some

approximations and corrections which have to be made due to non-asymptotic kinematics?

How big are the corrections? How close are we to asymptote?

Q: What will come out Q: What will come out from our marriage?from our marriage?

p p’

zx+

L

(z)

x-

+ = ?

THE ENDTHE END