3D structure

1
Delia Hasch
towards a 3D imaging of hadrons GPDs
a brief introduction (an experimentalists point
of view)
a personal selection of recent results
models data
conclusion perspectives
PKU-RBRC workshop on transverse spin physics,
University, June30-July 04, 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
why GPDs ?
? 3D structure of hadrons nucleon tomography
4
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
from lattice
5
why GPDs ?
? 3D structure of hadrons nucleon tomography
? complementary to TMDs
Wigner distribution (mother function)
probability to find a quark u in a nucleon P with
a certain polarisation in a position r and
momentum k
d3r
FT (d2kT)
TMD
GPD
? phenomena of single-spin asymmetries
6
Harut Avakian 2004
Quantum Phase-Space Distributions of Quarks
Probability to find a quark u in a nucleon P with
a certain polarization in a position r and
momentum k
Wpu(k,r) Mother Wigner distributions
d3r
d2kT dr
GPDs Hpu(x,x,t), GDAs Fudp(x,x)
FT
TMD PDFs fpu(x,kT), TMD FFs Dup(kT,z)
IPDs Wpu(x,rT),
GPD
x0
x0,t0
d2r
dx
d2kT
Measure momentum transfer to target Direct info
about spatial distributions
Measure momentum transfer to quark Direct info
about momentum distributions
PDFs fpu(x), FFs Dup(z)
Form Factors F1pu(t),F2pu(t )..
Some PDFs same in exclusive and semi-inclusive
analysis
H.Avakian, Nov 19, 2004
6
7
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 !
8
what do we know about GPDs ?
Q2gtgt, tltlt
appear in factorisation theorem for hard
exclusive processes
form factors
PDFs

anti-quarks
9
what do we know about GPDs ?
Q2gtgt, tltlt
appear in factorisation theorem for hard
exclusive processes
form factors
PDFs
anti-quarks
quarks
10
GPDs and the spin puzzle
nucleon spin
30
zero
X. Ji, 1997
requires orbital angular momentum
proton helicity flipped but quark helicity
conserved
11
how to access GPDs ?
lattice
12
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

lattice
? 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
13
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 )
14
the ideal experiment for measuring hard exclusive
processes
15
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 exist (yet)
16
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)
17
VM production _at_small x
W t dependences probe transition from soft ?
hard regime
r
f
J/Y
U
s Wd
? steeper energy dependence of s with increasing
hard scale
DVCS
18
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
19
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
21
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
?
23
exclusive pion production
?
PLB659(2008)
GPD model for sL VGG
Regge model JML
Vanderhaegen, Gichon, Guidal, 1999
J.M. Laget 2004
ds/dt
LO
dsL/dt
LOpower corrections

• data support order of power corrections

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

24
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)
need higher energies and/or calculation of sT
25
deeply virtual compton scattering DVCS
most clean channel for interpretation in terms of
GPDs (full factoristion proof)
?
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
27
first DVCS signals ALU
-- from interference term --
PRL87(2001)
CLAS _at_E 4.2 GeV
? sinf dependence indicates dominance of handbag
contribution
28
call for high statistics
JLab E1-DVCS beam-spin asymmetry
3D binning in x, Q2 and t
integrated over t
29
call for new analysis methods
HERMES combined analysis of charge
polarisation dependent data
? separation of interference term DVCS2
30
call for new analysis methods
HERMES combined analysis of charge
polarisation dependent data
? separation of interference term DVCS2
beam charge asymmetry
31
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
regge-ansatz for t-depend.
with D-term
regge-ansatz for t-dependence
dual
factorised t-dependence
Guzey, Teckentrup 2006
32
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
33
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

34
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
35
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

36
nevertheless first attempts to constrain Jq
Jq input parameter in ansatz for E
JHEP06(2008)
VGG
HallA, PRL99(2007)
37
nevertheless first attempts to constrain Jq
Jq input parameter in ansatz for E
JHEP06(2008)
dual
VGG
HallA, PRL99(2007)
VGG
HallA nDVCS ALU
PRL99(2007)
38
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 ?
39
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
complementary to TMDs relations GPDs ?? TMDs
M. Burkardt, M. Schlegel
increasing amount and precision of experimental
data
large flow of new data expected soon (JLab,
HERMES, COMPASS)
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
40
perspectives for GPDs
_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

108
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)
10
1
41
perspectives for GPDs TMDs
_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

108
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)
10
1