1. Generalized Parton Distributions and the Structure of the Nucleon
x=0.4
x=0.9
1.5
-1.5 1 -1
Volker D. Burkert
Jefferson Lab fm fm
April Meeting

2. Fundamental questions in hadron physics?
: Does the proton have finite size and structure?
Elastic scattering
the proton is not a point-like particle
charge and current distribution in the proton, F1/F2
: What is the internal structure of the proton?
Deep inelastic scattering
discover quarks
quark momentum and spin distributions q(x), Dq(x)
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,
charge/current distributions and quark momentum/spin
distributions fundamentally connected?

3. Beyond charge and quark distributions –
Generalized Parton Distributions (GPDs)
X. Ji, D. Mueller, A. Radyushkin ( ), …
M. Burkardt, A. Belitsky (2000) …
Infinite momentum frame
Transverse charge & current densities
Quark longitudinal
momentum & helicity
distributions
Correlated distributions in
transverse space - GPDs

4. From Holography to Tomography
An Apple
A. Belitsky, B. Mueller, NPA711 (2002) 118
mirror
mirror
detector
A Proton
mirror
mirror
By varying the energy and momentum transfer to the proton we probe its interior and generate tomographic images of the proton (“femto tomography”).

5. Deeply Virtual Exclusive Processes & GPDs
“handbag” mechanism x
Deeply Virtual Compton Scattering (DVCS)
hard vertices g
x – longitudinal quark
momentum fraction
x+x
x-x
2x – longitudinal
momentum transfer
–t – Fourier conjugate
to transverse impact
parameter t
H(x,x,t), E(x,x,t), . . xB x =
2-xB

6. [ ] ò Link to DIS and Elastic Form Factors [ ] ò ) ( ), , ~ q H - D =
Form factors (sum rules) [ ) ( , ~
) Dirac f.f. 1 t G x E dx H F1 q P A = ] ò -
) Pauli f.f. F2
DIS at x
=t=0 ) ( ), , ~ q H - D = ) , ( ~ t x E H [ ] ò - x +
- JG = = 1 ) , q( 2 E H
xdx Jq
Quark angular momentum (Ji’s sum rule)
X. Ji, Phy.Rev.Lett.78,610(1997)

7. GPDs A Unified Description of Hadron Structure Elastic form factors
Parton momentum
distributions
GPDs
Real Compton
scattering at high t
Deeply Virtual
Compton Scattering
Deeply Virtual Meson
production

8. Accessing GPDs through DVCS
dQ2dxBdtd
~ |DVCS + BH|2
BH : given by elastic form factors
DVCS: determined by GPDs
DsLU ~ BH Im(DVCS)sinf + higger twist.
~ |DVCS|2 + |BH|2 + BH*Im(DVCS)
DVCS BH
GPDs FF
ep epg
e-’ f
Qgg* p g e- g*
plane
ee’g* plane
gg*p

9. Separating GPDs through polarization
x = xB/(2-xB)
k = t/4M2
A = Ds 2s
s+ - s-
s+ + s- =
Polarized beam, unpolarized target: ~ ~
DsLU ~ sinf{F1H + x(F1+F2)H +kF2E}df
H, H, E
Kinematically suppressed
Unpolarized beam, longitudinal target: ~ ~
H, H
DsUL ~ sinf{F1H+x(F1+F2)(H + … }df
Unpolarized beam, transverse target:
H, E
DsUT ~ sinf{k(F2H – F1E) + ….. }df

10. Access GPDs through x-section & asymmetries
DIS measures at x=0
Quark distribution q(x)
-q(-x)
Accessed by cross sections
Accessed by beam/target spin asymmetry
t=0

11. First observation of DVCS/BH beam asymmetry
e+p e+gX
2001
e-p e-pX
CLAS
4.3 GeV
HERMES
27 GeV
-180
+180
f(deg)
Q2=2.5 GeV2
Q2=1.5 GeV2
A(f) = asinf + bsin2f
GPD analysis of CLAS/HERMES/HERA data in LO/ NLO shows results consistent with
handbag mechanism and lowest order pQCD
A. Freund, PRD 68, (2003), A. Belitsky, et al. (2003)
b/a << twist-3 << twist-2

12. e p epg DVCS/BH target asymmetry ~ AUL E=5.75 GeV
CLAS preliminary
e p epg
AUL
E=5.75 GeV
Longitudinally polarized
target
AUL~sinf{F1H+x(F1+F2)H...}df ~
<Q2> = 2.0GeV2
<x> = 0.2
<-t> = 0.25GeV2
Asymmetry observed at about the
expected magnitude. Much higher
statistics, and broad kinematical
coverage are needed.
HERMES data on deuterium target

13. First DVCS experiment with GPDs in mind
Twist-2 + twist-3: Kivel, Polyakov, Vanderhaeghen (2000) B
CLAS preliminary
ALU
E=5.75 GeV
<Q2> = 2.0GeV2
<x> = 0.3
<-t> = 0.3GeV2
f [rad]
Model with GPD parametrization and
quark kT corrections describes data.

