1. towards a 3D imaging of hadrons
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. generalised parton distributions (GPDs)
nucleon studied for decades:
form factors
location of partons in nucleon
parton distributions
longitudinal momentum fraction x
FF: transverse location of partons in the nucleon (independently of their long momentum): local operator, initial/finale states different  non-forward matrix element
Pdf: longitudinal momentum distributions (no info on transverse location): bilocal operator, initial/final states identical  forward matrix element
GPD: longitudinal momentum fraction x at transverse location b_perp: bilocal operator, initial/final states different  non-forward matrix element
generalised parton distributions (GPDs)
longitudinal momentum fraction x at transverse location b T
only known framework to gain information on 3D picture of hadrons

3. nucleon tomography FT (GPD) : momentum space  impact parameter space:
[M. Burkardt, M. Diehl 2002]
FT (GPD) : momentum space  impact parameter space:
probing partons with specified long. position b T
polarised nucleon:
u-quark
d-quark
[x=0]
from lattice

4. what do we know about GPDs ?Q2 t
Q2>>, t<<
appear in factorisation theorem for hard exclusive processes
form factors
PDFs
only ksi and t experimentally accessible | x is mute variable (integrated over)  deconvolution needed !
-ksi <x<ksi : GPDs relate initial and final states not only different in their kinematics but also with different parton content: qq-bar pair …
: nucleon helicity flip  don’t appear in DIS
 new information !

5. what do we know about GPDs ?Q2 t
Q2>>, t<<
appear in factorisation theorem for hard exclusive processes
form factors
PDFs
only ksi and t experimentally accessible | x is mute variable (integrated over)  deconvolution needed !
-ksi <x<ksi : GPDs relate initial and final states not only different in their kinematics but also with different parton content: qq-bar pair …
qq pair
quarks x ξ -ξ +1 -1
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 ? p0 h ρ0 PS mesons (p, h): H E
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 ~ ~ ~ ~ p0
2Du+Dd h
2Du-Dd
 DVCS most clean process for gaining information on GPDs ρ0
2u+d, 9g/4 ω
2u-d, 3g/4 f
s, g ρ+
u-d
J/ψ g
 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 (x=x) 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

10. the ideal experiment for measuring hard exclusive processes
high+variable beam energy
hard regime
wide kinematic range
high luminosity
small cross sections
measure in 3 kinematic variables simultanously
complete event reconstruction
 ensure exclusivity
… doesn’t exists (yet)…

11. the menu DVCS: from first signals  detailed measurements
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 @small x s ~ Wd
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 @small x s ~ e-b|t|
W & t dependences: probe transition from soft  hard regime r f
J/Y U
s ~ e-b|t|
 universality of b-slope para-meter: point-like configurations dominate

14. VM production: small  high x
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 arXiv ]
r0 cross kinematics of compass / hermes / jlab12

15. VM production: small  high x
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 arXiv ]
LO+power corrections
r0 Q2=3.8 GeV2
H1, Zeus
E665
Hermes
glue
glue+sea
valence+interference

16. VM production: small  high x
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 arXiv ]
LO+power corrections r0
W=90 GeV
Zeus H1
leading-tw
W=75 GeV
+power correction

17. exclusive pion production

18. exclusive pion production
[PLB659(2008)]
GPD model for sL: VGG
Regge model: JML LO
ds/dt
dsL/dt
LO+power corrections
data support order of power corrections
NLO corrections moderate << size of power corrections [Diehl,Kugler]

19. exclusive pion production
a vs t
[arXiv ]
ALU
A = a sinf
 any non-zero BSA indicates L-T interference (contribution not described in terms of GPDs)

20. deeply virtual compton scattering DVCS
most clean channel for interpretation in terms of GPDs 
DVCS
Bethe-Heitler
@HERMES/JLab:
DVCS << Bethe-Heitler
 leads to non-zero azimuthal asymmetries:

21. DVCS @amplitude level DsUT I~Ds ~ DsC ~ cosf ∙Re{ H + xH +… } ~
 different charges: e+ e-
DsC ~ cosf ∙Re{ H + xH +… } ~ H
polarisation observables:
DsLU ~ sinf∙Im{H + xH + kE} ~
DsUT
beam target H
DsUL ~ sinf∙Im{H + xH + …} ~ ~ H
DsUT ~ sin(f-fS)cosf ∙Im{k(H - E)+ … }
H, E
x = xB/(2-xB ),k = t/4M2
kinematically and JLab energies

22. first DVCS signals: ALU
-- from interference term --
[PRL87(2001)]
ALU
4.2 GeV
 sinf dependence indicates dominance of handbag contribution

23. call for high statistics
JLab: E1-DVCS beam-spin asymmetry
3D binning in x, Q2 and t
<-t> = 0.18 GeV2
<-t> = 0.30 GeV2
<-t> = 0.49 GeV2
<-t> = 0.76 GeV2
integrated over t

24. call for new analysis methods
HERMES: combined analysis of charge & polarisation dependent data
 separation of interference term + DVCS2

25. call for new analysis methods
HERMES: combined analysis of charge & polarisation dependent data
 separation of interference term + DVCS2
beam charge asymmetry

26. call for new analysis methods
HERMES: combined analysis of charge & polarisation dependent data
 separation of interference term + DVCS2
beam charge asymmetry: HERMES preliminary
GPD models:
w/o D-term
VGG
with D-term
dual
regge-ansatz for t-dependence
factorised t-dependence

27. 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

28. 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

29. a word about GPD models VGG: [Vanderhaegen, Guichon, Guidal 1999]
describes well AC and AUT data
fails for ALU
Ac favour ‘no D-term’  contradicts cQSM & lattice results
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
describes well spin-asymmetries
fails for unpol. cross sections (HallA)
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

30. …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
AHLT: Ahmad, Honkanen, Liuti, Taneja PRD75(2007)

31. …nevertheless: first attempts to constrain Jq
Jq input parameter in ansatz for E:
[arXiv: ]
[HallA, PRL99(2007)]
VGG
AHLT: Ahmad, Honkanen, Liuti, Taneja PRD75(2007)

32. …nevertheless: first attempts to constrain Jq
Jq input parameter in ansatz for E:
[arXiv: ]
dual
[HallA, PRL99(2007)]
VGG
AHLT: Ahmad, Honkanen, Liuti, Taneja PRD75(2007)
HallA nDVCS ALU
[PRL99(2007)]

33. …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 data & theory
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 @ 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 …
Luminosity(*1030/cm2/s)
109
“gold rush” for studying hard exclusive processes & GPDs
108
107
JLab
HERA: 3*10^31 cm^-2s^-1 (e/p : 27/920)
eRHIC: 4.4*10^32 cm^-2s^-1 (e/p : 10/250)
ELIC: 7.8*10^34 cm^-2s^-1 (e/p : 7/150)
106
ELIC
“extraction” of GPDs requires filling the gap in kinematic coverage
105
107
104
eRHIC
103
102
HERMES
HERA-collider
101
COMPASS 1 10
100 CM energy (GeV)