Transcript 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.

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
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
1960-1990: What is the internal structure of the proton?
• Deeply inelastic scattering
 discover quarks in ‘scaling’ of structure functions
 quark longitudinal momentum distribution
 quark helicity distribution
Nobel prize 1990 - J. Friedman, H. Kendall, R. Taylor
Today: How are these representations of the proton,
form factors and quark distributions, connected?
Form factors, parton
distributions,
and
GPDs
..
X. Ji, D. Muller, A. Radyushkin
..
A. Belitsky and D. Muller, Nucl.Phys.A711(2002)118
(Infinite momentum frame)
GPDs connect form factors
and parton distribution
Proton form factors,
transverse charge &
current distributions
Quark longitudinal
momentum & helicity
distributions
GPDs & Deeply Virtual Exclusive Processes
Deeply Virtual Compton Scattering (DVCS)
g
x+x
hard processes
x-x
xB
x=
2 - xB
t
(in the Bjorken regime)
H(x,x,t), E(x,x,t),..
GPDs are Q2 independent (only QCD evolution)
x + x, x-x = longitudinal momentum fraction
-t = Fourier conjugate to transverse impact parameter
Link to DIS and Elastic Form Factors
Link to DIS at x =t=0
H q ( x,0,0) = q( x), -q (-x)
~q
H ( x,0,0) = Dq( x), Dq (-x)
Link to form factors (sum rules)
~ ~
H , E , H q , E q ( x,x , t )
q
q
( x, x, t)
]
= F1 ( t ) Dirac FF
( x, x, t)
]
= F2 ( t) Pauli FF
 dx[H
q
 dx[E
q
1
q
1
q
1
1
~q x =
~q x =
dx
H
(
x
,
,
t
)
G
(
t
)
,
dx
E
,
A
q

 (x, , t) GP,q ( t)
-1
-1
Access to quark angular momentum (Ji’s sum rule)
1
1
1
J q = - JG =  xdx H q ( x, x,0) + Eq ( x, x,0)
2
2 -1
X. Ji, Phy.Rev.Lett.78,610(1997)
[
]
Modeling Generalized Parton Distributions
DIS only measures at x=0
Quark distribution q(x)
Accessed by beam/target
spin asymmetry
-q(-x)
t=0
Accessed by cross sections
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 scaling cross section for photons dominates at
high Q2 over meson production.
Access GPDs through DVCS - BH interference
d4
dQ2dxBdtd
~ |TDVCS + TBH|2
Eo = 11 GeV
Eo = 6 GeV
Eo = 4 GeV
BH
DVCS
BH
TBH : determined by Dirac & Pauli
form factors
TDVCS: determined by GPDs
Helicity difference:
Twist-2:
DVCS
DVCS/BH comparable,
allows asymmetry, cross
section measurements
(M. Vanderhaeghen, private communication)
~
D ~ sinIm{(F1H(x,x,t)+ k1(F1+F2)H(x,x,t)+k2F2E(x,x,t)}d
Measurement of exclusive DVCS with CLAS
Beam spin asymmetry
1999 data, E=4.2GeV
2001/2002 data E=5.75GeV,
very preliminary (15% sample)
Beam Spin Asymmetry
Phys. Rev. Lett. 87 (2001)
<-t> = 0.19GeV2
<xB>= 0.19
sin
xB = 0.2-0.4
- t = 0.2-0.5 GeV2
A. Belitsky et al.
A = asin + bsin2


