1. Hard exclusive processes -
experimental results and simulations for EIC
Andrzej Sandacz
Sołtan Institute for Nuclear Studies, Warsaw
DVCS at fixed target experiments and HERA
Vector Meson production at HERA
Transverse target spin asymmetry for ρ0 production
Exclusive π+ and π0 production
DVCS at EIC
EIC Collaboration Meeting, Stony Brook University, December 8, 2007

2. Generalized Parton Distributions
Factorisation:
Q2 large, -t<1 GeV2
hard
x+x
x-x
soft
GPDs P1 t P2 ~ ~
4 Generalised Parton Distributions : H, E, H, E
depending on 3 variables: x, x, t
for each quark flavour and for gluons
for DVCS gluons contribute only at higher orders in αs

3. GPDs properties, link to DIS and form factors
for P1 = P2 recover usual parton densities
no similar relations; these GPDs decouple for P1 = P2
needs orbital angular momentum between partons
Dirac
axial
pseudoscalar
Pauli
Ji’s sum rule
total angular momentum carried by quark flavour q
(helicity and orbital part)

4. ½ = ½ ΔΣ + ΔG + < Lzq > + < Lzg >
‘Holy Grails’ or the main goals
 GPD= a 3-dimensional picture of the partonic nucleon structure
or spatial parton distribution in the transverse plane
H(x, =0, t) → H(x,, rx,y )
probability interpretation
Burkardt y
x P r x z
Contribution to the nucleon spin puzzle
E related to the angular momentum
2Jq =  x (Hq (x,ξ,0) +Eq (x,ξ,0) ) dx
½ = ½ ΔΣ + ΔG + < Lzq > + < Lzg > t p q E

5. Observables and their relationship to GPDs
The imaginary part of amplitude T probes GPD at x = x
The real part of amplitude T depends on the integral of GPD over x
DGLAP
DGLAP
ERBL

6. DVCS Asymmetries measured up to now
 different charges: e+ e-
DsC ~ cosf ∙Re{ H + xH +… } ~ H
 polarization observables:
DsLU ~ sinf∙Im{H + xH + kE} ~ H
DsUL ~ sinf∙Im{H + xH + …} ~ ~ H
DsUT ~ sin(f-s)cos∙Im{k(H - E) + … }
H, E
x = xB/(2-xB ),k = t/4M2
kinematically suppressed

7. CLAS: DVCS - BSA Accurate data in a large kinematical domain
<-t> = 0.18 GeV2
<-t> = 0.30 GeV2
<-t> = 0.49 GeV2
<-t> = 0.76 GeV2
Accurate data in a large kinematical domain
Integrated over t

8. Results from JLAB Hall A E00-100
Q2 = 2.3 GeV2 xB = 0.36
PRL97, (2006)
Difference of polarized cross sections
Twist-2
Twist-3
Unpolarized cross sections
extracted twist-3 contribution small

9. s1int ~ dominant term at small |t| GPD !!!
No Q2 dependence: strong indication for scaling and handbag dominance

10. Towards E and Ju, Jd Hermes DVCS-TTSA: Hall A nDVCS-BSA:
Neutron obtained combining
deuteron and proton
F1 small and u & d cancel in
x=0.36 and Q2=1.9GeV2

11. the MODEL-DEPENDENT Ju-Jd extraction
Present status of
the MODEL-DEPENDENT Ju-Jd extraction
With VGG Code
Lattice hep-lat

12. Unpolarised DVCS cross sections from HERA
σDVCS at small xB (< 0.01) mostly sensitive to
Hg, Hsea
Q² and W dependence: NLO predictions
bands reflect experimental error on slope b: 5.26 < b < 6.40 GeV-2
- Wide range of Q2 - sensitivity to QCD evolution of GPDs
- Difference between MRS/CTEQ due to different xG at low xB
- Meaurements of b significantly constrain uncertainty of models

