Probing Generalized Parton Distributions (GPDs) in Exclusive Processes

Volker D. BurkertCharles Hyde-Wright

Xiangdong Ji

Fundamental questions in electron scattering GPD-sensitive results at low energies The dedicated 6 GeV program at Jlab What will we learn about the proton at 12 GeV? Summary

V. Burkert, Presentation to PAC23 on Physics at 12 GeV

Fundamental questions in electron scattering?

1950: Does the proton have finite size and structure?

• Elastic electron-proton scattering the proton is not a point-like particle but has finite size

charge and current distribution in the proton, GE/GM

Nobel prize 1961- R. Hofstadter

• Deeply inelastic scattering discover quarks in ‘scaling’ of structure functions

quark longitudinal momentum distribution quark helicity distribution

1960-1990: What is the internal structure of the proton?

Nobel prize 1990 - J. Friedman, H. Kendall, R. Taylor

Today: How are these representations of the proton, form factors and quark distributions, connected?

Proton form factors,transverse charge & current distributions

A. Belitsky and D. Muller, Nucl.Phys.A711(2002)118 ..

(Infinite momentum frame)

Quark longitudinalmomentum & helicity distributions

GPDs connect form factorsand parton distribution

Form factors, parton distributions, and GPDsX. Ji, D. Muller, A. Radyushkin

..

GPDs & Deeply Virtual Exclusive Processes

GPDs are Q2 independent (only QCD evolution) x + x = longitudinal momentum fraction -t = Fourier conjugate to transverse impact parameter

Deeply Virtual Compton Scattering (DVCS)

t

=xB

2 - xB

(in the Bjorken regime)

hard processes

H(x,,t), E(x,,t),..

x+ x-

Link to DIS and Elastic Form Factors

),,(~ ,~ , , txEHEH qqqq

Link to DIS at =t=0

)(),()0,0,(~)(),()0,0,(

xqxqxH

xqxqxHq

q

Link to form factors (sum rules)

)(),,(~ , )(),,(~

) Dirac FF(),,(

,

1

1,

1

1

1

tGtxEdxtGtxHdx

tF1txHdx

qPq

qAq

q

q

) Pauli FF(),,(1

tF2txEdxq

q

JG = 1

1

)0,,()0,,(21

21 xExHxdxJ qqq

Access to quark angular momentum (Ji’s sum rule)

X. Ji, Phy.Rev.Lett.78,610(1997)

Modeling Generalized Parton Distributions

Accessed by cross sections

Accessed by beam/target spin asymmetry

t=0

Quark distribution q(x)

-q(-x)

DIS only measures at =0

Scaling cross sections for photon and meson production

• The scaling cross section for photons dominates at high Q2 over meson production.

M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, PRD60, (1999), 94017

1/Q4

1/Q6

1/Q6

Access GPDs through DVCS - BH interference

d4dQ2dxBdtd ~ |TDVCS + TBH|2

~ sinIm{(F1H(,t)+ k1(F1+F2)H(,t)+k2F2E(,t)}d~Twist-2:

Helicity difference:

determined by Dirac & Pauli form factors

TDVCS: determined by GPDs

Eo = 11 GeV Eo = 6 GeV Eo = 4 GeV

BH

DVCS

(M. Vanderhaeghen, private communication)

DVCS/BH comparable, allows asymmetry, cross section measurements

DVCS BH

Measurement of exclusive DVCS with CLAS

GPD analysis of HERA/CLAS/HERMES datain LO/NLO , = 0.20 for CLAS in LOA. Feund, M. McDermott, M. Strikman, hep-ph/0208160

Beam

Spin

Asy

mm

etr

y

1999 data, E=4.2GeV

A. Belitsky et al.

Phys. Rev. Lett. 87 (2001)

= 0.202 ± 0.028stat ± 0.013sys (twist-2) = -0.024 ± 0.021stat ± 0.009sys (twist-3)

