3D structure

1
Delia Hasch
towards a 3D imaging of hadrons
a brief introduction (an experimentalists point
of view)
a personal selection of recent results
models data
conclusion perspectives
4th Electron-Ion-Collider workshop, Hampton
University, VA, May 19-23, 2008
2
nucleon studied for decades
form factors location of partons in nucleon
parton distributions longitudinal momentum
fraction x
only known framework to gain information on 3D
picture of hadrons
3
nucleon tomography
M. Burkardt, M. Diehl 2002
FT (GPD) momentum space ? impact parameter
space
probing partons with specified long. momentum
_at_transverse position b
T
polarised nucleon
d-quark
u-quark
x0
from lattice
4
what do we know about GPDs ?
Q2gtgt, tltlt
appear in factorisation theorem for hard
exclusive processes
form factors
PDFs

nucleon helicity flip ? dont appear in DIS
? new information !
5
what do we know about GPDs ?
Q2gtgt, tltlt
appear in factorisation theorem for hard
exclusive processes
form factors
PDFs

anti-quarks
6
GPDs and the spin puzzle
nucleon spin
30
zero
X. Ji, 1997
requires orbital angular momentum
proton helicity flipped but quark helicity
conserved
7
how to access GPDs ?
quantum number of final state selects different
GPDs

• VM (r, w, f) H E
• PS mesons (p, h) H E
• DVCS (g) H, E, H, E

? DVCS most clean process for gaining information
on GPDs
? meson provide info on quark flavours
VM quark and gluon GPDs appear at same order as
8
accessing GPDs caveats

• but only x and t accessible
  experimentally

• x is mute variable (integrated over)

? apart from cross-over trajectory (xx) GPDs not
directly accessible deconvolution needed !
(model dependent)

• GPD moments cannot be directly revealed,
• extrapolations t ? 0 are model dependent

e.g.
cross sections beam-charge asymmetry Re(T
DVCS )
beam or target-spin asymmetries Im(T DVCS )
9
the ideal experiment for measuring hard exclusive
processes
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the ideal experiment for measuring hard exclusive
processes
highvariable beam energy

• hard regime
• wide kinematic range

high luminosity

• small cross sections
• measure in 3 kinematic variables simultanously

complete event reconstruction
? ensure exclusivity
doesnt exists (yet)
11
the menu
data from exclusive VM over wide kinematic range
JLab ? HERMES ? COMPASS ? HERA-collider
? role of quarks and gluons
? NLO corrections
exclusive PS mesons production
? role of power corrections
DVCS from first signals ? detailed measurements
reminder for meson production factorisation only
for sL (sT suppressed by 1/Q2)
12
VM production _at_small x
W t dependences probe transition from soft ?
hard regime
r
f
J/Y
U
s Wd
? steep energy dependence of s in presence of the
hard scale
13
VM production _at_small x
W t dependences probe transition from soft ?
hard regime
r
f
J/Y
U
s e-bt
? universality of b-slope para-meter point-like
configurations dominate
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VM production small ? high x
0.2-0.5
10-3
10-1
xBj
HERA-collider COMPASS/HERMES JLab
g(sea) g(sea)qv (r,w) qv
(r,w)

• NLO corrections to VM production are large
  M.Diehl, W.Kugler arXiv0708.1121

• r0 cross section _at_typical kinematics of compass
  / hermes / jlab12

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VM production small ? high x
0.2-0.5
10-3
10-1
xBj
HERA-collider COMPASS/HERMES JLab
g(sea) g(sea)qv (r,w) qv
(r,w)

• despite LO GPD model (handbag fact.)
  S.Goloskokov, P.Kroll arXiv0711.4736

• LOpower corrections

r0 Q23.8 GeV2
H1, Zeus E665 Hermes
glue
gluesea
valenceinterference
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VM production small ? high x
0.2-0.5
10-3
10-1
xBj
HERA-collider COMPASS/HERMES JLab
g(sea) g(sea)qv (r,w) qv
(r,w)

• despite LO GPD model (handbag fact.)
  S.Goloskokov, P.Kroll arXiv0711.4736

• LOpower corrections

r0
W90 GeV
Zeus H1
leading-tw
W75 GeV
power correction
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exclusive pion production
?
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exclusive pion production
?
PLB659(2008)
GPD model for sL VGG
Regge model JML
ds/dt
LO
dsL/dt
LOpower corrections

