XVIII th International Symposium on Spin Physics

XVIIIth International Symposium on Spin Physics Charlottesville, October 6-11, 2008

GPDGPDs,s,

The Hunt for The Hunt for QQuark uark OOrbital rbital MMomentumomentum

(i) The nucleon spin puzzle(ii) Generalized parton distributions(iii) Deeply virtual Compton scattering(iv) Experimental access to E(Q2,x,,t)(v) Perspectives(vi) Experimental strategy(vii) Conclusions

Laboratoire de Physique Subatomique et de CosmologieGrenoble, France

Eric Voutier

?

zg

q

zq LGL 2

1

2

1

Orbital Momentum

of gluons(unknown)

Orbital Momentum of quarks and

antiquarks(first glimpse)

Helicity distributionsdescribing the longitudinal

polarization of quarks and antiquarks(known)

Gluon polarization(first data)

Eric VoutierThe nucleon spin puzzle

1/1SPIN2008, Charlottesville, October 6-11, 2008

Transversity distributions describing the transverse

polarization of quarks and antiquarks

(first experimental attempts)

B.L. Bakker, E. Leader, T.L. Trueman, PRD 70 (2004) 114001

gqq

sq

qq

TLxqdx,,,

)(2

1

2

1

Terra Incognita

Longitudinal spin sum rule

Generalized parton distributions (GPDs) procure the cement of the

nucleon spin puzzle, and more generally of the hadron structure.

Generalized parton distributions

1/6

Eric Voutier

SPIN2008, Charlottesville, October 6-11, 2008

GPDs are the appropriate framework to deal with the partonic structure of hadrons and offer the unprecedented possibility to access the spatial distribution

of partons.

Parton Imaging

M. Burkardt, PRD 62 (2000) 071503 M.Diehl, EPJC 25 (2002) 223

GPDs can be interpreted as a 1/Q resolution distribution in the

transverse plane of partons with longitudinal momentum x.

GPDs = GPDs(Q2,x,,t) whose perpendicular component of the momentum transfer to the nucleon is Fourier conjugate to the transverse position of partons.

GPDs encode the correlations between partons and contain information about the dynamics of the system like the angular momentum or the distribution of the strong forces experienced by quarks and gluons inside hadrons.

X. Ji, PRL 78 (1997) 610 M. Polyakov, PL B555 (2003) 57

A new light on hadron structure

The GPDs Framework


2/6

Eric Voutier


GPDs

x x

t

Coherence between quantum states of different helicity, longitudinal momentum and transverse position.

At leading twist, the partonic structure of the nucleon is described by 4 quark helicity conserving and chiral even GPDs and 4 quark helicity flipping and chiral odd GPDs (+8 gluon GPDs).

qqqq EHEH~

,~

,, qT

qT

qT

qT EHEH

~,

~,,

D. Müller et al., FP 42 (1994) 101 A.V. Radyushkin, PRD 56 (1997) 5524 X. Ji, PRL 78 (1997) 610

P. Hoodbhoy, X. Ji, PRD 58 (1998) 054006 M. Diehl, EPJC 19 (2001) 485

E’s arenew and unknown

distributions

)()0,0,( xqxH q )()0,0,(~

xqxH q )()0,0,( xqxH qT

)()0,0,( xgxxH g )()0,0,(~

xgxxH g 0)0,0,(~

,~

,, xEHEHgT

In the forward limit (t 0, 0), H’s reduce to the forward parton distributions (density, helicity, transversity).

E’s, which involve nucleon helicity flip, do not have a DIS equivalent.

x Initial longitudinal momentum fraction -2 Transferred longitudinal momentum fraction (skewness)

(-t)1/2 Momentum transfer to the nucleon


3/6

Eric Voutier


Form Factors

GPDs unify in the same universal framework parton distributions, form factors, and the spin of the nucleon.

t

GPDs

The first Mellin moments relate GPDs to Dirac (Hq), Pauli (Eq), axial ( ), and pseudo-scalar ( ) nucleon form factors.