<Q2>= 2.2GeV2
<xB> = 0.35
sin
a = 0.202 ± 0.028stat ± 0.013sys (twist-2)
b = -0.024 ± 0.021stat ± 0.009sys (twist-3)
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/0208160
A t
(1+t/0.71)2
Measurement of exclusive DVCS with CLAS
Longitudinal target spin
asymmetry
2000 data, E=5.65GeV, 10% sample
very preliminary
0.3
Target single spin asymmetry:
ep
AUL =
epg
AUL
asin + bsin2
<xB> = 0.25
<Q2> = 1.6 GeV2
<-t> = 0.25 GeV2
0.2
0.1
+ -UL
UL
+ +UL
UL
0.
~ + ..
DUL ~ KImF1H
-0.1
-0.2
Direct access to
a - twist-2
b - higher twist
~
H(x,x,t)
g*g(o)
Exclusive ep
epr0 production
Compare with GPD formalism and models
HERMES (27GeV)
CLAS (4.3 GeV)
xB=0.31
W=5.4 GeV
Q2 (GeV2)
xB=0.38
Q2 (GeV2)
GPD formalism approximately describes data at xB<0.35, Q2 >1.5 GeV2
The JLab Program @ 6 GeV
New equipment, full reconstruction of final state
• DVCS
CLAS and Hall A
Full reconstruction of final state ep
epg
ALU, D 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
• DVMP
CLAS
 ro, w production at W > 2 GeV, Q2 = 1.0 - 4.5 GeV2
 p0/h, p+ production
Kinematics coverage for deeply exclusive experiments
compete with other
experiments
no overlap with other
existing experiments
Upgraded CEBAF
complementary
& unique
The JLab GPD Program @ 12 GeV
DVCS:

DVCS/BH interference with polarized beam



Differential cross section


twist-2/3, Q2 evolution
linear combination of GPDs
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
DDVCS: Hard baryon spectroscopy ep
epg*
egD, (egN*)
e+e-
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)
D (Q2,xB,t)
 (Q2,xB,t)
DVCS with CLAS++ at 11 GeV
2% of all data points that are measured simultaneously.
Q2=2.75GeV2
xB = 0.35
-t = 0.25 GeV2
Q2=5.5GeV2
xB = 0.35
-t = 0.25 GeV2
DVCS/BH twist-2 with CLAS++ at 11 GeV
Sensitivity to models of GPDs
Q2, xB, t ranges
measured
simultaneously.
Measure ALU,
D and (DVCS)
simultaneously
DVCS/BH D interference projected for Hall A
E = 11 GeV
Q2 = 6 GeV2
xB = 0.37
L=1037cm-2s-1
400 hours
MAD spectrometer
ECAL @ -12.5o,
300 cm distance
SC array @ -7o
DVCS/BH D interference projected for Hall A
E = 11 GeV
Q2 = 7 GeV2
xB = 0.50
L=1037cm-2s-1
400 hours
MAD spectrometer
ECAL @ -12.5o,
300 cm distance
SC array @ -10.5o
Beam spin asymmetry projected data for Hall A
Separation of twist-2/twist-3
D ~ Asin + Bsin2
A: twist-2
B: twist-3
Deeply Virtual r0 Production at 11 GeV
CLAS++
 L/T Separation via
<xB> = 0.35
<-t> = 0.30
L
ro
p+p- decay
distribution and SCHC
• Test the Q
tot
2
evolution of
L , T => factorization
T
• Rosenbluth separation
=> test SCHC assumption
other kinematics measured simultaneously
CLAS++ - r0/w production with transverse target
AUT = -
2 D (Im(AB*))/p
|A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2
A ~ (euHu - edHd)
Asymmetry depends linearly
on the GPD E, which enters
Ji’s sum rule. At high xB strong
sensitivity to u-quark contributions.
B ~ (euEu - edEd)
L=1035cm-2s-1
2000hrs
L dominance
Q2= 5GeV2, DQ2=1
-t = 0.5GeV2 Dt = 0.2
K. Goeke, M.V. Polyakov, M. Vanderhaeghen
w has similar sensitivity to proton quark spin
HallC - SHMS & HMS - ep
ep+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.
 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 tchannel exchanges
• make connection to total quark spin by analysing S- and
D-wave exchanges
“Tomographic” Images of the Proton’s Quark Content
(Transverse space and IMF)
b = 1
-t
T
Impact parameter:
M. Burkardt NPA711 (2002)127
transversely polarized target
x
0
Extension to x > 0 , M. Diehl, Eur. Phys. J.C25 (2002)223
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.
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
Beam/target spin asymmetry
2000 data, E=5.65GeV, 10% sample
Beam-target double spin
asymmetry:
ep
epg
N++-N-+-(N+--N--)
ALL =
N+++N-+ +N+--N-Asymmetry dominated by
Bethe-Heitler, modulated by
DVCS (GPD) (~15%)
A. Belitsky et al., hep-ph/0112108
xB=0.25, Q2=2GeV2,-t=0.25GeV2
0.9
ALL
<xB> = 0.25
<Q2> = 1.6 GeV2
<-t> = 0.25 GeV2
0.6
0.3
g*g(o)
e p+n
Separated Cross section for ep
Rosenbluth separation for L/T
xB = 0.4-0.5
-t = 0.2-0.4GeV2
+ many other bins at
the same time
Measure
pp0, ph, KL,..
simultaneously
L
TOT
T
Extraction of GPD Hq(x,x,t) @ small t, xB
Asin
LU =
N
D
N = F1 H +
•
xB
(2-xB)
~
(F1+F2) H -
t
FE
4M2 2
Dominant contribution to H is Im(H)
1 [4(1-x )(HH* ~ ~
+ HH*) - xB2(HE* + EH* + .. )
B
(2-xB)2
~~
- (xB2 +(2-xB)2 t 2 )EE* B- x2 t 2 E E*]
4M
4M
1 - xB
= 4
( ImH )2 + ….
2
( 2 - xB )
D =
At small xB, t, ALU and N measure Im(H(x,x,t))
from which
extracted
Seq2(Hq(x,x,t)-Hq(-x,x,t))
may be
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 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 tchannel exchanges
H(x,x,t) = (1-x2)S An(x,t)Cn3/2 (x)
n=1
First moment:
dxxH (x,x,t) =
From Ji’s sum rule: JQ =
6
5
6
5
[B12(t)-
1
3
(B12(t) -2B10(t))x2]
(B10(0) + C10(0))
JQ can be extracted from S-wave exchange in t-channel!
Holographic Images of Objects
A. Belitsky, B. Mueller, NPA711 (2002) 118
An Apple
The Proton
detector
By measuring the t- dependence we may generate a
tomographic image of the proton
Deeply Virtual Exclusive Processes
Inclusive Scattering
q,Dq
Forward Compton Scattering
q,Dq
q =0
g*
g
Deeply Virtual Compton Scattering (DVCS)
g
x=
xB
2 - xB
(in the Bjorken regime)
t
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)
DVCS and GPDs
~ ~
GPDs: H, E unpolarized, H, E polarized
e.g. H(x, t, Q2) =

