Generalized Parton Distributions (GPD) to describe the nucleon Structure Experiments At JLab 6GeV, HERMES, H1/Zeus At COMPASS (At JLab 12 GeV, FAIR, EIC …) Nicole d’Hose CEA Saclay

The nucleon map Robust and exhaustive studies Deep inelastic scattering At DESY, + CERN + JLab (see DIS07) Elastic scattering At JLab (see excl.react.07) Semi-inclusive reactions -0.3 < g < 0.3 (COMPASS) => Large orbital momentum ? Exclusive reactions Nucleon tomography

Burkard,Belitsky,Müller,Ralston,Pire Parton Distribution H( x,,t ) GPDs  a 3-dimensional picture of the partonic nucleon structure Form Factor F( t ) Elastic Scattering ep ep p e * t = -Q² x boost y z r ry,z Px ep eX Deep Inelastic Scattering Q²xBj x p γ* Parton Density q ( x ) x boost x P z 1 y Hard Exclusive Scattering Deeply Virtual Compton Scattering Burkard,Belitsky,Müller,Ralston,Pire Generalized Parton Distribution H( x,,t ) ep ep p GPDs * Q² x+ x-  t x P y z r x boost ( Px, ry,z )

GPDs and relations to the physical observables γ, π, ρ, ω… factorization x+ξ x-ξ t The observables are some integrals of GPDs over x Dynamics of partons in the Nucleon Models: Parametrization Fit of Parameters to the data H, ,E, (x,ξ,t) “ordinary” parton density Elastic Form Factors Ji’s sum rule Intro 2Jq =  x(H+E)(x,ξ,0)dx x x H(x,0,0) = q(x) (x,0,0) = Δq(x)  H(x,ξ,t)dx = F(t)

Necessity of factorization to access GPDs Collins et al. Deeply Virtual Compton Scattering (DVCS): γ γ* Q2 p p’ GPDs x + ξ x - ξ t =Δ2 meson Gluon contribution L γ* Q2 γ hard x + ξ x - ξ soft GPDs Q2 large t << Q2 + γ* p p’ t =Δ2 Hard Exclusive Meson Production (HEMP): meson p p’ GPDs γ* x + ξ x - ξ hard soft L Q2 L t =Δ2 Quark contribution

Competition in the world and complementarity HERA Ix2 100GeV E=190, Gluons valence quarks valence quarks and sea quarks and gluons COMPASS 2010 JLab 12 GeV 2014 + FAIR + EIC

In DVCS and meson production we measure Compton Form Factor hard soft p p’ γ GPDs γ* x + ξ x - ξ t =Δ2 Q2 In DVCS and meson production we measure Compton Form Factor For example at LO in S: t, ξ~xBj/2 fixed DGLAP q(x) DGLAP DGLAP ERBL

1rst - 3-dim picture of the partonic nucleon structure 2 ultimate goals or the « Holy-Grail »: 1rst - 3-dim picture of the partonic nucleon structure or probability densities of quarks and gluons in impact parameter space H(x, , t) ou H( Px, ry,z )  measurement of Re(H) via VCS and BCA or Beam Charge Difference x P y z r x boost

2nd - Contribution to the nucleon spin knowledge 2 ultimate goals or the « Holy-Grail »: 2nd - Contribution to the nucleon spin knowledge ½ = ½ ΔΣ + ΔG + < Lzq > + < Lzg > the GPDs correlation between the 2 pieces of information: -distribution of longitudinal momentum carried by the partons -distribution in the transverse plane the GPD E is related to the angular momentum 2Jq =  x (Hq (x,ξ,0) +Eq (x,ξ,0) ) dx  with a transversely polarized target DVCS et MV  with a deuterium or neutron target DVCS t p q E

3-dim picture of the partonic nucleon structure 1rst goal: 3-dim picture of the partonic nucleon structure or probability densities of quarks and gluons in impact parameter space

GPDs in Lattice probability densities of quarks and gluons From Schierholz, JLab May 2007 probability densities of quarks and gluons in impact parameter space

Sensitivity to the 3-D nucleon picture Lattice calculation (unquenched QCD): Negele et al., NP B128 (2004) 170 Göckeler et al., NP B140 (2005) 399  fast parton close to the N center  small valence quark core  slow parton far from the N center  widely spread sea q and gluons m=0.87 GeV x Last result on 29 May 2007 First comprehensive full lattice QCD In the chiral regime with m =0.35 GeV Hägler et al., hep-lat 07054295 MIT, JLab-THY-07-651, DESY-07-077, TUM-T39-07-09 0.5 fm at small x measure H(x,0,t) as function of t 0.15fm at large x

