Generalized Parton Distributions (GPD)

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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 dHose CEA Saclay
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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 lt ?g lt 0.3
• (COMPASS)
• gt Large orbital
• momentum ?

Exclusive reactions Nucleon tomography
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GPDs and relations to the physical observables
?, p, ?, ?
factorization
x?
x-?
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,?,t)
ordinary parton density
Elastic Form Factors
Jis sum rule
2Jq ? x(HE)(x,?,0)dx
x
x
H(x,0,0) q(x)
(x,0,0) ?q(x)
? H(x,?,t)dx F(t)
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Necessity of factorization to access GPDs
Collins et al.
Deeply Virtual Compton Scattering (DVCS)

?
?
Q2

hard
x ?
x - ?
soft

GPDs
Q2 large t ltlt Q2 ?
p
p
t ?2
Hard Exclusive Meson Production (HEMP)
meson
L
t ?2
Quark contribution
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Competition in the world and complementarity
HERA
Ix2
Gluons valence quarks valence quarks
and sea quarks and gluons
COMPASS 2010 JLab 12 GeV 2014 FAIR EIC
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In DVCS and meson production we measure Compton
Form Factor

For example at LO in ?S
DGLAP
t, ?xBj/2 fixed
q(x)
DGLAP
DGLAP
ERBL
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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
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2 ultimate goals or the  Holy-Grail 

• 2nd - Contribution to the nucleon spin knowledge
• ½ ½ ?S ?G lt Lzq gt lt Lzg gt
• 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,?,0) Eq (x,?,0) ) dx
• ? with a transversely polarized target DVCS
  et MV
• ? with a deuterium or neutron target DVCS

E
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1rst goal 3-dim picture of the partonic
nucleon structure or probability
densities of quarks and gluons in impact
parameter space
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GPDs in Lattice
From Schierholz, JLab May 2007
probability densities of quarks and gluons
in impact parameter space
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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
0.15fm at large x

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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 lt mp/mp0.14
0.6 0.4 fm
Promising COMPASS domain
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2 Parametrizations of GPDs
Factorization H(x,?,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 ltb2?gt aln 1/x transverse extension
of partons in hadronic collisions
H(x,0,t) q(x) e t ltb?2gt q(x) / xat
(aslope of Regge traject.)
This ansatz reproduces the
Chiral quark-soliton model Goeke et
al., NP47 (2001)
More correct behavior at small and large x
ltb2?gt a (1-x) ln1/x B(1-x)2
to reproduce perfectly the proton form
factor
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2
3 frameworks or models for GPD
)
Q

t,
?,
(x,

Gluon domain Freund, Frankfurt, Strikman (FFS)
Schoeffel

• GPDS,V,g(x,?) ? QS,V,g(x)
• Dependence generated via the QCD evolution

Gluon quark domain (xlt0.2) 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
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DVCS cross sections ?(?p??p) at HERA

• FFS predictions HS,V,g(x,?) ? QS,V,g(x) _at_ 1
  GeV² PDF used ? CTEQ6M
• ? Dependence
  generated via the QCD evolution
• Predictions at NLO

Good description of the Q² and W dependences
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DVCS cross sections ?(?p??p) at HERA
Guzey predictions No difference between ----
Factorized and Regge motivated
t-dependence in the small x domain
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DVCS cross sections ?(?p??p)t(p-p)²
1996-2000 analysis
d?/dt d?/dtt0 exp(-bt) b6.02 /-
0.35 /- 0.39 GeV-2
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New H1 results on d?/dt
b(Q²)A(1-Blog(Q²/2)) A 6.98 /- 0.98
GeV-2 B 0.12 /- 0.03
Global value

• gt ?ltrT²gt0.65 fm
• gtgt valence quarks value
• b measurements _at_ H1 (low x)
• dominated by glue and sea quarks