=

g*
g
P( x + x )
P( x - x )
GPD’s
Hq(x, x, t, Q2)dx
x-x + ie
Hq(x, x, t, Q2)dx
+ ipHq(x, x, t, Q2)
x-x
real part
d3
dQ2dxBdt
imaginary part
cross section
difference
~ ~
= f (H, E, H, E)
Hq: Probability amplitude for N to emit a parton q with x+x and N’ to
absorb it with x- x.
Access GDPs in Deeply Virtual Exclusive Processes
DVMP
DVCS
hard gluon
Scaling cross sections for photon and
meson production
M. Vanderhaeghen, P.A.M. Guichon, M. Guidal,
PRD60, (1999), 94017
hard vertices
1/Q6
1/Q6
N*,D
DVCS depends
on all 4 GPDs and
u, d quarks
1/Q4
DVMP allows separation of
un(polarized) H, E (H, E)
GPDs, and contributions
of u, d quarks
M = r, w
H, E
M = p, h, K
H, E
Need to isolate g*L
g
• In hard scattering, photons
dominate at high Q2
2001/2002 data E=5.75GeV
2001/2002 data E=5.75GeV
sin
g,p0
sin
sin
xB
(25% data sample)
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
Snapshot of a Nucleon eliminate ?
(taken through a low resolution microscope)
valence quarks
How do we obtain modelindependent information?
quark spin
meson cloud
quark longitudinal/
transverse momentum
correlations
sea quarks
In DIS experiments we
probe one-dimensional
projections of the nucleon
orbital angular momentum
Longitudinal quark
momentum and helicity
distribution
We need to map out the
full nucleon wave function
to understand the internal
dynamics
q +q
q -q
0
0.5
x
1
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.