1. Prospects for GPD and TMD studies at the JLab Upgrade
Volker D. Burkert
Jefferson Lab
Introduction
JLab Upgrade and CLAS12
GPDs from DVCS and DVMP
TMDs from SIDIS and SSA
Summary
SIR Workshop – Jefferson Lab, May 17-20, 2005

2. GPDs, TMDs & PDFs z z y x x x 3-D Scotty 2-D Scotty 1-D Scotty
probablity
Calcium
Water
Carbon
This Workshop – GPDs, TMDs
Deeply Inelastic Scattering,
PDFs

3. JLab Upgrade to 12 GeV Energy
Add new hall
12 GeV
CHL-2
Enhance equipment in existing halls
Beam polarization
Pe > 80%
E= 2.2, 4.4, 6.6,
8.8, 11 GeV

4. Design luminosity = 1035cm-2s-1
CLAS12
Nearly full angle coverage for
tracking and g, n detection
High luminosity, 1035 cm-2s-1
Concurrent measurement
of deeply virtual exclusive,
semi-inclusive, and inclusive
processes. EC
Cerenkov
Drift
Chambers
TOF
Cerenkov
Torus
Central
Detector
Beamline
IEC
Design luminosity = 1035cm-2s-1

5. CLAS12

6. High Q2, low t ep eK+S0(gL(pp-)) event
CLAS12 - Central Detector
High Q2, low t ep eK+S0(gL(pp-)) event
Silicon tracker, calorimetry, ToF
Solenoid magnet,
Bcenter = 5 T K+ e- g p- p g e-

7. CLAS 12 - Expected Performance
Forward Detector Central Detector
Angular coverage:
Tracks (inbending) 8o o 40o - 135o
Tracks (outbending) 5o o o - 135o
Photons 2o o 40o - 135o
Track resolution:
dp (GeV/c) p p2 dpT=0.03pT
dq (mr) < 1 (>2.5 GeV/c) 8 (1 GeV/c)
df (mr) < 3 (> 2.5 GeV/c) (1 GeV/c)
Photon detection:
Energy range > 150 MeV > 60 MeV
dE/E (EC)/0.04(IEC) (1 GeV)
dq (mr) (1 GeV) (1 GeV)
Neutron detection:
heff (EC), 0.1 (TOF) (TOF)
Particle id:
e/p >>1000 ( < 5 GeV/c)
>100 ( > 5 GeV/c)
p/K (4s) < 3 GeV/c (TOF) GeV/c
GeV/c (CC)
p/p (4s) < 5 GeV/c (TOF) 1.2 GeV/c
GeV/c (CC)
K/p(4s) < 3.5 GeV/c (TOF) 0.9 GeV/c

8. Deeply Virtual Exclusive Processes -
Kinematics Coverage of the 12 GeV Upgrade
H1, ZEUS
H1, ZEUS
11 GeV
27 GeV
200 GeV
11 GeV
JLab Upgrade
12 GeV
COMPASS
W = 2 GeV
HERMES
Study of high xB domain
requires high luminosity
0.7

9. Acceptance for DVCS, SIDIS
Q2 > 2.5 GeV2
Forward Detector
Central Detector
ep egp qg
xB = 0.35 EC
IEC Q2
ep ep+X

10. Separating GPDs through polarization
ep epg
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

11. DVCS/BH- Beam Asymmetry~ ~
DsLU ~ sinf{F1H + x(F1+F2)H +kF2E}df
Ee = 11 GeV
ALU
ALU
CLAS preliminary
E=5.75 GeV
<Q2> = 2.0GeV2
<x> = 0.3
<-t> = 0.3GeV2
f [rad] B

12. CLAS12 - DVCS/BH- Beam Asymmetry
Ee = 11 GeV
Q2=5.5GeV2
xB = 0.35
-t = 0.25 GeV2
Luminosity = 720fb-1

13. CLAS12 - DVCS/BH Beam Asymmetry
e p epg
E = 11 GeV
DsLU~sinfIm{F1H+..}df
Sensitive to GPD H
Selected
Kinematics
L = 1x1035
T = 2000 hrs
DQ2 = 1 GeV2
Dx = 0.05

14. GPDs H from expected DVCS ALU data
bval=bsea=1
MRST02 NNLO
distribution
Q2=3.5 GeV2
Other kinematics measured concurrently p

15. CLAS12 - DVCS/BH Target Asymmetry
E = 11 GeV
L = 2x1035 cm-2s-1
T = 1000 hrs
DQ2 = 1GeV2
Dx = 0.05
e p epg
Longitudinally polarized
target ~
Ds~sinfIm{F1H+x(F1+F2)H...}df
CLAS preliminary
E=5.75 GeV
AUL
<Q2> = 2.5GeV2
<x> = 0.25
<-t> = 0.25GeV2

16. CLAS12 - DVCS/BH Target Asymmetry
Q2=2.2 GeV2, xB = 0.25, -t = 0.5GeV2
E = 11 GeV
Sample kinematics
e p epg
Transverse polarized target
Ds ~ sinfIm{k1(F2H – F1E) +…}df
AUTx Target polarization in scattering plane
AUTy Target polarization perpedicular to
scattering plane
Asymmetry highly sensitive to the u-quark contributions to proton spin.