Similar relations relate chiral odd GPDs to tensor form factors.

tFtxEdx qq2

1

1,,

tGtxEdx q

Pq

,,

~1

1

qH~ qE

~

qT

qT

qT xExHdx

1

10,0,0,0,

~2

independence from Lorentz invariance

Transverse spin-flavor dipole moment in an unpolarized nucleon

Energy Momentum Tensor

1

10,,0,,

2

1

2

1 xExHxdxLJ qqqqq

X. Ji, PRL 78 (1997) 610 M. Polyakov, PLB 555 (2003) 57 M. Burkardt, PRD 72 (2005) 094020

The second Mellin moments relate GPDs to the nucleon dynamics, i.e. parton angular momentum and strong forces distributions.

1

10,0,0,0,

~20,0,

4

1xExHxHxdxJ q

TqT

qT

q

Correlation between quark spin and angular momentum in an unpolarized

nucleon


4/6

Eric Voutier


GPDs

x x

k

k

'kkq

?

p

J.C. Collins, L. Frankfurt, M. Strikman, PRD56 (1997) 2982 X. Ji, J. Osborne, PRD 58 (1998) 094018 J.C. Collins, A. Freund, PRD 59 (1999) 074009

The key requirements for the experimental study of GPDs are luminosity and resolution.

GPD(Q2,x,,t)Probe tagging ()

Production of one additional particle ()

Final state identification

Exclusivity

p

t

22 'kkQ 22' pptqp

QxB

2

2

FactorizationInteraction with elementary partons (Q2>>M2)

Separation of perturbative and non-perturbative scales (-t<<Q2)

Hardness

Deep Exclusive Scattering

The factorization theorem allows to express the cross section for deep exclusive processes as a convolution of a known hard scattering kernel with an unkown soft matrix element related to the nucleon structure (GPDs).


5/6

Eric Voutier


GPDs

x x

t

DVCSDeeply Virtual

Compton Scattering

Longitudinal response only

GPDs

xx

DA

L

DVMPDeeply Virtual

Meson Production),(

),(

t

Hard gluon

GPDs can be accessed via exclusive reactions in the Bjorken kinematic regime.

The DVCS process is identified via double (e) or triple (eN) coincidences, allowing for small scale detectors and large luminosities.

Additional amplitudes contribute to the reaction process and interfere with the DVCS amplitude.

The identification of the DVMP process requires the detection of the meson disintegration products in large acceptance detectors.

Factorisation applies only to longitudinally polarized virtual photons whose contribution to the electroproduction cross section must be isolated.

Meson production acts as a GPD and a flavor filter.

x

)0,,( xH

GPDs enter the cross section of hard scattering processes via Compton form factors, that are integrals over the intermediate parton longitudinal momenta.

t

GPDs

x x

Q2 >> M2 -t << Q2

6/6

Generalized parton distributions Eric Voutier


),,(),,(),,( 1

1

1

1txi

x

txdx

ix

txdx

GPD

GPDGPDP

B

B

x

x

2

Photon Electroproduction

Eric Voutier

The Bethe-Heitler (BH) process where the real photon is emitted either by the incoming or outgoing electron interferes with DVCS.

DVCS & BH are indistinguishable but the BH amplitude is exactly calculable and known at low t.

The relative importance of each process is beam energy and kinematics dependent.

Deeply virtual Compton scattering

SPIN2008, Charlottesville, October 6-11, 2008 1/5

leptonic plane

e-’

p

e- *

hadronic plane

Out-of-plane angle entering the harmonic development of the reaction amplitudeA.V. Belitsky, D. Müller, A. Kirchner, NPB 629 (2002) 323

Polarization observables help to single-out the DVCS amplitude.

P0 = 6 GeV/c

γpepe

EHHF )(4

~)()()()( 22211 tF

M

ttFtFtFC I

Polarized Beam Cross Section Difference

Eric VoutierDeeply virtual Compton scattering


DVCSDVCSDVCSBHeBeB dddtdxdQ

d

dddtdxdQ

dTTTT mem

2

5

2

5

2

1J

The sDVCS,I are bilinear and linear combinations of GPDs at ±

C. Muñoz-Camacho et al., PRL 97 (2006) 262002

Twist-2

Twist-3

)2sin()sin()()(

),,()sin(),,(

2

1

2121

23

12

2

2

5

2

5

IIBDVCSB

eBeB

ssPP

tQxstQx

dddtdxdQ

d

dddtdxdQ

d

J

γpepe

Q2 = 2.3 GeV2

xB = 0.36Q2 = 2.3 GeV2

xB = 0.36

DVCS / Bethe-Heitler interference amplitudeDVCS amplitude

Imaginary part The DVCS process is associated with a non-zero polarized beam

signal.

