Generalized Parton DistributionsGeneralized Parton Distributions

1/ Generalized 1/ Generalized Parton Parton DistributionsDistributions

p-/2 p’(=p+2)

H,E(x,,t)H,E(x,,t)

~~

x-

t=2

x+

GPDsGPDs

(Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt)

light-cone dominance, nμ (1, 0, 0, -1) / (2 P+)

p-/2 p’(=p+2)

H,E(x,,t)H,E(x,,t)

~~

x-

t=2

x+

GPDsGPDs

Vector Ms : H,E

Large Q2, small t

PS Ms : H,E~ ~

(Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt)

: T lead. twist

Mesons : L

light-cone dominance, nμ (1, 0, 0, -1) / (2 P+)

{{[[Hq(x,,t)N(p’)N(p’)++N(p)N(p) + + Eq(x,,t)N(p’)iN(p’)i++N(p)]N(p)]

5 5 [[Hq(x,,t)N(p’)N(p’)+ + 5 5 N(p) +N(p) + Eq(x,,t)N(p’)N(p’)N(p)]N(p)]}}2M2M_ ~~

2M2M

_

_

_

H,E(x,,t)H,E(x,,t)

~~

x-

t=2

x+

{{[[Hq(x,,t)N(p’)N(p’)++N(p)N(p) + + Eq(x,,t)N(p’)iN(p’)i++N(p)]N(p)]

5 5 [[Hq(x,,t)N(p’)N(p’)+ + 5 5 N(p) +N(p) + Eq(x,,t)N(p’)N(p’)N(p)]N(p)]}}2M2M_ ~~

2M2M

_

_

_

Vector Ms : H,E

Large Q2, small t

PS Ms : H,E~ ~

(Ji, Radyushkin, Muller, Collins, Strikman, Frankfurt)

: T lead. twist

Mesons : L p-/2 p’(=p+2)

GPDsGPDs

light-cone dominance, nμ (1, 0, 0, -1) / (2 P+)

H, H, E, E (x,ξ,t)~ ~

“Ordinary” parton distributions

H(x,0,0) = q(x), H(x,0,0) = Δq(x) ~

x

Elastic form factors

H(x,ξ,t)dx = F(t) ( ξ)

x

Ji’s sum rule

2Jq = x(H+E)(x,ξ,0)dx

gq LGL 21

21

(nucleon spin)

x+ξ x-ξ

tγ, π, ρ, ω…

-2ξ

: do NOT appear in DIS NEW INFORMATION

xξ-ξ +

1-1 0anti-quark distribution

quark distribution

q q distribution amplitude

Cross-section measurementand beam charge asymmetry (ReT)

integrate GPDs over x

Beam or target spin asymmetrycontain only ImT,

therefore GPDs at x = and

(M.

Va

nde

rhae

gh

en)

1

1

1

1

),,(),,(

~),,(

~ tHidxx

txHPdx

ix

txHT DVCS

p p’

H,E,H,E~ ~x

tx

ExtensionsExtensions

RCS : p->p (intermediate t) (Radyushkin, Dihl, Feldman, Jakob, Kroll)

VCS : ep->e (Frankfurt, Polyakov, Strikman, Vanderhaeghen)

tDDVCS : ep->ep* (e+e-) (M.G., Vanderhaeghen, Belitsky, Muller,...)

IDVCS : pp->(Freund, Radyushkin,Shaeffer,Weiss)

tDVCS : p->p* (e+e-) (Berger, Pire, Diehl,...)

N-DVCS : eA->eA(Scopetta, Pire, Cano, Polyakov, Muller, Kirschner, Berger....)

Hybrids, pentaquarks,... (Pire, Anikin,Teryaev,...)

sDDVCS : ep->ep (Vanderhaeghen, Gorschtein,...)

_

- “Trivial” kinematical corrections

- Quark transverse momentum effects (modification of quark propagator)

- Other twist-4 ……

DES: finite Q2 corrections(real world ≠ Bjorken limit)

DES: finite Q2 corrections(real world ≠ Bjorken limit)

GPD evolution

O (1/Q)

O (1/Q2)

Dependence on factorization scale μ :

Kernel known to NLO

- Gauge fixing term- Twist-3: contribution from γ*L may be expressed in terms of derivatives of (twist-2) GPDs.

- Other contributions such as small (but measureable effect).