Sensitivity to the 3-D nucleon picture Chiral dynamics: Strikman et al., PRD69 (2004) 054012 Frankfurt et al., Ann. Rev. Nucl. Part. Sci. 55 (2005) 403 at large distance : gluon density generated by the pion cloud increase of the N transverse size for xBj < mπ/mp=0.14 0.6 0.4 fm Promising COMPASS domain

2 Parametrizations of GPDs Factorization: H(x,ξ,t) ~ q(x) F(t) or Regge-motivated t-dependence: is more realistic it considers that fast partons in the small valence core and slow partons at larger distance (wider meson cloud) it includes correlation between x and t <b2> = α’ln 1/x transverse extension of partons in hadronic collisions H(x,0,t) = q(x) e t <b2> = q(x) / xα’t (α’slope of Regge traject.) This ansatz reproduces the Chiral quark-soliton model: Goeke et al., NP47 (2001) More correct behavior at small and large x: <b2> = α’ (1-x) ln1/x + B(1-x)2 to reproduce perfectly the proton form factor

3 frameworks or models for GPD 2 (x, ξ, t, Q ) Gluon domain : Freund, Frankfurt, Strikman (FFS) + Schoeffel GPDS,V,g(x,)  QS,V,g(x) Dependence generated via the GPD evolution Gluon + quark domain (x<0.2): Guzey PRD74 (2006) 054027 hep-ph/0607099v1 Dual parametrization with Mellin moments decomposition QCD evolution + separation x,  and , t Quark domain: Vanderhaeghen, Guichon, Guidal (VGG) PRD60 (1999) 094017, Prog.Part.Nucl.Phys.47(2001)401-515 Double distribution x, a la Radyushkin

DVCS cross sections (*pp) at HERA FFS predictions: HS,V,g(x,)  QS,V,g(x) @ 1 GeV² : PDF used  CTEQ6M  Dependence generated via the GPD evolution Predictions at NLO Good description of the Q² and W dependences

DVCS cross sections (*pp) at HERA Guzey predictions: No difference between ---- Factorized and Regge motivated t-dependence in the small x domain

DVCS cross sections (*pp)[t=(p-p’)²] 1996-2000 analysis d/dt = [d/dt]t=0 exp(-b|t|) : b=6.02 +/- 0.35 +/- 0.39 GeV-2

New H1 results on d/dt Global value : b(Q²)=A*(1-B*log(Q²/2)) A = 6.98 +/- 0.98 GeV-2 B = 0.12 +/- 0.03 Global value : => <rT²>=0.65 fm >> valence quarks value b measurements @ H1 (low x) : dominated by glue and sea quarks no W dependence

+ and unpolarized target φ θ μ’ μ *  p DVCS + BH with polarized and charged leptons and unpolarized target φ θ μ’ μ *  p μ p BH calculable DVCS + dσ(μpμp) = dσBH + dσDVCSunpol + Pμ dσDVCSpol + eμ aBH Re ADVCS + eμ Pμ aBH Im ADVCS  Known expression Pμ  eμ  eμ Pμ  Twist-2 M11 >> Twist-3 M01 Twist-2 gluon M-11 Belitsky,Müller,Kirchner

with F1H dominance with a proton target F2E dominance with a neutron target (F1<<) (studied at JLab) very attractive for Ji’s sum rule study

Beam Spin cross section difference DVCS at JLab Hall A with polarized electrons Beam Spin cross section difference Twist-2 Twist-3 PRL97, 262002 (2006) Analysis in Φ Corrected for real+virtual RC (P. Guichon) Checked elastic cross-section @ ~1% - twist-2 and twist-3 extraction - twist-3 contributions very small

Q2 dependence and test of scaling DVCS at JLab Hall A with polarized electrons Q2 dependence and test of scaling <-t>=0.26 GeV2, <xB>=0.36 Twist-2 Twist-3 No Q2 dependence: strong indication for scaling behavior and handbag dominance

DVCS at JLab Hall A Total cross section dσ(μpμp) = dσBH + dσDVCSunpol + e aBH Re ADVCS C1 C0 C2 ! PRL97, 262002 (2006) but impossible to disentangle DVCS2 from the interference term

DVCS at JLab Hall B- CLAS with polarized electrons Beam Spin Asymmetry = ALU = Denominator(BH+VCS) E1-DVCS kinematical coverage and binning W2 > 4 GeV2 Q2 > 1 GeV2

E1-DVCS: Beam Spin Asymmetry as a function of xB and Q2 <-t> = 0.18 GeV2 <-t> = 0.30 GeV2 <-t> = 0.49 GeV2 <-t> = 0.76 GeV2 Accurate data in a large kinematical domain A vast program At JLab@12 GeV Integrated over t