A = sin + sin

Beam spin asymmetry

<-t> = 0.19GeV2

<xB>= 0.19

2001/2002 data E=5.75GeV,very preliminary (15% sample)

sin AUL

sin AUL

xB = 0.2-0.4- t = 0.2-0.5 GeV2

<Q2>= 2.2GeV2

<xB> = 0.35

A t(1+t/0.71)2

Measurement of exclusive DVCS with CLAS

AUL = ULUL

Target single spin asymmetry:

e p ep

UL ~ KImF1H + .. ~

ULUL

H(,t) ~ Direct access to

- twist-2 - higher twist

Longitudinal target spin asymmetry

sinsin2

<xB> = 0.25 <Q2> = 1.6 GeV2

<-t> = 0.25 GeV2 AUL

2000 data, E=5.65GeV, 10% sample

very preliminary

Exclusive ep ep production

W=5.4 GeV

HERMES (27GeV)

xB=0.38

xB=0.31

CLAS (4.3 GeV)

Q2 (GeV2)

Q2 (GeV2)

GPD formalism approximately describes data at xB<0.35, Q2 >1.5 GeV2

Compare with GPD formalism and models

The JLab Program @ 6 GeV

Full reconstruction of final state ep ep ALU, for several Q2 bins xB ,, t- dependence

Im(TDVCS) Kinematical dependence of DVCS observables and GPDs Leading and higher twist contributions, QCD corrections Modeling of GPDs

CLAS and Hall A • DVCS

CLAS• DVMP

o, production at W > 2 GeV, Q2 = 1.0 - 4.5 GeV2

production

New equipment, full reconstruction of final state

Kinematics coverage for deeply exclusive experiments

ELFE

no overlap with otherexisting experiments

compete with other experiments

Upgraded CEBAFcomplementary& unique

The JLab GPD Program @ 12 GeV

DVCS: DVCS/BH interference with polarized beam

twist-2/3, Q2 evolution linear combination of GPDs

Differential cross section moments of GPDs

DVCS/BH interference with polarized targets access different combinations of GPDs

DVMP: Establish kinematics range where theory is tractable (if not known) Separation of flavor- and spin-dependent GPDs () Access Jq contributions at xB >0.15

DDVCS: Allows access to x = kinematics ep ep* e+e-

DVCS: Hard baryon spectroscopy ep e, (eN*)

Quark distributions in transverse coordinates

DVCS/BH projected for CLAS++ at 11 GeV

Q2, xB, t rangesmeasured simultaneously.

A(Q2,xB,t) (Q2,xB,t)

(Q2,xB,t)

972 data pointsmeasured simultaneously + high t (not shown)

DVCS with CLAS++ at 11 GeV

2% of all data points that are measured simultaneously.

Q2=5.5GeV2

xB = 0.35 -t = 0.25 GeV2

Q2=2.75GeV2

xB = 0.35 -t = 0.25 GeV2

DVCS/BH twist-2 with CLAS++ at 11 GeV

Q2, xB, t rangesmeasured simultaneously.

Measure ALU,

and DVCSsimultaneously

Sensitivity to models of GPDs

DVCS/BH interference projected for Hall A

L=1037cm-2s-1

400 hours

MAD spectrometerECAL @ -12.5o, 300 cm distanceSC array @ -7o

E = 11 GeVQ2 = 6 GeV2

xB = 0.37

L=1037cm-2s-1

400 hours

MAD spectrometerECAL @ -12.5o, 300 cm distanceSC array @ -10.5o

E = 11 GeVQ2 = 7 GeV2

xB = 0.50

DVCS/BH interference projected for Hall A

Beam spin asymmetry projected data for Hall A

AsinBsin

A: twist-2 B: twist-3

Separation of twist-2/twist-3

Deeply Virtual Production at 11 GeV

CLAS++

L/T Separation via decay distribution and SCHC

• Test the Q2 evolution of L, T => factorization

L

T

tot

<xB> = 0.35<-t> = 0.30

• Rosenbluth separation => test SCHC assumption

other kinematics measured simultaneously

CLAS++ -/ production with transverse target

2 (Im(AB*))/ T

t/4m2) - ReUT

A ~ (euHu - edHd)