(here for DVCS)

2/ Study on the2/ Study on the(x,t) correlation of the GPDs(x,t) correlation of the GPDs

(in coll. with M. Vanderhaeghen,

A. Radyushkin & M. Polyakov)

H(x,0,b )=FT H(x,0,t)

(Burkhardt)

y

xpz

b

x

f x b( , )

1

0

xz

b

The The GPDGPDs contains contain information information on the on the longitudinallongitudinal ANDAND transversetransverse distributions ofdistributions ofthethe partons partons in the nucleonin the nucleon

GPDs in impact parameter spaceGPDs in impact parameter space

N 'N

3-D picture of the nucleon3-D picture of the nucleon (femto-graphy of the nucleon)(femto-graphy of the nucleon)

(Belitsky)

GPDsGPDs : : tt dependence ( dependence ( small –small –t t ))

evaluate for ξ = 0 : model and

t = 0 :

t ≠ 0 :

2 free parameters : ’1,’2 Fit 4 form factors : G E,M p,n

LOW -t ( -t < 1 GeV2

) : Regge model Goeke, Polyakov,

Regge trajectory :

valence model for

E

Vanderhaeghen (2001)

proton proton & & neutron neutron charge radiicharge radii

GPV Regge model

Regge slope

experiment

F1u = uv(x)1/(x ’t)dx

1

0

r 21,p =-6’ lnx(euuv+eddv)dx

proton proton electromagnetic form electromagnetic form factorsfactors

GPV Regge model

forward parton distributions

at = 1 GeV2 (MRST2002 NNLO)

neutron neutron electromagnetic form electromagnetic form factorsfactors

GPV Regge model

Large t power behavior is fixed by large x (->1) behavior

GPDsGPDs : : tt dependence ( dependence ( large –t large –t )) modified Regge model : M.G., Polyakov, Radyushkin, Vanderhaeghen (2004)

Hq(x,,t)=q(x)x-t=q(x)e-t ln(x)

F1(t)->1/t2, F2(t)->1/t4 (t>>)

if q(x) ~ (1-x) then FF->1/t(+1)

2/ Large x behavior of E should be different from H :

extra (1-x) power q for q(x)

if q(x)->(1-x) then FF->1/t(+1)/2 (Drell-Yan-West relation)

exp(- α΄ t lnx) -> exp(- α΄ (1 – x) t lnx)

M. Burkardt (2002)

1/

proton proton electromagnetic form electromagnetic form factorsfactors

GPRV modified Regge

modelGPV Regge model

’ = 1.105 GeV-2

u = 1.713

d = 0.566

neutron neutron electromagnetic form electromagnetic form factorsfactors

GPRV modified Regge

model

GPV Regge model

proton proton Dirac & Pauli form factorsDirac & Pauli form factors

GPRV modified Regge

model

GPV Regge model

x

b (fm)

N -> N -> ΔΔ transition form factorstransition form factors

GPRV modified

Regge model

GPV Regge

model

in large Nc limit

PROTON M2q 2 Jq

valence model M1

(GPV 01)

2 Jq

valence model M2

(GPRV 04)

2 Jq

Lattice

QCDSF 03

u 0.40

0.69 0.63 0.734 ± 0.135

d 0.22 -0.07 -0.06 -0.085 ± 0.088

s 0.03 0.03 0.03

u + d + s

0.65 0.65 0.60 0.65 ± 0.16

quark contribution to quark contribution to proton proton spinspin

with

valence models for eq(x) :

M1 :

M2 :

PROTON 2 Jq

valence model M2

(GPRV 04)

ΔqHERMES

(1999)

2 Lq

u 0.63 0.57 ± 0.04 0.06 ± 0.04

d -0.06 -0.25 ± 0.08 0.19 ± 0.08

s 0.03 -0.01 ± 0.05 0.04 ± 0.05

u + d + s

0.60 0.30 ± 0.10 0.30 ± 0.10

orbital angular momentum orbital angular momentum carried by quarkscarried by quarks

evaluated at μ2 = 2.5 GeV2

SummarySummary

Generalized Parton Distributions (GPDs)

x-t correlations and nucleon form factors 3 parameters (’,u,d) GPDs

describe all existing data (GE,Mp,n)

spin of nucleon / lattice QCD

The actorsThe actors

JLab

Hall A Hall B Hall C

p-DVCS

n-DVCS

Vector mesons

p-DVCS

d-DVCS

Pseudoscalar mesons

DESYHERMES ZEUS/H1

Vector & PS mesons

DVCS

CERNCOMPASS

Vector mesons

DVCS

+ theory (almost) everywhere

JLab(Ee=6 GeV):CLAS/Hall B (2001+2005) and Hall A (2004)

HERA (Ee=27 GeV) : HERMES and ZEUS/H1 (up to 2006)

CERN (E=200 GeV) : COMPASS (2007 ?)

