2-3D imaging of the nucleon: Generalized Parton Distributions

Franck Sabatié Nov. 25th 2008

CEA Saclay - SPhN

Why Generalized Parton Distributions ?

Properties, applications

Deeply Virtual Compton Scattering to access GPDs

Experimental history

6 GeV DVCS experiments in Halls A and B

Conclusion

Many thanks to the spokesperson of Halls A & B experiments whom I took slides from !

Non-local, Diagonal

2 )2/()2/( Fpsyyps

15 )2/()2/( gpsyyps

Deep Inelastic Scattering

Local, Off-diagonal

EM GGpssp , )0()0(''

PA GGpssp , )0()0('' 5

Elastic scattering

Hofstadter (1958)

Taylor et al. (1969)

p, s p’, s’

q

p, s

q

X

2

Im

p, s p, s

q q

Optical theoremand factorization

qp

QxB .2

2

Forward Compton

Amplitude

The electromagnetic probe for the nucleon structure

A natural extension: non-local, off-diagonal matrix elements

x + ξ

x - ξ

P - Δ/2 P + Δ/2GPD (x, ξ ,t)

The structure of the nucleon can be described by 4 Generalized Parton Distributions :

(x + ξ) and (x - ξ) : longitudinal momentum fractions of quarks

Vector : : H (x, ξ ,t)

Tensor : : E (x, ξ ,t)

Axial-Vector : : H (x, ξ ,t)

Pseudoscalar : : E (x, ξ ,t)

~~

Mueller

(1995)

*Qhard2 large t = Δ2

low –t process : -t << Qhard

2

Ji, Radyushkin

(1996)x +

ξx - ξ

P - Δ/2 P + Δ/2GPD (x, ξ ,t)

at large Q2 : QCD factorization theorem hard exclusive processes can be described by 4 Generalized Parton Distributions:

(x + ξ) and (x - ξ) : longitudinal momentum fractions of quarks

Vector : : H (x, ξ ,t)

Tensor : : E (x, ξ ,t)

Axial-Vector : : H (x, ξ ,t)

Pseudoscalar : : E (x, ξ ,t)

~~

And its golden process : Deeply Virtual Compton Scattering

Why Generalized Parton Distributions are the way to go !

Elastic Scatteringtransverse quark distribution in coordinate space

DISlongitudinal

quark distributionin momentum space

DES (GPDs)fully-correlated

quark distribution in both coordinate and

momentum space

GPDs yield 3-dim quark structure of the nucleon

Burkardt (2000, 2003)

Belitsky, Ji, Yuan (2003)

Properties, applications

first moments : nucleon electroweak form factors

ξ-independence :

Lorentz invariance

P - Δ/2 P + Δ/2

Δ

Pauli

Dirac

axial

pseudo-scalar

forward limit : ordinary parton distributions

unpolarized quark distributions

polarized quark distributions

: do NOT appear in DIS … new information

They contain what we know already through sum rules and kinematical limits: Form Factors, parton distributions

They contain what we know already through sum rules and kinematical limits: Form Factors, parton distributions

Through the space-momentum correlation, they give access to the Orbital Angular Momentum (OAM) carried by partons inside the nucleon : Finally an end to the spin crisis ?

Properties, applications

1

01

1 1lim ( , , ) ( , , )

2 2q q q q

tJ L xdx H x t E x t

Ji’s sum rule :

Related to momentum fraction carried by

quarks

Best accessible using transverse polarized target. While waiting,

neutron DVCS is sensitive to E

Moments of GPDs are calculable in Lattice QCD. Lowest moments have already been computed for valence quarks.

They contain what we know already through sum rules and kinematical limits: Form Factors, parton distributions

Through the space-momentum correlation, they give access to the Angular Orbital Momentum (AOM) carried by partons inside the nucleon : Finally an end to the spin crisis ?

Using the same correlation, nucleon tomography and even 3D-imaging can be envisioned !x

b┴ (fm)

Properties, applications

M. Burkardt, M. Diehl (2002)

sea quarks

3D-imaging (full dependence needed !)