B ~ (euEu - edEd)

Asymmetry depends linearlyon the GPD E, which enters Ji’s sum rule. At high xB strongsensitivity to u-quark contributions.

has similar sensitivity to proton quark spin

K. Goeke, M.V. Polyakov, M. Vanderhaeghen

Q2= 5GeV2,Q2=1 -t = 0.5GeV2 t = 0.2

L=1035cm-2s-1

2000hrs

L dominance

HallC - SHMS & HMS - ep e+n

Expected errors for L/T separation at high Q2:

t=tmin

From Observables to GPDs

Procedures to extract GPDs from experimental data are currently under intense development.

Fit parametrizations of GPDs to large sets of data. • Constraint by “forward” parton distribution• Polynomiality conditions• Elastic form factors• Meson distribution amplitudes

Approximations for certain kinematics (small , t), allow extraction of dominant GPDs (e.g. H(,t)) directly.

Partial wave expansion techniques. • generalized quark distributions given by sum over t-channel exchanges• make connection to total quark spin by analysing S- and D-wave exchanges

“Tomographic” Images of the Proton’s Quark Content

Extension to M. Diehl, Eur. Phys. J.C25 (2002)223

transversely polarized target

M. Burkardt NPA711 (2002)127

Impact parameter:

-tb = T

(Transverse space and IMF)

GPDs uniquely connect the charge & current distributions with the forward quark distributions measured in DIS.

Current data demonstrate the applicability of the GPD framework at modest Q2.

A program to study the proton GPDs has been developed for the CEBAF 12 GeV upgrade covering a broad range of kinematics and reactions.

This program will provide fundamental insights into the internal quark dynamics of the proton.

Summary

The program of Deeply Exclusive Experiments at Jefferson Lab is continuing the breakthrough experiments to study the internal nucleon structure at a new level. It has the potential to revolutionize hadronic physics with electromagnetic probes.

Measurement of exclusive DVCS with CLAS

2000 data, E=5.65GeV, 10% sample

ALL =

Beam-target double spin asymmetry:

e p ep

Asymmetry dominated by Bethe-Heitler, modulated by DVCS (GPD) (~15%)

A. Belitsky et al., hep-ph/0112108xB=0.25, Q2=2GeV2,-t=0.25GeV2

<xB> = 0.25 <Q2> = 1.6 GeV2

<-t> = 0.25 GeV2

uncorrected data

not for d

istributio

n

ALL

Beam/target spin asymmetry

Separated Cross section for ep en

L

T

TOT

Rosenbluth separation for L/T

xB = 0.4-0.5-t = 0.2-0.4GeV2

+ many other bins atthe same time

Measurep, p, K,..

simultaneously

Extraction of GPD Hq(,t) @ small t, xB

[4(1-xB)( HH* H

~H*) - x2(HE* + EH* + .. )~

- (x2 +(2-xB)2 )EE* - x2 ]

t4M2 E

~E* ~

(2-x

B)2D =

t4M2

= 4 ( ImH )2 + ….x

x

H ~

ALU = sin

t

4M2D

N = F1H + (F1+F2) - F2Ex

B

(2-xB)

• Dominant contribution to H is Im(H)

At small xB, t, ALU and N measure Im(H(t))

from which e2(Hq(,t)-Hq(-,t)) may be

extracted

q

V.Korotkov, W.D.Novak NPA711 (2002) 175

From Observables to GPDs

Procedures to extract GPDs from experimental data are currently under intense development.

