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

Generalized Parton Distributions
and the Structure of the Nucleon
x=0.4
1.5
x=0.9
Volker D. Burkert
Jefferson Lab
1
0
0
fm
fm
-1
-1.5
April Meeting
Fundamental questions in hadron physics?
1950-1960: 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
1960-1990: What is the internal structure of the proton?
• Deep inelastic scattering
 discover quarks
 quark momentum and spin distributions q(x), Dq(x)
Today: How are these representations of the proton,
charge/current distributions and quark momentum/spin
distributions fundamentally connected?
Beyond charge and quark distributions –
Generalized Parton Distributions (GPDs)
X. Ji, D. Mueller, A. Radyushkin (1994-1997), …
M. Burkardt, A. Belitsky (2000) …
Infinite momentum frame
Transverse charge &
current densities
Correlated distributions in
transverse space - GPDs
Quark longitudinal
momentum & helicity
distributions
From Holography to Tomography
A. Belitsky, B. Mueller, NPA711 (2002) 118
mirror
An Apple
mirror
mirror
A Proton
mirror
By varying the energy and momentum transfer to the
proton we probe its interior and generate tomographic
images of the proton (“femto tomography”).
detector
Deeply Virtual Exclusive Processes & GPDs
“handbag” mechanism
Deeply Virtual Compton Scattering (DVCS)
hard vertices
x+x
g
x – longitudinal quark
momentum fraction
x-x
2x – longitudinal
momentum transfer
x
–t – Fourier conjugate
to transverse impact
parameter
t
H(x,x,t), E(x,x,t), . .
x=
xB
2-xB
Link to DIS and Elastic Form Factors
Form factors (sum rules)
 dx [H ( x, x, t) ] = F1 ( t)
Dirac f.f.
 dx [E ( x, x, t) ] = F2 ( t )
Pauli f.f.
1
DIS at x =t=0
H ( x,0,0) = q( x), -q (-x)
~
H ( x,0,0) = Dq( x), Dq (-x)
1
1
1
~ x =
~
dx
H
(
x
,
,
t
)
G
(
t
)
,
dx
E
,
A
q

 (x, x, t) = GP,q ( t)
-1
-1
~ ~
H , E , H , E ( x,x , t )
Quark angular momentum (Ji’s sum rule)
1
1
1
Jq = - JG =  xdx Hq(x, x,0)+ Eq(x, x,0)
2
2 -1
X. Ji, Phy.Rev.Lett.78,610(1997)
[
]
A Unified Description of Hadron Structure
Elastic form factors
Parton momentum
distributions
GPDs
Deeply Virtual
Compton Scattering
Real Compton
scattering at high t
Deeply Virtual Meson
production
Accessing GPDs through DVCS
DVCS
ep
epg
BH
GPDs
gg*p plane
e-’
e-
g*
ee’g* plane
g
Qgg*
p