Gluons

Twist-2

Twist-3

DVCSBHDVCSBHeB dddtdxdQ

dTTTT e 2

222

5

The cDVCS,I are bilinear and linear combinations of Compton form factors.

Unpolarized Cross Section

Eric VoutierDeeply virtual Compton scattering



EEHHFF )(4

)()()()()( 22212

1 tFM

ttFtFtFCC II

Q2 = 2.3 GeV2

xB = 0.36Q2 = 2.3 GeV2

xB = 0.36

γpepe

The magnitude of the DVCS process is seen as a deviation from the pure BH cross section.

Bethe-Heitler amplitude

DVCS amplitude DVCS / Bethe-Heitler interference amplitude

)3cos()2cos()cos(

)()(

),,(

)2cos()cos(),,(

)2cos()cos()()(

),,(

321021

23

2102

2

21021

21

2

5

IIIIB

DVCSDVCSDVCSB

BHBHBHB

eB

ccccPP

tQx

ccctQx

cccPP

tQx

ddφdtdxdQ

σd

Real part

E00-110 p-DVCSP.Y. Bertin, C.E. Hyde, R. Ransome, F. Sabatié et al.

Twist-two contributions dominate the DVCS cross section and are Q2 independent in the measured kinematics range. Twist-three contributions to the cross section are small and are Q2 independent within error bars.


Deeply virtual Compton scattering Eric Voutier


Experimental results support the dominance of the handbag diagram at Q2 as low as 2

GeV2.

Beam Spin Asymmetry

Deeply virtual Compton scattering Eric Voutier


F.-X. Girod et al., PRL 100 (2008) 162002

2coscos1

sin)(

)(55

55

tdtc

tadd

ddA

JJ

@ CLAS (5.77 GeV)γ pepe

GPDs Twist-2

JML / Regge

GPDs Twist-3

Calculations based on hadronic degrees of freedom, within a Regge approach, are in fair agreement with data up to 2.3 GeV2.

GPD based calculations reproduce reasonably well the main features of the data.

The angular dependence of the asymmetries is compatible with expectations from leading-twist

dominance.

F.-X. Girod talk in GPD parallel session

F. Ellinghaus,W.-D. Nowak, A.V. Vinnikov, Z. Ye EPJ C46 (2006) 729

Z. Ye, Doctorat Thesis, Universität Hamburg (2006)

)~

,,(~

4

4)(

2212

122

HEHE

EHF

OFFM

t

FFM

tC ITP

)

~,

~,,(

~

4

~~

4)(

22212

122

EHEHEE

EHF

OFFFM

t

FFM

tC ITP

DVCS Transverse Target Asymmetry

Experimental access to E(Q2,x,,t) Eric Voutier


Twist-2

A.V. Belitsky, D. Müller, A. Kirchner, NPB 629 (2002) 323 M. Diehl, S. Sapeta, EPJC 41 (2005) 515

B. Zihlmann talk in GPD parallel session

)sin()cos()()cos()sin()(

),,(,,

,,, 2

455

55

SITPS

ITP

BSS

SSSUT

CC

tQxdd

ddA

FF

2/6

Eric Voutier


Experimental access to E(Q2,x,,t)

DVMP Transverse Target Asymmetry

pρpγ LL

Tra

nsv

ers

e T

arg

et

Asy

mm

etr

y

xB

2Ju+Jd

pωpγ LL

Tra

nsv

ers

e T

arg

et

Asy

mm

etr

y

xB

2Ju-Jd

The s-channel helicity conservation (SCHC) allows to extract the longitudinal/transverse ratio from the angular distribution of the decay products of the vector mesons, avoiding a Rosenbluth separation.

The longitudinal polarization of the vector meson is obtained from the angular distribution of the decay products.

Transversally polarized proton targets are of primary importance for the determination of E(Q2,x,,t).