Z

r┴

GPDs as Wigner distribution can be used to picture quarks in the proton

The associated Wigner distribution is a function of position r and Feynman momentum x: f(r,x)

One can plot the Wigner distribution as a 3D function at fixed x

A GPD model satisfying known constraint:

A. Belitsky, X. Ji, and F. Yuan (2003)

Müller, Ji, Radyushkin, …

Collins, Freund

GPDs from Theory to Experiment

Theory

x+ x-

t

GPDs

Handbag Diagram

Physical process

Experiment

Factorization theorem states:In the suitable asymptotic limit, the handbag diagram is the leading contribution to DVCS.

Q2 and largeat xB and t fixed

but it’s not so simple…

1. Needs to be checked !!!1

1

1

1

( , , ) +

( , ,

- i + ( , )

, )

DVCS

GPD x t

GPD x tT dx

x

GPD x tdx

i

P x

2. The GPDs enter the DVCS amplitude as an integral over x:- GPDs appear in the real part through a PP integral over x- GPDs appear in the imaginary part but at the line x=

Experimental observables linked to GPDs

3. Experimentally, DVCS is undistinguishable with Bethe-Heitler

However, we know FF at low t and BH is fully calculable

Using a polarized beam or a Longitudinally polarized target, one defines 2 observables :

42

2

4 4

2

2

m2 I

ReBH BH D

DVC

B

BH

C

S

V S

B

dT T

dx dQ dtd

d dT

dx dQ d

T

tdT

At JLab energies,|TDVCS|2 was expectedsmall… but…

42 2

2

4 42 2

2

2

Im2

Re DVCBH BH DVCS

B

BH DVCS DVCSDVCS

B

SdT T T

dx dQ dtd

d dT T T

dx dQ

T

tT

d d

Kroll, Guichon, Diehl, Pire, …

The cross-section difference accesses the imaginary part of DVCS and therefore GPDs at x =

1

1

1

1

( , , ) +

( , ,

- i + ( , )

, )

DVCS

GPD x t

GPD x tT dx

x

GPD x tdx

i

P x

The total cross-section accessesthe real part of DVCS and therefore an integral of GPDs over x

Observables and their relationship to GPDs

=0 limit, parton distributions

=1 limit, « distribution amplitude »

negative antiquarks

e-’

pe-*

hadronic plane

leptonic plane

42

1 0 1 22

22

4 42

2

0 1 2 3

1 2

( , , , ) cos cos 2

( , , , ) cos cos 2 cos3

( , , , ) sin sin 2

BH

I I I

BH BH

I

BB

B

BB

I I

dx Q t c c c

dx dQ dtd

x Q t

d dx Q t

dx dQ dtd

c c c c

s s

Into the harmonic structure of DVCS

|TBH|2

Interference term

Belitsky, Müller, Kirchner

GPD information lies in the s and c coefficients and can be extracted from the harmonic analysis of the DVCS cross-sections

21 1 2 2

21 1 2 2

2 22 1

sin ( ) ( / 4 )

sin ( ) ( / 4 )

cos sin( ) ( / 4 ) ( / 4 ) ...

LU

LU

SUT

F F F H t M F E d

F F F H t M F E d

t M F

H

H t M FE d

H

Exploiting the harmonic structure of DVCS with polarization

2A

Depending on the experiment, measurement of and or

The difference of cross-sections is a keyobservable to extract GPDs

With polarized beam and unpolarized target:

With unpolarized beam and Longitudinally polarized target:

With unpolarized beam and Transversely polarized target:

0

20

40

60

80

100

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007

Year

# o

f p

ap

ers

Theory GPD

Total GPD

Exp. GPD

Timeline

Invention of GPDs my Müller, who needed the theoretical object for his thesis work

Ji and Radyushkin show how the GPDs are interesting, and how to access them. Collins and Freund prove the factorization, Diehl, Pire and Gousset point out the rich harmonic structure of DVCS

First experimental paper usingH1-ZEUS non-dedicated data: Observation of DVCS at very low x

First dedicated DVCS experiment proposed and accepted by a PAC:E00-110, proton DVCS in Hall A Jefferson Lab.

HERMES and CLAS publish non-dedicated data on DVCS in the same PRL issue. They both show a large sine wave in the BSA, proving they indeed deal with the interference of DVCS and BH.