Fit parametrizations of GPDs to large sets of data. • Constraint by “forward” parton distribution• Polynomiality conditions

Approximations for certain kinematics (small , t), allow extraction of dominant GPDs (e.g. H(,t)) directly

Partial wave expansion techniques (Polyakov, A. Shuvaev). • generalized quark distributions given by sum over t-channel exchanges xt(1-x2) An(,t)C3/2 (x) nn=1

dxxxt [B12(t)- (B12(t) -2B10(t))2]

First moment:

JQ = (B10(0) + C10(0))From Ji’s sum rule:

JQ can be extracted from S-wave exchange in t-channel!

Holographic Images of Objects

detector

The Proton

An Apple

A. Belitsky, B. Mueller, NPA711 (2002) 118

By measuring the t- dependence we may generate a tomographic image of the proton

Deeply Virtual Exclusive Processes Inclusive Scattering Forward Compton Scattering

= 0q,qq,q

Deeply Virtual Compton Scattering (DVCS)

t

=xB

2 - xB

(in the Bjorken regime)

Probe the internal nucleon dynamics through interferences of amplitudes, H(x,,t) , E(x,,t). …. (GPDs) ( D. Muller et al. (1994), X. Ji (1997), A. Radyushkin (1997)

..

e.g. H(, t, Q2) = Hq(x, , t, Q2)dx

x- + i

Hq(x, , t, Q2)dx

x-+ iHq(, , t, Q2)

cross section difference

d3

dQ2dxBdt= f ( H, E, H, E)

Hq: Probability amplitude for N to emit a parton q with x+ and N’ toabsorb it with x- .

GPDs: H, E unpolarized, H, E polarized~~

DVCS and GPDs

~ ~

)( xP )( xP

GPD’s

= real part imaginary part

Access GDPs in Deeply Virtual Exclusive Processes

DVMP allows separation of un(polarized) H, E (H, E) GPDs, and contributions of u, d quarks

DVCS DVMP

DVCS dependson all 4 GPDs andu, d quarks

M = H, E

M = H, E

hard vertices

hard gluon

1/Q4

1/Q6

1/Q6

• In hard scattering, photons dominate at high Q2

Scaling cross sections for photon andmeson productionM. Vanderhaeghen, P.A.M. Guichon, M. Guidal, PRD60, (1999), 94017

Need to isolate *L

N*,

2001/2002 data E=5.75GeV

(25% data sample)

xB

sinAUL

2001/2002 data E=5.75GeV

not for d

istributio

n

sin AUL

sin AUL

Deeply Virtual Meson Production

Final state selects the quark flavors u, d, s => probes the GPD structure complementary to DVCS Filter for spin-(in)dependent GPDs

Coverage for deeply virtual exclusive experiments

CLAS 4.3GeV

Snapshot of a Nucleon

(taken through a low resolution microscope)

valence quarks

sea quarks

correlations

meson cloud

quark spin

orbital angular momentum

quark longitudinal/ transverse momentum

x 10 0.5

In DIS experiments weprobe one-dimensionalprojections of the nucleon

Longitudinal quark momentum and helicitydistribution

q + q

q - q

How do we obtain model-independent information?

We need to map out thefull nucleon wave functionto understand the internaldynamics

eliminate ?

Summary

• Knowledge of GPDs will allow to construct “tomographic” respresentations of the nucleon’s quark and spin distributions in transverse space and infinite momentum frame.

• GPDs can be accessed in deeply virtual exclusive processes at moderately high Q2. Broad theoretical support is available to extract the fundamental physics.

• DVCS + DVMP () give access to the total quark contributions to the nucleon spin.

• A broad program for DVCS and DVMP is proposed for Jlab covering a wide range of kinematics in several channels, largely inaccessible at other labs.

• The upgrade energy of 12 GeV allows to reach high Q2. We can make use of asymmetry and cross section measurements to determine GPDs.

• Data from zero’th generation experiments show feasibility of the program.