Generalized Parton Distributions Summary for SIR2005@Jlab
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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
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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
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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
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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
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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
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Burkardt
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Burkardt
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Wakamatsu
observation at low energy scale :
(from polarized DIS)
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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
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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
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Non-Perturbative IssuesNon-Perturbative Issues
Does factorization work ?Instanton mediated processes ?
Hoyer, Boer
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Boer
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GPDs ON A LATTICE
Zanotti
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Zanotti
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Zanotti
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Fleming
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Fleming
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Fleming
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Fleming
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GPDs for nuclei ?GPDs for nuclei ?
Liutti
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Nowak
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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
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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
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Nowak
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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
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Nowak
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Nowak
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Ellinghaus
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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
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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
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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
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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
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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
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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
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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)
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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
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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
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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