« DES » in the world« DES » in the world

e

p

e’

p’

The epThe ep ep ep process process

DVCSDVCS

e

p

e’

p’

e

p

e’

p’

Bethe-HeitlerBethe-Heitler

GPDs

...

2

1''

5

dt

d

dt

d

dtddkd

d LTV

ee

1

1V

Vete

B ECxQ 1,2

Energy dependenceEnergy dependence

BH

DVCS

Calculation (M.G.&M.Vanderhaeghen)

e

p

e’

p’

The epThe ep ep ep process process

DVCSDVCS

e

p

e’

p’

e

p

e’

p’

Bethe-HeitlerBethe-Heitler

Interference between the 2 processes : if the electronbeam is polarised => beam spin asymmetry

GPDs

First experimental signaturesFirst experimental signatures

Magnitude and Q2 dependence of DVCS X-section (H1/ZEUS)

First observations of DVCS beam asymmetries

CLAS HERMES

DVCS

First observations of DVCS charge asymmetry (HERMES)

All in basic agreement with theoretical predictions

2 2

2

1.25 GeV

0.19

0.19 GeV

B

Q

x

t

Phys.Rev.Lett.87:182002,2001

4.8 GeV data (G. Gavalian)

PRELIMINARY

0.15 < xB< 0.41.50 < Q2 < 4.5 GeV2

-t < 0.5 GeV2

PRELIMINARY

PRELIMINARY

5.75 GeV data (H. Avakian &L. Elhouadrhiri)

CLAS/DVCS at 4.8 and 5.75 GeVCLAS/DVCS at 4.8 and 5.75 GeV

γ*Lρ

Handbag diagram calculation (frozen s) can account for CLAS and HERMES data on σL(ep->ep)

Q2(GeV2)

CLAS 4.2 GeV data (C. Hadjidakis, hep-ex/0408005)

W=5.4 GeV

HERMES (27GeV)A. Airapetian et al., EPJC 17

σL(ep->ep)

Regge (Laget)

GPD (MG-MVdh)

Mesons

proton proton & & neutron neutron charge radiicharge radii

GPV Regge model

Regge slope

experiment

F1u = uv(x)1/(x ’t)dx

1

0

r 21,p =-6’ lnx(euuv+eddv)dx

<x ><x >00

<x ><x >-1 -1

t=0t=0

<x ><x >11

DDsDDs

« D-term »« D-term »kk

GPDsGPDs

Pion cloudPion cloudTrans. Mom. of partonsTrans. Mom. of partons

F (t), G (t)F (t), G (t)1,21,2 A,PSA,PS

q(x),q(x),q(x)q(x)

R (t),R R (t),R (t)(t)AA VVJJqq

(z)(z)

Deconvolution needed !Deconvolution needed !x : mute variable

p p’

H,E,H,E~ ~

x

tx

Hq(x,,t) but only and t accessible experimentally

d

dQ d dt2

B

~ AH (x,,t,Q )2q

x-idx +BE (x,,t,Q )2

q

x-idx +….

1 1

-1 -1

2

= xB1-x /2B t=(p-p ’)2

x = xB !

/2

Compton ScatteringCompton Scattering

“ “DVCS” (Deep Virtual Compton Scattering)DVCS” (Deep Virtual Compton Scattering)

GPDs probe the nucleon at GPDs probe the nucleon at amplitudeamplitude level level

q(x)~<p|q(x)~<p|(x)(x)(x)|p ’>(x)|p ’> H(x,H(x,)~<p|)~<p|(x-(x-))(x+(x+)|p ’>)|p ’>

pp p’p’

x+x+ x-x-

zz00 1100 11 zz

pp p’p’

x+x+ x-x-x<x<::x>x>::

DIS :DIS : DES :DES :

pp p’p’

xx xx

pp p’p’

x+x+ x-x-

( )b

0 b

y

xz

b

Transverse Transverse localisation of the localisation of the partons partons in the nucleonin the nucleon(independently(independently of their of their longitudinallongitudinal momentum) momentum)

Form FactorsForm Factors

N 'N

'ee

x

)(xf

1

0

y

xpz

xz

LongitudinalLongitudinal momentum distributionmomentum distribution(no (no information information on the on the transversetransverse localisation) localisation)

Parton DistributionParton Distribution

N

'ee

(Belitsky et al.)(Belitsky et al.)

F1s (t)= [s(x)-s(x)]/ (x ’t)dx=0

1

-1

Nucleon strangeness : FNucleon strangeness : F11ss

_

[s(x)-s(x)]dx=01

-1

But : /

_