no W dependence
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DVCS BH with polarized and charged leptons
and unpolarized target
ds(µp?µp?) dsBH dsDVCSunpol Pµ
dsDVCSpol eµ aBH Re ADVCS
eµ Pµ aBH Im ADVCS
? Known expression
Pµ ?
eµ ?
eµ Pµ ?
Twist-3 M01
Twist-2 M11
Twist-2 gluon M-11
gtgt
Belitsky,Müller,Kirchner
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with
F1H dominance with a proton target F2E
dominance with a neutron target (F1ltlt) (studied
at JLab) very attractive for Jis sum rule
study
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DVCS at JLab Hall A with polarized
electrons
Beam Spin cross section difference
Twist-2 Twist-3
PRL97, 262002 (2006)
Analysis in F
- twist-2 and twist-3 extraction - twist-3
contributions very small
Corrected for realvirtual RC (P.
Guichon) Checked elastic cross-section _at_ 1
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DVCS at JLab Hall A with polarized
electrons
Q2 dependence and test of scaling
lt-tgt0.26 GeV2, ltxBgt0.36
Twist-2 Twist-3
No Q2 dependence strong indication for scaling
behavior and handbag dominance
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DVCS at JLab Hall A Total cross
section
ds(µp?µp?) dsBH dsDVCSunpol e aBH Re ADVCS
C1 C0 C2
!
PRL97, 262002 (2006)
but impossible to disentangle DVCS2 from the
interference term
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DVCS at JLab Hall B- CLAS with polarized
electrons
Beam Spin Asymmetry ALU
Denominator(BHVCS)
E1-DVCS kinematical coverage and binning
W2 gt 4 GeV2 Q2 gt 1 GeV2
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E1-DVCS Beam Spin Asymmetry as a function of xB
and Q2
Accurate data in a large kinematical domain
A vast program At JLab_at_12 GeV
Integrated over t
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DVCS at HERMES with polarized electrons
Beam Spin Asymmetry ALU
Denominator(BHVCS)
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DVCS at HERMES Beam Spin Asymmetry ALU
Data 96/97 (published PRL87 (2001)) and 2000
(prelim, hep-ex/0212019)
0
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DVCS at HERMES Beam Spin Asymmetry ALU

Comparison to VGG predictions
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DVCS at HERMES Beam Spin Asymmetry ALU

Comparison to Guzeys predictions
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DVCS at HERMES Beam Charge Asymmetry AC

hep-ex/0605108, PRD (2007)
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DVCS at HERMES Beam Charge Asymmetry AC
hep-ex/0605108, PRD (2007)
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µ
?
?
Beam Charge Asymmetry at E? 100 GeV COMPASS
prediction
µ
p
?
6 month data taking in 2010 250cm H2 target 25
global efficiency
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µ
?
?
Beam Charge Asymmetry at E? 100 GeV COMPASS
prediction
µ
p
?
VGG double-distribution in x,?
model 1 H(x,?,t) q(x) F(t)
model 2 and 2 correl x and t
ltb2?gt a ln 1/x
H(x,0,t) q(x) e t ltb?2gt q(x) /
xat a slope of Regge traject.
a0.8 a1.1
Guzey Dual parametrization
model 3 also Regge-motivated
t-dependence with a1.1
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C1cos?
?
VGG prediction
model 2
model 1
model 2
model 1
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Superiority of a Beam Charge Difference
measurement ? determined within an accuracy of
10 at xBj 0.05 and 0.1
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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(2?) p3 cos(3?)
p1 is found well gt 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-)
tgt0.05 GeV²
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2nd goal hunting for the GPD E and Lq
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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

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DVCS at HERMES Transverse Target Spin
Asymmetry
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DVCS at HERMES Transverse Target Spin
Asymmetry
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DVCS on the neutron at JLab/HallA/ E03-106
Beam Spin Asymmetry
MODEL-DEPENDENT Ju-Jd extraction
LD2 target 24000 fb-1 xB0.36, Q21.9 GeV2
Lattice hep-lat 07054295
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Hägler et al., hep-lat 07054295
MIT, JLab-THY-07-651,
DESY-07-077, TUM-T39-07-09
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Hägler et al., hep-lat 07054295 MIT,
JLab-THY-07-651, DESY-07-077, TUM-T39-07-09
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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
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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
Goloskokov and Kroll
Long targ-spin
Vector Meson production filter of GPDs
H?0 1/?2 (2/3 Hu 1/3 Hd 3/8 Hg) H? 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
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1- Hard exclusive meson production
Collins et al. (PRD56 1997) -factorization
applies only for ?L -probably at a larger Q2
Different flavor contents H?0 1/?2 (2/3 Hu
1/3 Hd 3/8 Hg) H? 1/?2 (2/3 Hu 1/3 Hd
1/8 Hg) H? -1/3 Hs - 1/8 Hg
under study with present COMPASS data
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E1-DVCS ALU(90) as a function of t models
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strikman