K. Goeke, M. Polyakov, M. Vanderhaeghen, PPNP 47 (2001) 401 S.V. Goloskokov, P. Kroll, arXiv/hep-ph:0809.4126

3/6SPIN2008, Charlottesville, October 6-11, 2008

Eric VoutierExperimental access to E(Q2,x,,t)

DVMP Longitudinal Cross Section

S.A. Morrow et al., arXiv/hep-ex:0807.3834

pρpγ LL @ CLAS (5.74 GeV)

Standard GPD calculations fail to reproduce data in the valence region, while successfull at large W.

Data can be interpreted in terms of hadronic degrees of freedom, following a Regge approach.

Data can be interpreted in terms of partonic degrees of freedom via strongly modified GPDs, via a D-term like adjusted component.

2222 MQWQxB

VGG / GPDs

GK / GPDsJML / Regge

VGG++ / GPDs

The question is asked whether current GPD parametrizations must be revisited or DVMP cannot be interpreted GPD wise in the valence

region ?

Neutron Target

EHHF )(4

~)()()( 22211 tF

M

ttFtFtFC I

n

Suppressed because F1(t) is small

Suppressed because of cancellation between u and d quarks

From polarized beam cross section difference

Neutron targets allow to access the least known and constrained GPD

that appears in the nucleon spin sum rule.

Neutron targets provide new linear combinations of GPDs

tEtEe qq

qq ,,,,2 Em

Neutron and proton targets are sensitive to the u quark flavor and, following isospin symmetry, appear then complementary.

Eric VoutierExperimental access to E(Q2,x,,t)


E03-106 n-DVCSP.Y. Bertin, C.E. Hyde, F. Sabatié, E. Voutier et al.

deedneenpeepXeeD ),(),(),(),(

S. Ahmad et al., PR D75 (2007) 094003

M. Vanderhaeghen et al., PR D60 (1999) 094017

M. Mazouz et al., PRL 99 (2007) 242501

The twist-2 effective harmonic coefficients of the neutron are small, compatible with zero.

The measured t-dependence can be used to constrain the parametrization of the GPD E, within a particular model.

Impulse approximation

Q2 = 1.9 GeV2 xB = 0.36

M. Mazouz et al., PRL 99 (2007) 242501

Experimental access to E(Q2,x,,t) Eric Voutier


)sin()()(

),,()sin(

)()(

),,(

2

11

21

23

121

23

2HD

5

2HD

52222

Id

dd

BdIn

nn

Bn

eBeB

sPP

tQxs

PP

tQx

dddtdxdQ

d

dddtdxdQ

d

J

Twist-2

γ nene

6/6

Eric Voutier


u

M. Mazouz et al., PRL 99 (2007) 242501

Measurements off neutron are sensitive to

Jd

(u quark in the neutron)

Measurements off proton are sensitive to

Ju

(u quark in the proton)

1

)()(),( 2

min2exp2exp

2,exp

22min

i isystistat

iJJ

VGGIni

In

dutt

tCtCJJ

duFF mm

A. Airapetian et al., arXiv/hep-ex:0802.2499

Model Dependent Quark Angular Momenta

d

A.W. Thomas, arXiv/hep-ph:0803.2775

Neutrons are a mandatory step in the hunt for the quark orbital momentum.

Experimental access to E(Q2,x,,t)

E08-021 -DVCSH. Avakian, V. Burkert, M. Guidal, R. Kaiser, F. Sabatié et al.

Perspectives

1/6

Eric Voutier


p

G. Thorn talk in Polarized Sources & Targets parallel session

Advantages

The HDice frozen spin target figures a large spin relaxation time (~1 year) at operational temperature (0.5 K) and field (0.9 T).

High T -> high cooling power compensates beam heatingLow B -> ideal for transverse polarization @ CLAS

Pure target -> small physics background & faster data taking

Low Z -> small bremsstrahlung background (e-)

Drawbacks

The many delicate processes between production and operation make the complete system quite complex. Operation with an electron beam is promising but has not yet been established.

The technical feasability of electron experiments with the

HDice target has to be demonstrated.

HD is condensed into the target cell with ~2000 50 µm Al wires soldered to a copper cooling ring

HD (77%) Al(16%) C2ClF3 (7%)HDice Lab @ JLab

A. Sandorfi et al., Proc. of the Workshop on Exclusive Reactions, Edts. P. Stoler and A. Radyushkin, World Scientific (2008) 425.

Eric Voutier

E07-007 & E08-025 p-DVCS & n-DVCSP.Y. Bertin, C.E. Hyde, C. Muñoz Camacho, J. Roche et al.