14. CLAS Hall A First Dedicated DVCS Experiments at JLab
=> Full reconstruction of all final state particles e, p, g
=> High luminosity
Hall A
x, t, Q2 - dependence of Im(DVCS)
in wide kinematics. Constrain GPD
models.
PbWO4
Electromagnetic
calorimeter
s.c.
solenoid
CLAS
Currently taking data
Azimuthal and Q2 dependence
of Im(DVCS) at fixed x.
Test Bjorken scaling.
Data taking completed

15. ò DVCS/BH Beam-Charge Asymmetry HERMES ~ The e+- e- beam asymmetry
measures real part of
convolution integral for GPDs. H ( x
, t ) x- = ò q
(x, dx ~
Improved statistics and control of
systematic expected in future run
Measurements proposed for
COMPASS experiment at CERN in
m+-m-.
DsC ~ cosf{F1H + x(F1+F2) H +kF2E}df

16. GPDs – Flavor separation
DVMP
DVCS
longitudinal only
hard gluon
hard vertices
DVCS cannot separate u/d quark
contributions.
M = r/w select H, E, for u/d flavors
M = p, h, K select H, E

17. Exclusive ep epr0 production
W=5.4 GeV
HERMES (27GeV)
CLAS (4.3 GeV)
xB=0.38
Q2 (GeV2)
GPD formalism approximately
describes CLAS and HERMES
data Q2 > 2 GeV2

18. JLab Upgrade to 12 GeV Energy
A much better machine
for GPD studies ….
Add new hall
CHL-2
Enhance equipment in existing halls

19. Deeply Virtual Exclusive Processes -
Kinematics Coverage of the 12 GeV Upgrade
unique to JLab
High xB only reachable
with high luminosity
H1, ZEUS
JLab Upgrade

20. CLAS12 Luminosity > 1035cm-2s-1 EC Cerenkov Drift Chambers TOF
Torus
Central
Detector
Beamline
IEC
Luminosity > 1035cm-2s-1

21. DVCS/BH- Beam Asymmetry
Ee = 11 GeV
ALU
With large acceptance,
measure large Q2, xB, t
ranges simultaneously.
A(Q2,xB,t)
Ds(Q2,xB,t)
s (Q2,xB,t)

22. CLAS12 - DVCS/BH- Beam Asymmetry
Ee = 11 GeV
Q2=5.5GeV2
xB = 0.35
-t = 0.25 GeV2
ALU 1 -1

23. CLAS12 - DVCS/BH Beam Asymmetry
Projected data:
e p epg
E = 11 GeV
DsLU~sinfIm{F1H+..}df
Integrated
luminosity ~ 720 fb-1
L = 1x1035
T = 2000 hrs
DQ2 = 1 GeV2
Dx = 0.05

24. Exclusive r production on transverse target
A ~ 2Hu + Hd
AUT ~
Im(AB*) r0
B ~ 2Eu + Ed
AUT r0 xB
A ~ Hu - Hd
B ~ Eu - Ed r+
Asymmetry depends linearly
on the GPD E in Ji’s sum rule.
r0 and r+ measurements
allow separation of Eu, Ed
CLAS12 projected
K. Goeke, M.V. Polyakov,
M. Vanderhaeghen, 2001

25. quark flavor separation
Images of the Proton’s Quark Content
M. Burkardt (2002)
b - Impact parameter T
u(x,b ) by bx
x=0.3
x=0.5
x=0.1
transverse polarized target
uX(x,b ) T
dX(x,b ) T
d(x,b ) T
quark flavor separation Hu Eu Hd Ed
Target polarization

26. Summary The discovery of Generalized Parton Distributions
has opened up a new and exciting area of hadron
physics that needs exploration in dedicated
experiments.
Moderate to high energy, very high luminosity,
and large acceptance spectrometers are needed
to measure GPDs in deeply virtual exclusive processes.
The JLab 12 GeV Upgrade will provide the tools to
do this well and explore the nucleon at a deeper level.