d4
dQ2dxBdtd
FF
~ |DVCS + BH|2
~ |DVCS|2 + |BH|2 + BH*Im(DVCS)
BH : given by elastic form factors
DVCS: determined by GPDs
DLU ~ BH Im(DVCS)sin + higger twist.
Separating GPDs through polarization
+ - D
A = + +  - =
2
x = xB/(2-xB)
k = t/4M2
Polarized beam, unpolarized target:
~
DLU ~ sin{F1H + x(F1+F2)H +kF2E}d
~
H, H, E
Kinematically suppressed
Unpolarized beam, longitudinal target:
DUL
~
~ sin{F H+x(F +F )(H + … }d
1
1
2
~
H, H
Unpolarized beam, transverse target:
DUT ~ sin{k(F2H – F1E) + ….. }d
H, E
Access GPDs through x-section & asymmetries
DIS measures at x=0
Quark distribution q(x)
Accessed by beam/target
spin asymmetry
-q(-x)
t=0
Accessed by cross sections
First observation of DVCS/BH beam asymmetry
e+gX
e+p
e-p
2001
e-pX
CLAS
4.3 GeV
HERMES
27 GeV
Q2=1.5 GeV2
Q2=2.5 GeV2
-180
0
(deg)
+180
GPD analysis of CLAS/HERMES/HERA data in
LO/ NLO shows results consistent with
handbag mechanism and lowest order pQCD
A. Freund, PRD 68,096006 (2003), A. Belitsky, et al. (2003)
A() = asin + bsin2
b/a << 1
twist-3 << twist-2
DVCS/BH target asymmetry
ep
epg
AUL
CLAS preliminary
E=5.75 GeV
Longitudinally polarized
target
~
AUL~sin{F1H+x(F1+F2)H...}d
Asymmetry observed at about the
expected magnitude. Much higher
statistics, and broad kinematical
coverage are needed.
<Q2> = 2.0GeV2
<x> = 0.2
<-t> = 0.25GeV2
HERMES data on deuterium target
First DVCS experiment with GPDs in mind
ALU
CLAS preliminary
E=5.75 GeV
<Q2> = 2.0GeV2
<x> = 0.3
<-t> = 0.3GeV2
 [rad]
B
Twist-2 + twist-3: Kivel,
Polyakov, Vanderhaeghen
(2000)
Model with GPD parametrization and
quark kT corrections describes data.
First Dedicated DVCS Experiments at JLab
Hall A
=> Full reconstruction of all final state particles e, p, g
=> High luminosity
CLAS
s.c.
solenoid
PbWO4
Electromagnetic
calorimeter
Azimuthal and Q2 dependence
of Im(DVCS) at fixed x.
Test Bjorken scaling.
Data taking completed
x, t, Q2 - dependence of Im(DVCS)
in wide kinematics. Constrain GPD
models.
Currently taking data
DVCS/BH Beam-Charge Asymmetry
HERMES
The e+- e- beam asymmetry
measures real part of
convolution integral for GPDs.
H(x, t ) =
DC

Hq(x, x, t )dx
x-x
~
~ cos{F H + x(F +F ) H +kF E}d
1
1
2
2
 Improved statistics and control of
systematic expected in future run
 Measurements proposed for
COMPASS experiment at CERN in
m+-m-.
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
Exclusive ep
eprL0 production
HERMES (27GeV)
CLAS (4.3 GeV)
W=5.4 GeV
xB=0.38
Q2 (GeV2)
GPD formalism approximately
describes CLAS and HERMES
data Q2 > 2 GeV2
JLab Upgrade to 12 GeV Energy
A much better machine
for GPD studies ….
Add new
hall
CHL-2
Enhance equipment
in existing halls
Deeply Virtual Exclusive Processes Kinematics Coverage of the 12 GeV Upgrade
unique to JLab
H1, ZEUS
High xB only reachable
with high luminosity
CLAS12
EC
Cerenkov
Drift
Chambers
TOF
Cerenkov
Torus
Central
Detector
Beamline
IEC
Luminosity > 1035cm-2s-1
DVCS/BH- Beam Asymmetry
Ee = 11 GeV
ALU
With large acceptance,
measure large Q2, xB, t
ranges simultaneously.
A(Q2,xB,t)
D(Q2,xB,t)
 (Q2,xB,t)
CLAS12 - DVCS/BH- Beam Asymmetry
Ee = 11 GeV
1
ALU
-1
Q2=5.5GeV2
xB = 0.35
-t = 0.25 GeV2
CLAS12 - DVCS/BH Beam Asymmetry
Projected data:
ep
epg
E = 11 GeV
DLU~sinIm{F1H+..}d
Integrated
luminosity ~ 720 fb-1
L = 1x1035
T = 2000 hrs
DQ2 = 1 GeV2
Dx = 0.05
Exclusive r production on transverse target
AUT ~ Im(AB*)
r0
A ~ 2Hu + Hd
B ~ 2Eu + Ed
r+
A ~ Hu - Hd
B ~ Eu - Ed
AUT
Asymmetry depends linearly
on the GPD E in Ji’s sum rule.
r0 and r+ measurements
allow separation of Eu, Ed
r0
CLAS12 projected
K. Goeke, M.V. Polyakov,
M. Vanderhaeghen, 2001
xB
Images of the Proton’s Quark Content
M. Burkardt (2002)
dX(x,b )
T
T
by
uX(x,b )
T
T
u(x,b )
transverse polarized target
d(x,b )
T
b - Impact parameter
x=0.1
bx
x=0.3
quark flavor
separation
x=0.5
Hu
Eu
Target polarization
Ed
Hd
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.