Generalized Parton Generalized Parton DistributionsDistributions

Summary for SIR2005@JlabSummary for SIR2005@Jlab

Michel Garçon (Saclay)Michel Garçon (Saclay)Pervez Hoodbhoy (Islamabad)Pervez Hoodbhoy (Islamabad)

Wolf-Dieter Nowak (DESY)Wolf-Dieter Nowak (DESY)

20 May 200520 May 2005

When integrated over p, one gets the When integrated over p, one gets the coordinate space density coordinate space density ρρ(x)=|(x)=|ψψ(x)|(x)|22

When integrated over x, one gets the When integrated over x, one gets the coordinate space density n(p)=|coordinate space density n(p)=|ψψ(p)|(p)|22

),(),(),( pxWpxdxdpOpxO

Wigner parton distributions (WPD)Wigner parton distributions (WPD)

X. Ji

Wigner distributions for quarks in Wigner distributions for quarks in protonproton

Wigner operator (Wigner operator (X. Ji,PRL91:062001,2003X. Ji,PRL91:062001,2003))

Wigner distribution: “Wigner distribution: “densitydensity” for quarks ” for quarks having having position position rr and 4-momentum k and 4-momentum k (off-(off-shell)shell)

X. Ji

Wigner parton distributions & Wigner parton distributions & offspringsoffsprings

Mother Dis. W(r,p)

q(x, rq(x, r, , kk))

TMDPD q (x, kTMDPD q (x, k))

Red. Wig.Red. Wig.q(x,r)q(x,r)

PDF q(x) Density ρ(r)

X. Ji

Reduced Wigner Distributions and Reduced Wigner Distributions and GPDsGPDs

The 4D reduced Wigner distribution f(The 4D reduced Wigner distribution f(rr,x) is ,x) is related torelated to Generalized parton distributions Generalized parton distributions (GPD)(GPD) H and E through simple FTH and E through simple FT,,

t= – q2

~ qz

H,E depend only on 3 variables. There is a rotational symmetry in the transverse plane..

X. Ji

Burkardt

Burkardt

Wakamatsu

observation at low energy scale :

(from polarized DIS)

From Holography to Tomography

An Apple

A. Belitsky, B. Mueller, NPA711 (2002) 118

By varying the energy and momentum transfer to the proton we probe its interior and generate tomographic images of the proton (“femto tomography”).

detector

A Proton

mirror

mirror

mirror

mirror

Burkert

Imaging quarks at fixed Feynman-xImaging quarks at fixed Feynman-x

For every choice of x, one can use the Wigner For every choice of x, one can use the Wigner distributions to picture the nucleon in 3-space; distributions to picture the nucleon in 3-space; quantum phase-space tomography!

z

bx

by

X. Ji

Non-Perturbative IssuesNon-Perturbative Issues

Does factorization work ?Instanton mediated processes ?

Hoyer, Boer

Boer

GPDs ON A LATTICE

Zanotti

Zanotti

Zanotti

Fleming

Fleming

Fleming

Fleming

GPDs for nuclei ?GPDs for nuclei ?

Liutti

Nowak

Kinematical domainKinematical domain

Collider :H1 & ZEUS 0.0001<x<0.01

Fixed target :JLAB 6-11GeV SSA,BCA?HERMES 27 GeV SSA,BCA

COMPASS could provide data on : Cross section (190 GeV) BCA (100 GeV) Wide Q2 and xbj ranges

Limitation due to luminosity

E=

19

0,

10

0G

eV

Nx2

Burtin

Separating GPDs through polarization

LU~ sin{F1H + (F1+F2)H +kF2E}d~

Polarized beam, unpolarized target:

Unpolarized beam, longitudinal target:

UL~ sin{F1H+(F1+F2)(H + … }d~

Unpolarized beam, transverse target:

UT~ sin{k(F2H – F1E) + …. }d

= xB/(2-xB)

k = t/4M2

H, H, E

Kinematically suppressed

H, H~

H, E

A =

=

~

ep ep

Burkert

Nowak

DVCSDVCS DVMPDVMP

GPDs – Flavor separation

hard vertices

hard gluon

DVCS cannot separate u/d quarkcontributions.

longitudinal only

M = select H, E, for u/d flavorsM = , K select H, E

Burkert

Nowak

Nowak

Ellinghaus

Exclusive production on transverse target

2 (Im(AB*))/ T

t/4m2) - ReUT

A ~ 2Hu + Hd

B ~ 2Eu + Ed0

K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001

Q2=5 GeV2

Eu, Ed needed forangular momentum sum rule. 0

B

Burkert

ep→epγ (DVCS) BSA CLAS 4.2 GeV Published PRL

CLAS 4.8 GeV Preliminary

CLAS 5.75 GeV Preliminary

(+ σ) Hall A 5.75 GeV Fall 04

CLAS 5.75 GeV Spring 05

ep→epγ (DVCS) TSA CLAS 5.65 GeV Preliminary

e(n)→enγ (DVCS) BSA Hall A 5.75 GeV Fall 04

ed→edγ (DVCS) BSA CLAS 5.4 GeV under analysis

ep→epe+e- (DDVCS) BSA CLAS 5.75 GeV under analysis

ep→epρ σL CLAS 4.2 GeV Published PLB

CLAS 5.75 GeV under analysis

ep→epω (σL) CLAS 5.75 GeV Accepted EPJA

+ other meson production channels π, η, Φ under analyses in the three Halls.