DVCS at HERMES with polarized electrons Beam Spin Asymmetry = ALU = Denominator(BH+VCS)

DVCS at HERMES Beam Spin Asymmetry = ALU Data 96/97 (published PRL87 (2001)) and 2000 (prelim, hep-ex/0212019) ~ 0

DVCS at HERMES Beam Spin Asymmetry = ALU Comparison to VGG predictions

DVCS at HERMES Beam Spin Asymmetry = ALU Comparison to Guzey’s predictions

DVCS at HERMES Beam Charge Asymmetry = AC hep-ex/0605108, PRD (2007)

DVCS at HERMES Beam Charge Asymmetry = AC hep-ex/0605108, PRD (2007)

μ’  * μ  p Beam Charge Asymmetry at E = 100 GeV COMPASS prediction 6 month data taking in 2010 250cm H2 target 25 % global efficiency Q2 xBj 7 6 5 4 3 2 0.05 0.1 0.2

α’ slope of Regge traject. α’=1.1 μ’  * Beam Charge Asymmetry at E = 100 GeV COMPASS prediction μ  p VGG: double-distribution in x, model 1: H(x,ξ,t) ~ q(x) F(t) model 2 and 2*: correl x and t <b2> = α’ ln 1/x H(x,0,t) = q(x) e t <b2> = q(x) / xα’t α’ slope of Regge traject. α’=0.8 α’=1.1 Guzey: Dual parametrization model 3: also Regge-motivated t-dependence with α’=1.1

 ’ determined within an accuracy of ~10% at xBj =0.05 and 0.1 C1cos VGG prediction model 2 model 1 model 2 model 1 2 Superiority of a Beam Charge Difference measurement ’ determined within an accuracy of ~10% at xBj =0.05 and 0.1

BCA = + - - / + + - ~ p1 cos()+ p2 cos()+ p3 cos() Beam Charge Asymmetry at H1 HERA II data with 291 pb-1 analysed (equally shared in the e+ & e- samples) BCA = + - - / + + - ~ p1 cos()+ p2 cos()+ p3 cos() p1 is found well > 0 (a first indication of a non factorised (x,t) model ?) Large potential to examine the GPD(x,t) ( p1 M11 p3 M-11 -p2 negligible-) |t|>0.05 GeV²

2nd goal: hunting for the GPD E and Lq

Model-Dependent Constraint on Ju and Jd Through the modeling of GPD E 1-Transversaly polarised target In Meson production : In DVCS : 2-Neutron target - liquid deuterium target

DVCS at HERMES Transverse Target Spin Asymmetry

DVCS at HERMES Transverse Target Spin Asymmetry

MODEL-DEPENDENT Ju-Jd extraction DVCS on the neutron at JLab/HallA/ E03-106 Beam Spin Asymmetry MODEL-DEPENDENT Ju-Jd extraction LD2 target 24000 fb-1 xB=0.36, Q2=1.9 GeV2 Lattice hep-lat 07054295 VGG Code GPD model : LO/Regge/D-term=0 Goeke et al., Prog. Part. Nucl. Phys 47 (2001), 401.

Hägler et al., hep-lat 07054295 MIT, JLab-THY-07-651, DESY-07-077, TUM-T39-07-09

Hägler et al., hep-lat 07054295 MIT, JLab-THY-07-651, DESY-07-077, TUM-T39-07-09

and still many results will come in the future years GPD measurement =major part of the future programs at COMPASS (2010) at JLab 12 GeV (2014) at FAIR, EIC…

Towards a complete experiment on GPDs Vector Meson production: only two leading-twist observables Transv targ-spin Note ALL which has been measured in COMPASS is not leading twist Long targ-spin Goloskokov and Kroll Vector Meson production: filter of GPDs Hρ0 = 1/2 (2/3 Hu + 1/3 Hd + 3/8 Hg) Hω = 1/2 (2/3 Hu – 1/3 Hd + 1/8 Hg) H = -1/3 Hs - 1/8 Hg Pseudo Scalar Meson production: idem with Htilde and Etilde

1- Hard exclusive meson production 1/Q4 1/Q6 vector mesons pseudo-scalar mesons H,E ~ Scaling predictions: meson p p’ GPDs g* x + ξ x - ξ t =Δ2 L hard soft Collins et al. (PRD56 1997): -factorization applies only for *L -probably at a larger Q2 Different flavor contents: Hρ0 = 1/2 (2/3 Hu + 1/3 Hd + 3/8 Hg) Hω = 1/2 (2/3 Hu – 1/3 Hd + 1/8 Hg) H = -1/3 Hs - 1/8 Hg under study with present COMPASS data

E1-DVCS : ALU(90°) as a function of |t| + models JM Laget VGG twist-2+3 VGG twist-2

+ strikman