1. Probing Generalized Parton Distributions (GPDs) in Exclusive Processes
Volker D. Burkert
Charles 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

2. 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 R. Hofstadter
Deeply inelastic scattering
discover quarks in ‘scaling’ of structure functions
quark longitudinal momentum distribution
quark helicity distribution
: What is the internal structure of the proton?
Nobel prize J. Friedman, H. Kendall, R. Taylor
We can soon celebrate a half century of electron scattering. So, we can ask what are the most fundamental questions that have been addressed in electron scattering.
Today: How are these representations of the proton,
form factors and quark distributions, connected?

3. Form factors, parton distributions, and GPDs
X. Ji, D. Muller, A. Radyushkin ..
Proton form factors,
transverse charge & current distributions
A. Belitsky and D. Muller, Nucl.Phys.A711(2002)118 ..
(Infinite momentum frame)
Quark longitudinal
momentum & helicity
distributions
GPDs connect form factors
and parton distribution
This question has been addressed theoretically by introducing the GPDs, independently by several theorists, most notably by Ji, Muller and Anatoly, and many more joint them during the past 5 years.

4. GPDs & Deeply Virtual Exclusive Processes
Deeply Virtual Compton Scattering (DVCS) t g
x = xB
2 - xB
(in the Bjorken regime)
hard processes
H(x,x,t), E(x,x,t),..
x+x
x-x
These objects can be accessed experimentally in Deeply Virtual Exclusive Processes, most notably in Deeply Virtual Compton Scattering, or DVCS.
GPDs are Q2 independent (only QCD evolution)
x + x, x-x = longitudinal momentum fraction
-t = Fourier conjugate to transverse impact parameter

5. [ ] ò Link to DIS and Elastic Form Factors [ [ ] ] ò å ò å ò ò ) , ( ~x E H q
Link to DIS at
=t=0 ), - D =
Link to form factors (sum rules) 1 [ ] ò å dx H q ( x , x , t ) = F1 ( t
) Dirac FF q 1 [ ] ò å [ ] ò - x +
- JG = = 1 ) , ( 2 E H
xdx J q
Access to quark angular momentum (Ji’s sum rule)
X. Ji, Phy.Rev.Lett.78,610(1997) dx E q ( x , x , t ) = F2 ( t
) Pauli FF q 1 1 ~ ~ ò dx H q ( x , x , t ) = G ( t ) , ò dx E q ( x , x , t ) = G ( t )
GPD H is reduced to the quark momentum distribution at xi=0, t-0, and H~ to the helicity distribution in this limit.
Note that E and E~ have no correspondence in the parton picture. The x-moments of GPD H and E are given by the Dirac, and Pauli form factors, and H~ and E~ by the axial ff and the induced pseudoscalar ff.
An important conncetion is made with the total quark
angular momentum contribution to the proton spin in
Ji's sum rule. A , q P , q - 1 - 1

6. Modeling Generalized Parton Distributions
Quark distribution q(x)
-q(-x)
DIS only measures at x=0
Accessed by cross sections
Accessed by beam/target spin asymmetry
t=0
How do GPDs look like?
This shows a model representation of GPD H at t=0.
H is plotted as a function of x and xi. DIS can access only the
slice at xi=0 with the usual quark distirbutions here and the negative antiquark distributions.
As we go away from xi=0 we dial into two-parton correlations.
With increasing xi the quark's momenta are increasingly different in size and the two quaks look more and more like
a quar-anti-quark pair or meson. This is why the shape of this
surface changes dramatically.

7. Scaling cross sections for photon and meson production
M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, PRD60, (1999), 94017
1/Q6 g
1/Q6
1/Q4
The experimental tools to access the GPD surfaces are photon
production and meson production. The scaling cross sections are shown here.
The scaling cross section for photons dominates at high Q2 over meson production.

8. Access GPDs through DVCS - BH interference
Eo = 11 GeV
Eo = 6 GeV
Eo = 4 GeV BH
DVCS
(M. Vanderhaeghen, private communication)
DVCS/BH comparable,
allows asymmetry, cross
section measurements
d4
dQ2dxBdtd
~ |TDVCS + TBH|2 BH
DVCS
TBH : determined by Dirac & Pauli
form factors
TDVCS: determined by GPDs
Ds ~ sinfIm{(F1H(x,x,t)+ k1(F1+F2)H(x,x,t)+k2F2E(x,x,t)}df ~
Twist-2:
Helicity difference:

9. Measurement of exclusive DVCS with CLAS
GPD analysis of HERA/CLAS/HERMES data
in LO/NLO , a = 0.20 for CLAS in LO
A. Feund, M. McDermott, M. Strikman, hep-ph/
Beam Spin Asymmetry
1999 data, E=4.2GeV
A. Belitsky et al.
Phys. Rev. Lett. 87 (2001)
a = ± 0.028stat ± 0.013sys (twist-2)
b = ± 0.021stat ± 0.009sys (twist-3)
A = asinf + bsin2f
Beam spin asymmetry
<-t> = 0.19GeV2
<xB>= 0.19
2001/2002 data E=5.75GeV,
very preliminary (15% sample)
sinf
AUL
xB =
- t = GeV2
<Q2>= 2.2GeV2
<xB> = 0.35
A t
(1+t/0.71)2