Dedicated DVCS experiment with CLAS proposed/accepted:E01-113, proton DVCS in Hall B

Intense theoretical work begings: higher twist effects, corrections, models, interpretation of various F.T., full harmonic description, …

Dedicated DVCS experiment in Hall A proposed/accepted:E03-106, neutron DVCS in Hall A

The three JLab experiments take data within 1 year (2004-2005), about 4 years after the first proposition to the JLab PAC.

Publications fromJLab experiments

What we have so far (1): Very first non-dedicated data

PRL 97, 072002 (2006)

JLab/Hall B - E1 & HERMES

JLab/Hall B - Eg1

Both results show, with a limited statistics, a sin behavior(necessary condition for handbag dominance)

ALU

AUL

CLAS: PRL 87, 182002 (2001) HERMES: PRL 87, 182001 (2001)

CLAS ALU: globally exclusive

CLAS AUL: fully exclusive

HERMES: not exclusive

What we have so far (2): Hall A DVCS dedicated run

E00-110 and E03-106Two pioneering high precision experiments (p and n)

Electromagnetic CalorimeterProton Array

HRS spectrometer in Hall A6GeV80% polarized

No Q2 dependencesincontribution→ GPD access

Scattering at thequark level !

And two important results !

Proton target:Scaling at 6 GeV

(PRL97, 262002,2006)

Neutron target:A model-dependent constraint on total

quark angular momentum

(PRL99, 242501, 2007)

What we have so far (3): Hall B DVCS dedicated run

…jusqu’à l’installationdans le Hall B.

Supraconducting solenoidInner Calorimeter

E1-DVCS:an experiment in a large kinematical domain

5.75 GeV beam85% polarizationLarge statisticsHalf taken in 2005(currently running2nd half)

Integrated over t

E1-DVCS : DVCS Asymmetry as a function of xB and Q2

<-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2

-The largest data sample to date !-More data coming-Cross-section analysis ongoing

The amplitude of the sincan beexpressed in termsof GPDs

PRL100, 162002 (2008)

Where we stand now and …

Findings from past experiments:

-The feasibility of exclusive experiments both in Halls A (small acceptance, large luminosity) and B (large acceptance, small luminosity) was demonstrated.

-DVCS seems to scale early, at least in its polarization observable, unlike meson electroproduction.

-The measurement of cross sections in addition to asymmetries is particularily important since the total cross section is only partly known. However, even the total cross section cannot be fully deconvoluted at fixed beam energy.

-The accurate measurement of GPD-related observables (with polarized beam and L/T targets) over a wide kinematical range in xB, Q2 and t will be necessary to extract OAM information and perform nucleon tomography !

-Meson electroproduction and the use of various targets will be necessary for GPD and quark flavour decomposition.

What comes next

More statistics

More polarization observables

Full cross section separation

2nd half of unpolarizedtarget E1-DVCS run in Hall B

(ongoing)

Full separation of the DVCStotal cross section in Hall A

for proton and « neutron » targets(2010)

EG1-DVCS experiment withLong. polarized target

(2009)+

Transverse target DVCS inHall B(2011)

2nd Half of E1-DVCS runs with improvements

…jusqu’à l’installationdans le Hall B.

Supraconducting solenoidInner Calorimeter

New trigger system for inner calorimeterNew shielding (higher luminosity)

5.9 GeV beam85% polarizationDouble statistics>>Run until Jan.’08

CLAS Detector High acceptance Large kinematical coverage Detection of charged and neutral particles

Electron Beam Energy 6 GeV Polarization ~ 75%

Solid Target Longitudinally polarized NH3 target Polarization ~ 75% 12C & 15N target

Inner Calorimeter (IC)High resolution calorimeter to detect photons at small angles (4o to 15o)

EG1-DVCS : starting in Feb. 2009

DVCS with longitudinally polarized target

Region 1 DC

Typical ep event

Dynamically polarized NH3

5 Tesla magnetic field

B/B ≈ 10-4

1K LHe cooling bath

NH3 polarization:75%

12C, 15N, and 4He targets to measure the dilution factor

Magnet provides natural Moller shielding but blocks high angle particles (esp. protons)

Hall B longitudinally polarized target

Inner calorimeter (PbWO4)

424 crystals, 16 mm long, pointing geometry, ~ 1.2 degree/crystal,

APD readout

Calibration via π0→γγ

σ = 7.5 MeV

Mγγ (GeV)