13. t dependence of DVCS cross section
New H1 results on slopes - DIS07
DIS06

14. Lessons from DVCS at H1/ZEUS
Skewing parameter R=Im DIS / Im DVCS ~ 0.5
Good agreement with NLO predictions
GPDs ≡ PDFs at low scale; skewing generated by QCD evolution
Sensitivity to Hg ; 15% change of Hg => 10% change of cross section
Real part of DVCS amplitude – small effect, few%
Low sensitivity to b(Q2) vs. b(const.)
Interplay of Rs (sea) and Rg (gluons)
Color dipole phenomenology (no GPDs) also a satisfacory description

15. Hard exclusive meson production
4 Generalised Parton Distributions (GPDs)
for each quark flavour and for gluons
GPDs depend on 3 variables: x, x, t
factorisation proven only for σL
σT suppressed of by 1/Q2
necessary to extract longitudinal contribution to observables (σL , …)
allows separation and wrt quark flavours
H E Vector mesons (ρ, ω, φ)
H E Pseudoscalar mesons (π, η) ~
Flavour sensitivity of DVMP on the proton ρ0
2u+d, 9g/4 ω
2u-d, 3g/4 φ
s, g ρ+
u-d
J/ψ g
conserve flip nucleon helicity
quarks and gluons enter at the same order of αS
wave function of meson (DA Φ)
additional information/complication

16. Dipole models for exclusive VM production at small x
at small x sensitivity mostly to gluons
at very small x huge NLO corrections, large ln(1/x) terms (BFKL type logs)
pQCD models to describe colour dipole-nucleon cross sections and meson WF
dipole transv. size W-dep t-dep.
large weak steep
small strong shallow
Frankfurt-Koepf-Strikman (FKS) Phys.Rev. D57 (1998) 512
Martin-Ryskin-Teubner (MRT) Phys.Rev. D62 (2000)
sensitivity to different gluon density distibutions
Farshaw-Sandapen-Shaw (FSS) Phys.Rev. D69 (2004)
Kowalski-Motyka-Watt (KMW) Phys.Rev. D74 (2006)
sensitivity to ρ0 wave function
Dosch-Fereira (DF) hep-ph/ (2006)

17. Recent ZEUS results on exclusive ρ0 production
significant increase of precision + extended Q2 range
2 < Q2 < 160 GeV2
32 < W < 180 GeV
2∙10-4 < xBj < 10-2
| t | < 1 GeV2
96-00 data: 120 pb-1
arXiv: [hep-ex]
W-dependence σ ∞ Wδ
steeper energy dependence with increasing Q2

18. W-dependence for hard exclusive processes at small xϕ
J/ψ ϒ
steep energy dependence for all vector mesons in presence of hard scale
Q2 and/or M2
‘universality’ of energy dependence at small x?
at Q2+M2 ≈ 10 GeV2 still significant difference between ρ and J/ψ

19. dσ / dt - ρ0 example (1 out of 6) Fit
ZEUS
Fit
shallower t-dependence with increasing Q2

20. t-dependence for hard exclusive processes at small x
b-slopes decrease with increasing scale
approximate ‘universality’ of slopes as a function of (Q2 + M2)
Q2 and/or M2
approaching a limit ≈ 5 GeV-2 at large scales
recent data suggestive of possible ≈ 15% difference between ρ and J/ψ

21. Selected results on R = σL/σT for ρ0 production
the same W- and t-dependence for σL and σT
δL ≈ δT
bL ≈ bT
the same size of the longitudinal and transverse γ* involved in hard ρ0 production
i.e. contribution of large qqbar fluctuations of transverse γ* suppressed

22. Comparison to ‘dipole models’
extensive comparison of the models to recent ZEUS ρ0 data in
arXiv: [hep-ex]
below just selected examples
considered models describe qualitatively all features of the data reasonably well
recent ZEUS data are a challenge; none of the models gives at the moment
satisfactory quantitative description of all features of the data