10. Measurement of exclusive DVCS with CLAS
AUL =
sUL-sUL
Target single spin asymmetry:
e p epg
DsUL ~ KImF1H + .. ~
sUL+sUL + -
H(x,x,t)
Direct access to
a - twist-2
b - higher twist
Longitudinal target spin
asymmetry
asinf + bsin2f
<xB> = 0.25
<Q2> = 1.6 GeV2
<-t> = 0.25 GeV2
AUL
0.1
-0.1
0.2
0.3
-0.2 0.
fg*g(o)
2000 data, E=5.65GeV, 10% sample
very preliminary

11. Exclusive ep epr0 production
Compare with GPD formalism and models
W=5.4 GeV
HERMES (27GeV)
xB=0.38
xB=0.31
CLAS (4.3 GeV)
Q2 (GeV2)
GPD formalism approximately describes data at xB<0.35, Q2 >1.5 GeV2

12. New equipment, full reconstruction of final state
The JLab 6 GeV
New equipment, full reconstruction of final state
DVCS
CLAS and Hall A
Full reconstruction of final state ep epg
ALU, Ds for several Q2 bins xB , F, t- dependence
Im(TDVCS)
Kinematical dependence of DVCS observables and GPDs
Leading and higher twist contributions, QCD corrections
Modeling of GPDs
CLAS
DVMP
ro, w production at W > 2 GeV, Q2 = GeV2
p0/h, p+ production

13. Kinematics coverage for deeply exclusive experiments
no overlap with other
existing experiments
compete with other
experiments
ELFE
Upgraded CEBAF
complementary
& unique

14. 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 (ro, w, p0,h, K+,0 )
Access Jq contributions at xB >0.15
Quark distributions in transverse coordinates
DDVCS: Allows access to x = x kinematics
ep epg* e+e-
DDVCS: Hard baryon spectroscopy ep egD, (egN*)

15. DVCS/BH projected for CLAS++ at 11 GeV
972 data points
measured
simultaneously +
high t (not shown)
Q2, xB, t ranges
measured
simultaneously.
A(Q2,xB,t)
Ds (Q2,xB,t)
s (Q2,xB,t)

16. 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

17. DVCS/BH twist-2 with CLAS++ at 11 GeV
Sensitivity to models of GPDs
Q2, xB, t ranges
measured
simultaneously.
Measure ALU,
Ds and s(DVCS)
simultaneously

18. DVCS/BH Ds interference projected for Hall A
E = 11 GeV
Q2 = 6 GeV2
xB = 0.37
L=1037cm-2s-1
400 hours
MAD spectrometer o,
300 cm distance
SC -7o

19. DVCS/BH Ds interference projected for Hall A
E = 11 GeV
Q2 = 7 GeV2
xB = 0.50
L=1037cm-2s-1
400 hours
MAD spectrometer o,
300 cm distance
SC -10.5o

20. Beam spin asymmetry projected data for Hall A
Separation of twist-2/twist-3
Ds ~ Asinf + Bsin2f
A: twist-2
B: twist-3

21. CLAS++ Deeply Virtual r0 Production at 11 GeV sL/sT Separation via
stot
<xB> = 0.35
<-t> = 0.30
sL/sT Separation via
ro p+p- decay
distribution and SCHC
Test the Q2 evolution of sL , sT => factorization
Rosenbluth separation => test SCHC assumption
other kinematics measured simultaneously

22. CLAS++ - r0/w production with transverse target
2 D (Im(AB*))/p
Asymmetry depends linearly
on the GPD E, which enters
Ji’s sum rule. At high xB strong
sensitivity to u-quark contributions. T
AUT = -
|A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2
A ~ (euHu - edHd)
B ~ (euEu - edEd)
K. Goeke, M.V. Polyakov, M. Vanderhaeghen
Q2= 5GeV2,
DQ2=1
-t = 0.5GeV2
Dt = 0.2
L=1035cm-2s-1
2000hrs
sL dominance
w has similar sensitivity to proton quark spin

23. HallC - SHMS & HMS - ep ep+n
Expected errors for L/T separation at high Q2:
t=tmin

24. From Observables to GPDs
Procedures to extract GPDs from experimental data are currently under intense development.
Approximations for certain kinematics (small x, t), allow extraction of dominant GPDs (e.g. H(x,x,t)) directly.
Fit parametrizations of GPDs to large sets of data.
Constraint by “forward” parton distribution
Polynomiality conditions
Elastic form factors
Meson distribution amplitudes
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

25. “Tomographic” Images of the Proton’s Quark Content
(Transverse space and IMF)
transversely polarized target
M. Burkardt NPA711 (2002)127 1
Impact parameter: -t
b = T x
Extension to x > 0 , M. Diehl, Eur. Phys. J.C25 (2002)223

26. Summary 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.

27. 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.

