1. 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

2. 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

3. 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 )

4. 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)

5. 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

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

7. 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

8. 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

9. 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

10. 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

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

12. 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
MIT, JLab-THY ,
DESY , TUM-T
0.5 fm at small x
measure H(x,0,t) as function of t
0.15fm at large x

13. Sensitivity to the 3-D nucleon picture
Chiral dynamics: Strikman et al., PRD69 (2004)
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 fm
Promising
COMPASS
domain

14. 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

15. 3 frameworks or models for GPD2
(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) hep-ph/ v1
Dual parametrization with Mellin moments decomposition
QCD evolution separation x,  and , t
Quark domain: Vanderhaeghen, Guichon, Guidal (VGG)
PRD60 (1999) , Prog.Part.Nucl.Phys.47(2001)
Double distribution x, a la Radyushkin

16. 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

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

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

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

20. + 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

21. 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

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

23. 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

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

25. 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

26. 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 GeV
Integrated over t

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

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

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

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

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

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

33. 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

34. α’ slope of Regge traject. α’=1.1μ’  *
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

35.  ’ 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

36. 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

37. 2nd goal:
hunting for the GPD E and Lq

38. 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

39. DVCS at HERMES Transverse Target Spin Asymmetry

40. DVCS at HERMES Transverse Target Spin Asymmetry

41. 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
VGG Code
GPD model : LO/Regge/D-term=0
Goeke et al., Prog. Part. Nucl. Phys 47 (2001), 401.

42. Hägler et al., hep-lat
MIT, JLab-THY ,
DESY , TUM-T

43. Hägler et al.,
hep-lat
MIT, JLab-THY ,
DESY , TUM-T

44. 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…

46. 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 = /3 Hs - 1/8 Hg
Pseudo Scalar Meson production: idem with Htilde and Etilde

47. 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. (PRD ):
-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 = /3 Hs - 1/8 Hg
under study with
present COMPASS data

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

49. + strikman