A. Camsonne, C.E. Hyde, M. Mazouz et al.

)cos()()(

),,(),,( 10

21

232

22

2

5

In

In

nn

BnDVCSnBnn

eB

n ccPP

tQxctQxBH

dddtdxdQ

d

),,(

),,(

)()(

12

2

23

21 tQx

tQx

PP Bn

Bn

nn

-0.36

0E ~

0E ~

Within the VGG model, the neutron pure DVCS

amplitude is sensitive to E .

E~

DVCSnC

22 GeV9.136.0 QxB

A.V. Belitsky, D. Müller, A. Kirchner, NP B629 (2002) 323

Perspectives


The pure DVCS contribution to the cross section is separated from the interference contribution, in the twist-2 approximation, taking advantage of the beam energy dependence of the kinematic factors.

Twist-2

E05-114 -DVCSA. Biselli, L. Elouadrihri, K.Joo, S. Nicolai et al.

Perspectives

3/6

Eric Voutier


p

A.V. Belitsky, D. Müller, A. Kirchner, NP B629 (2002) 323

A. Biselli and H. Egiyan talks in GPD parallel session

EEHH~

)(4

)(1

)()(1

2)()(

~)( 22121211

tF

M

ttFtFtFtFtFtFC I

LP

Access to another Compton form factor,that is another linear combination of GPDs

)3sin()2sin()sin()()(

),,(

)2sin()sin(),,(2

1

,3,2,121

25

,2,12

42

5

2

5

ILP

ILP

ILP

B

DVCSLP

DVCSLPB

eBeB

sssPP

tQx

sstQxdddtdxdQ

d

dddtdxdQ

d

Gluons

Twist-2

Twist-3

Access to the imaginary part of H from the target spin

asymmetry.

H~

Access to the real part from double polarization

observable.

55

55

dd

ddULA90GeV3.230.0 22 QxB

Perspectives

4/6

Eric Voutier


R. Kaiser talk in GPD parallel session

The GPDs World

xB

One may expect to get a reasonable mapping of the GPDs in the

intermediate and valence regions by 2020.

H1, ZEUS, HERMES, JLab 6 GeV are providing the first but limited data sets.

The energy upgrade of the CEBAF accelerator allows access to the high xB region which requires large luminosity.

The DVCS project at COMPASS will explore intermediate xB (0.01-0.10) with a reasonable overlap with the JLab 12 GeV kinematic domain.

Perspectives Eric Voutier


GPDs @ JLab 12 GeV

Several experiments will measure DVCS (Hall A & B) and DVMP (Hall B) with (un)polarized beam and target, extending the experimental techniques and methods developed at 6 GeV.

An eventual transversally polarized target program in Hall B is attached to the technical success of the HDice target.

The development of neutron detection capabilities in the central detector region (Hall B) and of polarized neutron targets sustaining high beam currents (Hall A) are investigated.

D(e,e’n)p

5/6

D(e,e’n)p



GPDs @ COMPASS

μ

p’

μ’

The GPDs program is part of the COMPASS Phase II (2010-2015) proposal to be submitted to CERN in 2008-2009.

Step 1 (~2011) to constrain H

d(+, ) + d(-, ) Im(F1 H) sin d(+, ) - d(-, ) Re(F1 H) cos

Step 2 (~2013) to constrain E

d(, S) - d(, S+π) Im(F2 H – F1 E) sin (- S) cos

The first step of this program requires a 4 m long recoil proton detector (RPD) together with a 2.5 m long LH2 target. An additional electromagnetic calorimeter will enlarge the kinematical coverage at large xB.

The second step requires either a transversally polarized NH3 target inserted in the RPD or a new SciFi (?) RPD inserted in the existing NH3

target system. %80μGeV190100 ,

Experimental strategy Eric Voutier


γpepe

Q2 = 2.3 GeV2 xB = 0.36

Compton Form factors

M. Guidal, arXiv/hep-ph:0807.2355

Within a fitting code relying on a leading order and leading twist description of the DVCS amplitude, it was shown that a reliable and model-independent extraction of the real and imaginary parts of each Compton form factor requires a minimal number of observables.

Cross section (, single and double polarized cross section differences (ij) should be measured; asymmetries are providing additional constraints but are not enough selective by themselves.