η

SC Helmholtz magnet

EG1-DVCS setup

Photon detection in IC and EC (view from target)

A dedicated CLAS experiment with longitudinally polarized target will provide a statistically significant measurement of the kinematical dependences of the DVCS target SSA

6 GeV run with NH3 longitudinally polarized target (CLAS + IC) 60 days of beam time, luminosity 15 x 1033/cm²/s

Target Spin Asymmetry, most sensitive to GPD H~

CLAS eg1

• CLAS (eg1+IC) projected

>Detection of the ep final state

>Background from unpolarized

nucleons highly suppressed by

geometry cuts

AUL as a function of xB, Q2 and t

25 days of HD (+5 days of H, D, empty target) 4cm HD, 2 nA beam polarization 80% HD-Ice target polarization (H-75%,D-25%)

• Target upstream to increase acceptance for ’s and 0, no IC• Beam on target at ~0.2o, at target center it will be parallel (use small steering magnets)• Use additional (existing) magnet to correct electron beam deflection.•Use Mini-torus for Moller electron shielding.

Run conditions

Transverse target DVCS with CLAS and HD-ice

Heat extraction through thin aluminum wires

>Can operate at T~500-750mK withlong spin relaxation times (months)>Low dilution, small holding field>HD lab under dev., in-beam cryostat design

HD ice target

Successfully used at BNL in LEGSUpcoming photon run E06-101

+ tests with electron beam in 2010

CLAS configuration

proton

Transverse asymmetry is large and has strong sensitivity to GPD E and the quark angular momentum contributions.

E=0

A significant portion of events (~20%) all final state particles are detected in CLAS. This allows cross checks.

Error barswith epX

AUT sensitivity to GPD E

Double spin asymmetry with transverse target is also sensitive to GPD E, and probes different parts of the (x,) space.

proton

E=0

E=0

ALT sensitivity to an integral over the GPD E

1

1

( , ,..

).LT P dx

xE x t

The next generation Hall A experiments

Two new high precision experiments (p and n) for a full cross section separation

ExpandedElectromagnetic Calorimeter

(132 blocks > 208 blocks)No moreProton Array

(less dead timeand not needed)

HRS spectrometer in Hall A6GeV80% polarized

New trigger logic (higher threshold + π0 trigger)

>Detection of enough π0 to subtract correctly the contamination

and determine the π0 electro-production polarized cross sections.

>Remove the systematic error due to the uncertainty on the

contamination of DVCS-like π0 channel.

UV curing systemfor high luminosity

running

Electromagnetic Calorimeter (upgraded)

Full separation of the electroproduction cross section

2

1 23

4 4

1 2 1

)cos

(

DVCS

I

BHDVCS

II I I

d C

Cf

d

C

The are fully calculable AND depend on the beam energy.

The C are different combinations of GPDs.

With two beam energies, one can fully separate all component of the twist-2 cross-section.

Note: most of the twist-3 contribution does not mix with twist-2.

At twist-2:4 DVCSd

4 Id

DVCS² contribution is predicted large

2

1 23

4 4

1 2 1

)cos

(

DVCS

I

BHDVCS

II I I

d C

Cf

d

C

2

11 DVCDVCS IS IC Cand are predicted to be the same size !

VGG model

Separation at two different Q²

Twist-3

2DVCSC

I1C

Twist-3

2DVCSC

I1C 2

IC

2IC

2 21.9 GeVQ

2 22.3 GeVQ

Separation for the neutron

previous systematics

new systematics

Ine C I I

n ne C C DVCSnC 2DVCSC

I1C 2

IC2 22.3 GeVQ

Conclusion

Soon, there will be a wealth of new data from all possible configurations in DVCS :

Polarized beam, Longitudinally and Transversely polarized target

In addition, a full separation of the DVCS cross section for proton and neutron will allow for a careful study of the relative sizes of the interference and DVCS².

A real phenomenology work has just started, trying to relate DVCS observables to GPDs (via Compton Form Factors) in an model-independent fashion. This work will soon be in full speed and will allow to reach our goals, i.e. to fully understand the 3D quark structure of the nucleon.

All this work will be extended to 11 GeV. DVCS will then be complemented by meson electroproduction for flavor and GPD separation.