• data support order of power corrections

• NLO corrections moderate ltlt size of power
  corrections Diehl,Kugler

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exclusive pion production
a vs t
?
arXiv0711.4736
ALU
A a sinf
? any non-zero BSA indicates L-T interference
(contribution not described in terms of GPDs)
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deeply virtual compton scattering DVCS
most clean channel for interpretation in terms of
GPDs
?
DVCS
Bethe-Heitler
_at_HERMES/JLab DVCS ltlt Bethe-Heitler
? leads to non-zero azimuthal asymmetries
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DVCS _at_amplitude level
IDs
? different charges e e- (only _at_HERA!)
H
H

H
DsUT sin(f-fS)cosf Imk(H - E)
H, E
kinematically suppressed _at_HERMES and JLab energies
x xB/(2-xB ),k t/4M2
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first DVCS signals ALU
-- from interference term --
PRL87(2001)
CLAS _at_E 4.2 GeV
? sinf dependence indicates dominance of handbag
contribution
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call for high statistics
JLab E1-DVCS beam-spin asymmetry
3D binning in x, Q2 and t
integrated over t
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call for new analysis methods
HERMES combined analysis of charge
polarisation dependent data
? separation of interference term DVCS2
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call for new analysis methods
HERMES combined analysis of charge
polarisation dependent data
? separation of interference term DVCS2
beam charge asymmetry
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call for new analysis methods
HERMES combined analysis of charge
polarisation dependent data
? separation of interference term DVCS2
beam charge asymmetry HERMES preliminary
w/o D-term
GPD models
VGG
with D-term
regge-ansatz for t-dependence
dual
factorised t-dependence
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call for new analysis methods
HERMES combined analysis of charge
polarisation dependent data
? separation of interference term DVCS2
beam spin asymmetry HERMES preliminary
regge-ansatz for t-dependence
GPD models
VGG
factorised t-dependence
regge-ansatz for t-dependence
dual
factorised t-dependence
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a word about GPD models
VGG Vanderhaegen, Guichon, Guidal 1999

• double distributions factorised or
  regge-inspired t-dependence

• D term to restore full polynomiality

• skweness depending on free parameters bval bsea

• includes tw-3 (WW approx)

dual Guzey, Teckentrup 2006

• GPDs based on infinite sum of t channel
  resonances

• factorised or regge-inspired t-dependence

• tw-2 only

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a word about GPD models
VGG Vanderhaegen, Guichon, Guidal 1999

• double distributions factorised or
  regge-inspired t-dependence

• D-term to restore full polynomiality

• skweness depending on free parameters bval bsea

• includes tw-3 (WW approx)

dual Guzey, Teckentrup 2006

• GPDs based on infinite sum of t channell
  resonances

• factorised or regge-inspired t-dependence

• tw-2 only

? call for new, more sophisticated
parametrisations of GPDs
more models on the way e.g. generalisation of
Mellin transform technique
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nevertheless first attempts to constrain Jq
observables sensitive to E (Jq input parameter
in ansatz for E)

• DVCS AUT HERMES
• nDVCS ALU Hall A
• r0 AUT HERMES

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nevertheless first attempts to constrain Jq
Jq input parameter in ansatz for E
arXiv0802.2499
VGG
HallA, PRL99(2007)
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nevertheless first attempts to constrain Jq
Jq input parameter in ansatz for E
arXiv0802.2499
dual
VGG
HallA, PRL99(2007)
HallA nDVCS ALU
PRL99(2007)
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nevertheless first attempts to constrain Jq
Jq input parameter in ansatz for E
? demonstrates model dependence of these analyses
? data are free to be re-used at any time with
new models ?
34
conclusions
GPDs
contain a wealth of new information on hadron
structure at parton level ? only known
framework allowing a 3D imaging of hadrons ?

BUT they are intricate functions
data
increasing amount and precision of experimental
data
large flow of new data expected soon

• JLab6GeV dedicated DVCS/DVMP experiments
• HERMES with recoil detector
• VM production from COMPASS with p target

theory
standard models/parametrisations of GPDs too
simple
? models should describe large variety of
different observables over wide kinematic range
prior to any conclusion about GPDs from data
call for new, more sophisticated parametrisations
35
perspectives
_at_ new facilities

• high beam energy (hard regime, wide kinematic
  range)
• very high luminosity (small xsections, multi-D
  analyses)
• complete event reconstruction (ensure
  exclusivity)

? exploration of new channels WACS, time like
DVCS,
? ideas for accessing GPDs _at_LHC, _at_GSI,
Luminosity(1030/cm2/s)
109
JLab_at_12GeV

• gold rush for studying hard exclusive
  processes GPDs

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107
JLab
106

• extraction of GPDs requires filling the gap in
  kinematic coverage

ELIC
105
107
104
eRHIC
103
102
HERMES
HERA-collider
101
COMPASS
100 CM energy (GeV)
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