29. Measurement of exclusive DVCS with CLAS
Beam/target spin asymmetry
2000 data, E=5.65GeV, 10% sample
ALL =
N++-N-+-(N+--N--)
N+++N-+ +N+--N--
Beam-target double spin
asymmetry:
e p epg
<xB> = 0.25
<Q2> = 1.6 GeV2
<-t> = 0.25 GeV2
0.9
ALL
0.6
Asymmetry dominated by Bethe-Heitler, modulated by DVCS (GPD) (~15%)
0.3
uncorrected data
not for distribution
fg*g(o)
A. Belitsky et al., hep-ph/
xB=0.25, Q2=2GeV2,-t=0.25GeV2

30. Separated Cross section for ep e p+n
Rosenbluth separation for s / s L T x =
+ many other bins at B
-t = GeV 2
the same time
Measure
pp0, ph, KL,..
simultaneously s L s
TOT s T

31. Extraction of GPD Hq(x,x,t) @ small t, xB~
ALU =
sinf t
4M2 N D
N = F1H (F1+F2) F2E xB
(2-xB)
Dominant contribution to H is Im(H)
[4(1-xB)( H H* ~
H*) - x2(HE* + EH* + .. ) +
- (x2 +(2-xB) )EE* - x ] t
4M2 E E* 1
(2-xB)2
D = B
= ( ImH )2 + ….
1 - xB
( 2 - xB )2
V.Korotkov, W.D.Novak NPA711 (2002) 175
At small xB, t, ALU and N measure Im(H(x,x,t))
from which Se2(Hq(x,x,t)-Hq(-x,x,t)) may be
extracted q

32. 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 x, t), allow extraction of dominant GPDs (e.g. H(x,x,t)) directly
Partial wave expansion techniques (Polyakov, A. Shuvaev).
generalized quark distributions given by sum over t-channel exchanges
H(x,x,t) = (1-x2) An(x,t)C3/2 (x) S n
n=1
dxxH (x,x,t) = [B12(t) (B12(t) -2B10(t))x2] 1 3
First moment: 6 5 6 5
JQ = (B10(0) + C10(0))
From Ji’s sum rule:
JQ can be extracted from S-wave exchange in t-channel!

33. Holographic Images of Objects
An Apple
A. Belitsky, B. Mueller, NPA711 (2002) 118
detector
The Proton
By measuring the t- dependence we may generate a
tomographic image of the proton

34. Deeply Virtual Exclusive Processes
Inclusive Scattering
Forward Compton Scattering
q,Dq
q,Dq q
= 0 D
eeply V
irtual C
ompton S
cattering (
DVCS ) t g
x = xB
2 - xB
(in the Bjorken regime) g*
Probe the internal nucleon dynamics through interferences
of amplitudes, H(x,x,t) , E(x,x,t). …. (GPDs)
( D. Muller et al. (1994), X. Ji (1997), A. Radyushkin (1997) ..

35. ò ò DVCS and GPDs ~ ~ ~ ~ g GPDs : H, E unpolarized , H, E polarized g* ) ( x + P ) ( x - P ò H q
(x, x
GPD’s
, t, Q 2 ) dx
e.g. H ( x
, t, Q 2
) = x- x
+ i e ò H q
(x, x
, t, Q 2 ) dx =
+ i p H q ( x , x
, t, Q 2 ) x- x
imaginary part
cross section
real part
difference d 3 s ~ ~
= f ( H , E , H , E ) dQ 2 dx dt B H q :
Probability amplitude for N to
emit a
parton
q with x+ x
and N’ to
absorb it with x- x .

36. Access GDPs in Deeply Virtual Exclusive Processes
Scaling cross sections for photon and
meson production
M. Vanderhaeghen, P.A.M. Guichon, M. Guidal, PRD60, (1999), 94017
DVCS
DVMP
hard gluon
hard vertices
1/Q6
1/Q6
N*,D
1/Q4
DVCS depends
on all 4 GPDs and
u, d quarks
DVMP allows separation of
un(polarized) H, E (H, E)
GPDs, and contributions
of u, d quarks g
M = r, w
H, E
M = p, h, K
H, E
In hard scattering, photons dominate at high Q2
Need to isolate g*L

37. g,p0 AUL not for distribution xB 2001/2002 data E=5.75GeV
sinf
AUL
2001/2002 data E=5.75GeV
g,p0
AUL
sinf xB
(25% data sample)

38. 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

39. Coverage for deeply virtual exclusive experiments
CLAS 4.3GeV

40. Snapshot of a Nucleon eliminate ? x
(taken through a low resolution microscope)
valence quarks
sea quarks
correlations
meson cloud
quark spin
orbital angular momentum
quark longitudinal/
transverse momentum x 1
0.5
In DIS experiments we
probe one-dimensional
projections of the nucleon
Longitudinal quark
momentum and helicity
distribution
q + q
q - q
How do we obtain model-
independent information?
We need to map out the
full nucleon wave function
to understand the internal
dynamics

41. 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 (r, w) 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.