GPD Reaction Obs. Expt Status

),,( tH From

ep → epX

Dedicated set-up

),,(~

tH ),,( tE

),,( txH

x

duEH )(,

x

duEH )2(,

)( du

M.Garcon

0 asymmetry (two photons required)

Exclusive ep ep

S. Chen

A

5.65 GeV run with NH3 longitudinally polarized target, Q2 up to 4.5 GeV2

M.Garcon

DVCS with a polarized target in CLASDVCS with a polarized target in CLAS

* Detect all 3 particles in the final state (e,p,γ) to eliminate contribution from N (but calorimeter is at too large angles) ,

* Apply kinematical cuts to suppress ep→epπ0 contribution.

* Remaining Φ-dependent π0 contribution (10-40%) extracted from MC.

* π0 asymmetry measured

DDVCS(Double Deeply Virtual Compton Scattering)

DDVCS(Double Deeply Virtual Compton Scattering)

γ*T γ*T

M. Guidal & M. Vanderhaeghen, PRL 90A. V. Belitsky & D. Müller, PRL 90

The (continuously varying)virtuality of the outgoing

photon allows to “tune” thekinematical point (x,ξ,t) at

which the GPDs are sampled (with |x | < ξ).

e- e+

e-

p p

e- ),),',((~Im tqxHT DDVCS

DDVCS-BH interference generates abeam spin asymmetry sensitive to

M.Garcon

DDVCS: first observation of ep → epe+e-DDVCS: first observation of ep → epe+e-

* Positrons identified among large background of positive pions

* ep→epe+e- cleanly selected (mostly) through missing mass ep→epe+X

* Φ distribution of outgoing γ* and beam spin asymmetry extracted(integrated over γ* virtuality)

A problem for both experiment and theory:

* 2 electrons in the final state → antisymmetrisation was not included in calculations,

→ define domain of validity for exchange diagram.

* data analysis was performed assuming two different hypotheses

either detected electron = scattered electron

or detected electron belongs to lepton pair from γ*

Hyp. 2 seems the most valid

→ quasi-real photoproduction of vector mesons

but…

Lepton pair squared invariant mass

M.Garcon

W=5.4 GeV

HERMES (27GeV)

xB=0.38

CLAS (4.3 GeV)

Q2 (GeV2)

GPD formalism approximately describes CLAS and HERMES data Q2 > 2 GeV2

Exclusive ep ep productionL

Burkert

Deeply virtual meson productionDeeply virtual meson production

Meson and Pomeron (or two-gluon) exchange …

… or scattering at the quark level ?

π, f2, Pρρ00 ((σσ), ), ff22, P, P

ωω ππ, , ff22, P, P

ΦΦ PP

Flavor sensitivity of DVMP on the proton:

ω

ρρ00 2u+d, 9g/42u+d, 9g/4

ωω 2u-d, 3g/42u-d, 3g/4

ΦΦ s, gs, g

ρρ++ u-du-d

γ*LωL

6

2

4

),(),,)((

1)(1

Q

tfdxdztxbEaH

ixz

z

QQdt

d MSL

(Photoproduction)

Exclusive ρ meson production: ep → epρExclusive ρ meson production: ep → epρ

CLAS (4.2 GeV)

Regge (JML)

C. H

adji

daki

s et

al.,

PL

B 6

05

GPD formalism (beyond leading order) describes approximately data

for xB<0.4, Q2 >1.5 GeV2

GPD (MG-MVdh)

CLAS (5.75 GeV)

Analysis

in progres

s

Two-pion invariant mass spectra

M.Garcon

Exclusive production on transverse target

Im(AB*) AUT ~

Asymmetry depends linearlyon the GPD E in Ji’s sum rule.

and measurements allow separation of Eu, Ed

A ~ 2Hu + Hd

B ~ 2Eu + Ed0

K. Goeke, M.V. Polyakov, M. Vanderhaeghen, 2001

A ~ Hu - Hd

B ~ Eu - Ed+

AUT

xB

CLAS12 projected

Burkert

GPD CHALLENGESGPD CHALLENGES

Goal: map out the full dependence onGoal: map out the full dependence on

Develop models consistent with known forward Develop models consistent with known forward distributions, form factors, polynomiality distributions, form factors, polynomiality constraints, positivity,…constraints, positivity,…

More lattice moments, smaller pion masses, More lattice moments, smaller pion masses, towards unquenched QCD,…towards unquenched QCD,…

Launch a world-wide program for analyzing Launch a world-wide program for analyzing GPDs perhaps along the lines of CTEQ for PDFs. GPDs perhaps along the lines of CTEQ for PDFs.

High energy, high luminosity is needed to map High energy, high luminosity is needed to map out GPDs in deeply virtual exclusive processes out GPDs in deeply virtual exclusive processes such as DDVCS (JLab with 12GeV unique).such as DDVCS (JLab with 12GeV unique).

2, , ,x t Q