Dispersion relation constraints are expected to improve this picture by reducing the number of required observables and/or improving the accuracy of the fitting procedure.

Current and z0 data suggest that VGG predictions underestimate slightly the imaginary part of H and miss the real

part.

jz 00 zj

Imaginary parts Real parts

It remains a theoretical concern to extract GPDs from CFFs.

A.V. Belitsky, D. Müller, arXiv/hep-ph:0809.2890

Conclusions

1/2

Eric Voutier

Summary

GPDs offer the unique opportunity to access the contribution of the quark angular momentum to the spin of the nucleon.

In this effort, neutron and transversally polarized proton targets are mandatory steps.


Special thanks to François-Xavier Girod, Michel Guidal, Nicole d’Hose, Malek Mazouz, Andy Sandorfi

Together with the evolution of lattice QCD calculation capabilities, the road towards a comprehensive and quantitative

understanding of the nucleon structure is OPEN!!

The exploration of the GPD world has been starting at DESY & JLab and will continue at JLab 12 GeV and COMPASS with high precision and exclusive experiments.

Recent phenomenological & theoretical developments tend to indicate that this world should be efficiently mapped with the measurement of a limited set of

observables.

Eric VoutierPerspectives

SPIN2008, Charlottesville, October 6-11, 2008Hall

B

HDice Lab

HDice Lab @ JLab

HDice Lab design and infrastructure – Nov’08 Building construction – (Feb’09, Jun’09)

Cryogenic infrastructure – (Apr’09, Sep’09) Polarized target tests – (Sep’09, Nov’09)

Design & construction of a new In-Beam Cryostat for CLAS – (May’08, Jul’10) Set of polarized targets for experiments – (Mar’10, Aug’10)

Installation in Hall B – (Jul’10, Sep’10) run – (Sep’10, Apr’11)

Electron beam tests – (Apr’11) e run – (Nov’11, Dec’11)

Courtesy of A. Sandorfi

Eric Voutier

InCe DVCSnC

Experimental data are taken for LH2 and LD2 targets at 4.82 GeV/c and 6.00 GeV/c.

The LD2-LH2 yields binned in (k, Mx2, , t) are

fitted with Monte-Carlo simulated yields taking into account experimental and radiative effects.

Unpolarized Cross Section

Projected systematics

Perspectives


P R O J E C T E D D A T A

InIn CC e

Eric Voutier

n-DVCS @ CLAS 12INFN Frascati, INFN Genova, IPN Orsay, LPSC Grenoble, University of Glasgow …

… European initiative towards the central detector …

Neutron detection at laboratory angles larger than 40° would allow an efficient and fully exclusive study of the n-DVCS process up to the

valence region.

The possibility of developing neutron detection capabilities in the central region of CLAS12 is forseen.

A. El Alaoui (LPSC Grenoble) (2008)


Perspectives

ToF scintillators

Vertex detector

Neutron detector

5 T @ target

D(e,e’n)p


Polarized Neutron Target

sin~

41 22

EEHM

ttF m

Longitudinal Target Spin Asymmetry

Transverse Target Spin Asymmetry

HEEHm10DVCSc

E-EEH

HE-E

HHE-E

~1

4M

t

11

2

1~

142

1~

11

2

42

22

2

1

221

22

2

220

m

m

mm

tFs

ξtF

M

tc

tFM

tξ

y

ytF

M

tc

I

I

I

The twist-2 target spin asymmetries are derived below in the case of a polarized neutron, assuming that the Dirac form factor and the non spin-flip polarisation dependent GPD are 0.

The most sensitive coefficient to E appears to originate from the pure DVCS amplitude while the kinematical factors enhance H in the other coefficients.

sincoscossinsin 1100 SI

SI

SIDVCS sccc

A. Belitsky, D. Müller, A. Kirchner, NP B629 (2002) 323


Eric Voutier

Forward Calorimeter

Forward Cerenkov(LTCC)

Beamline Instrumentation

Preshower Calorimeter

Forward Drift Chambers

Inner Cerenkov(HTCC)

SuperconductingTorus Magnet

Central Detector

Inner Calorimeter

Forward Time-of-Flight

Detectors

CLAS12


Perspectives

Documents

XVIII th International Symposium on Spin Physics