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 Deep Inelastic Scattering Local, Off-diagonal Elastic scattering Hofstadter (1958) Taylor et al. (1969)  p, s p’, s’ q  p, s q X 2 Im   p, s qq Optical theorem and factorization 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/2P + Δ/2 GPD (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)

* Q hard 2 large t = Δ 2 low –t process : -t << Q hard 2 Ji, Radyushkin (1996) x + ξ x - ξ P - Δ/2P + Δ/2 GPD (x, ξ,t) at large Q 2 : 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 Scattering transverse quark distribution in coordinate space DIS longitudinal quark distribution in momentum space DES (GPDs) f ully-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/2P + 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

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 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┴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. Q 2 and large at x B and t fixed but it’s not so simple… 1. Needs to be checked !!! 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 : At JLab energies, |T DVCS | 2 was expected small… but… Kroll, Guichon, Diehl, Pire, …

The cross-section difference accesses the imaginary part of DVCS and therefore GPDs at x =  The total cross-section accesses the 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 -’  p e-e- ** hadronic plane leptonic plane  Into the harmonic structure of DVCS |T BH | 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

Exploiting the harmonic structure of DVCS with polarization Depending on the experiment, measurement of  and  or The difference of cross-sections is a key observable to extract GPDs With polarized beam and unpolarized target: With unpolarized beam and Longitudinally polarized target: With unpolarized beam and Transversely polarized target:

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 using H1-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 ( ), about 4 years after the first proposition to the JLab PAC. Publications from JLab experiments

What we have so far (1): Very first non-dedicated data PRL 97, (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) A LU A UL CLAS: PRL 87, (2001) HERMES: PRL 87, (2001) CLAS A LU : globally exclusive CLAS A UL : fully exclusive HERMES: not exclusive

What we have so far (2): Hall A DVCS dedicated run E and E Two pioneering high precision experiments (p and n) Electromagnetic Calorimeter Proton Array HRS spectrometer in Hall A 6GeV 80% polarized

No Q 2 dependence sin  contribution → GPD access Scattering at the quark level ! And two important results ! Proton target: Scaling at 6 GeV (PRL97, ,2006) Neutron target: A model-dependent constraint on total quark angular momentum (PRL99, , 2007)

What we have so far (3): Hall B DVCS dedicated run …jusqu’à l’installation dans le Hall B. Supraconducting solenoid Inner Calorimeter E1-DVCS: an experiment in a large kinematical domain 5.75 GeV beam 85% polarization Large statistics Half taken in 2005 (currently running 2 nd half)

Integrated over t E1-DVCS : DVCS Asymmetry as a function of x B and Q 2 = 0.18 GeV 2 = 0.30 GeV 2 = 0.49 GeV 2 = 0.76 GeV 2 -The largest data sample to date ! -More data coming -Cross-section analysis ongoing The amplitude of the sin  can be expressed in terms of GPDs PRL100, (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 x B, Q 2 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 2 nd half of unpolarized target E1-DVCS run in Hall B (ongoing) Full separation of the DVCS total cross section in Hall A for proton and « neutron » targets (2010) EG1-DVCS experiment with Long. polarized target (2009) + Transverse target DVCS in Hall B (2011)

2 nd Half of E1-DVCS runs with improvements …jusqu’à l’installation dans le Hall B. Supraconducting solenoid Inner Calorimeter New trigger system for inner calorimeter New shielding (higher luminosity) 5.9 GeV beam 85% polarization Double 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 NH 3 target  Polarization ~ 75%  12 C & 15 N target Inner Calorimeter (IC) High resolution calorimeter to detect photons at small angles (4 o to 15 o ) EG1-DVCS : starting in Feb DVCS with longitudinally polarized target Region 1 DC Typical ep  event

 Dynamically polarized NH 3  5 Tesla magnetic field   B/B ≈  1K LHe cooling bath  NH 3 polarization:75%  12 C, 15 N, and 4 He 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 (PbWO 4 ) 424 crystals, 16 mm long, pointing geometry, ~ 1.2 degree/crystal, APD readout Calibration via π 0 →γγ σ = 7.5 MeV M γγ (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 NH 3 longitudinally polarized target (CLAS + IC) 60 days of beam time, luminosity 15 x /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

A UL as a function of x B, Q 2 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 ~0.2 o, 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~ mK with long 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 LEGS Upcoming photon run E 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 bars with epX A UT 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 A LT sensitivity to an integral over the GPD E

The next generation Hall A experiments Two new high precision experiments (p and n) for a full cross section separation Expanded Electromagnetic Calorimeter (132 blocks > 208 blocks) No more Proton Array (less dead time and not needed) HRS spectrometer in Hall A 6GeV 80% polarized New trigger logic (higher threshold + π 0 trigger) >Detection of enough π 0 to subtract correctly the contamination and determine the π 0 electro-production polarized cross sections. >Remove the systematic error due to the uncertainty on the contamination of DVCS-like π 0 channel. UV curing system for high luminosity running

Electromagnetic Calorimeter (upgraded)

Full separation of the  electroproduction cross section 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:

DVCS² contribution is predicted large and are predicted to be the same size ! VGG model

Separation at two different Q² Twist-3

Separation for the neutron previous systematics new systematics

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.