17. GPDs – Flavor separation
DVMP
DVCS
long. only
hard gluon
hard vertices
Photons cannot separate u/d quark
contributions.
M = r0/r+ select H, E, for u/d flavors
M = p, h, K select H, E

18. CLAS12 – L/T Separation ep epro (p+p-)sT
xB =
-t = GeV2
Other bins measured
concurrently
Projections for 11 GeV
(sample kinematics)
Test of Bjorken scaling
Power corrections?

19. Exclusive r0 production on transverse target
2D (Im(AB*))/p T
AUT = -
|A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2
A ~ 2Hu + Hd r0
Q2=5 GeV2
B ~ 2Eu + Ed
Eu, Ed needed for
angular momentum
sum rule. r0
K. Goeke, M.V. Polyakov,
M. Vanderhaeghen, 2001 B

20. Exclusive r+ with transverse target
Strong sensitivity
to d-quark
contributions.
A ~ Hu - Hd
B ~ Eu - Ed r+
CLAS
5.7 GeV n
AUT r+

21. [ ] ò Quark Angular Momentum Sum Rule
With GPDs Hu, Hd, Eu, Ed obtain access to total quark
contribution to proton angular momentum. Large x
contributions important. [ ] ò - x +
- J G = = 1 ) , q( 2 E H
xdx
J q
X. Ji, Phy.Rev.Lett.78,610(1997)

22. Transverse Momentum Dependent PDFs (TMDs)
Probability to find a quark u in a nucleon P with a certain polarization in a position r and momentum k
Wpu(x,k,r) “Parent” Wigner distributions
TMD PDFs: fpu(x,kT),g1,f┴1T, h┴1L
d3r
Measure momentum transfer to quark.
TMD
d2kT
(FT)
GPD
GPDs: Hpu(x,x,t), Epu(x,x,t),…
Measure momentum transfer to nucleon.

23. SIDIS at leading twist e Boer e p Mulders e p transversity Sivers
Off-diagonal PDFs vanish if quarks only in s-state! In addition T-odd PDFs require FSI (Brodsky et al., Collins, Ji et al. 2002)

24. Azimuthal Asymmetry – Sivers Effect
Originates in the quark distribution. It is measured in the azimuthal asymmetry with transverse polarized target.
sin(f-fs)
f1T D1 T
AUT ~ k
Requires: non-trivial phase from the
FSI + interference between different
helicity states (S. Brodsky)

25. SIDIS Azimuthal Asymmetry - Sivers effect
(P /M)AUT
sin(f-fs) T
Probes orbital angular momentum of quarks by measuring the
imaginary part of s-p-wave interference in the amplitude.
Extraction of Sivers function f1T from asymmetry. T

26. CLAS12 - Sivers function from AUT (p0)
Efremov et al
(large xB behavior of f1T from GPD E)
In large Nc limit:
F1T=∑qeq2f1T┴q
f1Tu = -f1Td
CLAS12
projected
CLAS12
projected xB xB

27. Azimuthal Asymmetry - Collins Effect
sUT ~ k h1H1
sin(f+fs) T
Access to transversity distribution and
fragmentation of polarized quarks.

28. Tomographic Images of the Nucleon
x=0.4
1.5
-1.5 fm
x=0.9 1 -1
X. Ji
u-quark charge density
distribution y z
dX(x,b ) T
uX(x,b ) T
CAT scan slice
of human abdomen
flavor
polarization
M. Burkardt
Ed(x,t)
Eu(x,t)

29. Double DVCS (DDVCS) e-p e-pe+e- DDVCS DVCS asymmetry Cross section
DDVC rates reduced
by more than factor 200

30. CLAS12 – Acceptance for DDVCS

31. Summary The JLab 12 GeV Upgrade is essential for the study of nucleon
structure in the valence region with high precision:
- deeply virtual exclusive processes (DVCS, DVMP)
- semi-inclusive meson production with polarized beam
and polarized targets
Provide new and deeper insight into
- quark orbital angular momentum contributions
to the nucleon spin
- 3D structure of the nucleon’s interior and correlations
- quark flavor polarization
- …..
CLAS12 will be world wide the only full acceptance, general
purpose detector for high luminosity electron scattering
experiments, and is essential for the GPD/TMD program.

32. New Collaborators are
welcome!

33. Additional Slides

34. Sivers effect in the target fragmentation
xF>0 (current fragmentation)
xF<0 (target fragmentation)
xF - momentum in the CM frame
Wide kinematic coverage of CLAS12 allows studies of hadronization in the target fragmentation region

35. Collins Effect and Kotzinian-Mulders Asymmetry
sUL ~ k h1LH1 KM T
Measures the Collins fragmentation with longitudinally polarized target. Access to the real part of s-p wave interference amplitudes.

36. Collins Effect and Kotzinian-Mulders Asymmetry
sUL ~ (1-y) h1LH1 KM T
Measures the Collins fragmentation with longitudinally polarized target. Access to the real part of s-p wave interference amplitudes.

37. CLAS12 - L(1115) Polarization`
CLAS12 - L(1115) Polarization
E = 11 GeV
ep eL(pp-)X (SIDIS) K
K*(892)

38. L polarization in the target fragmentationΛ 1 2