23. Comparison to GPD model
Goloskokov-Kroll
‘Hand-bag model’; GPDs from DD using CTEQ6
power corrections due to kt of quarks included
arXiv:0708,3569[hep-ph]
both contributions of γ*L and γ*T calculated
W=90 GeV
■ H1
□ ZEUS
W=90 GeV
ZEUS (recent)
σ/10
W=75 GeV
complete calculation
leading twist only (in collinear approx.)
leading twist prediction above full calculation, even at Q2 = 100 GeV2
≈ 20%
contribution of σT decreases with Q2, but does not vanish even at Q2 = 100 GeV2
≈ 10%
sea quark contribution, including interference with gluons, non-negligible
25% at Q2 = 4 GeV2

24. Transverse target spin asymmetry for exclusive ρ0 production
Give access to GPD E related to the orbital angular momentum of quarks
Ji’s sum rule q q
So far GPD E poorly constrained by data; mostly by Pauli form factors
The asymmetry defined as
to disentangle contributions from γL and γT the distribution of ρ0 decay polar angle needed in addition
Diehl and Sapeta
The asymmetry defined as
to disentangle contributions from γL and γT the distribution of ρ0 decay polar angle needed in addition
Diehl and Sapeta
Eur. Phys. J.C 41, 515 (2005)

25. Method for L/T separation used by HERMES
A. Rostomyan and J. Dreschler arXiv:
Angular distribution W(cos θ, φ, φs) and Unbinned Maximum Likelihood fit
Assuming SCHC
Simultaneous fit of 12 parameters of azimuthal distributions
Im (E*H) / |H|2
a prerequisite for the method: determination of acceptance correction
as a function of cos θ, φ and φs

26. ρ0 transverse target spin asymmetry from HERMES
Transversely polarised proton target, PT ≈ 75% data, pb-1
for the first time ρ0 TTSA extracted separately for γ*L and γ*T

27. ρ0 transverse target spin asymmetry from HERMES
in a model dependent analysis data favours positive Ju
in agreement with DVCS results from HERMES

28. ρ0 transverse target spin asymmetry from COMPASS
obtained using Double Ratio Method
Transversely polarised deuteron target (6LiD), PT ≈ 50% data
obtained using Double Ratio Method
in bins of ϑ = φ – φS:
u (d) are for upstream (downstream) cell of polarised target
arrows indicate transverse polarisation of corresponding cells
raw asymmetry ε from the fit to DR(η)
dilution factor f ≈ 0.38

29. ρ0 transverse target spin asymmetry from COMPASS
new
asymmetry for deuteron target consistent with zero
ongoing work on:
longitudinal/transverse separation
separation of incoherent/coherent
in 2007 data taken with transversely polarised proton target (NH3)

30. Exclusive π+ production from HERMES e p → e n π+~ ~
at leading twist σL sensitive to GPDs H and E
at small |t’| E dominates as it contains t-channel pion-pole ~
L/T separation not possible at HERMES, σT expected to be supressed as 1/Q2
σL VGG LO
σL VGG LO+power corrections
σT + ε σL Regge model (Laget)
LO calculations strongly underestimate the data
data support magnitude of the power corrections (kt and soft overlap)
Regge calculations provides good description of the magnitude of σtot
and of t’ and Q2 dependences

31. Beam spin asymmetry in exclusive π0 production from CLAS~
at leading twist σL sensitive to GPD H
e p → e p π0
no t-channel pion-pole (in contrast to exclusive π+ production)
any non-zero BSA would indicate L-T interference, i.e. contribution not described
in terms of GPD’s
preliminary
a fit α sinφ
Regge model (Laget)
pole terms (ω, ρ, b1) + box diagrams (cuts)
first measurement of BSA for exclusive π0 production above resonance region
sizeable BSA (0.04 – 0.11) indicate that both T and L amplitudes contribute
necessity for L/T separation and measurements at higher Q2

32. Cross sections for exclusive π0 production from JLAB HALL A DVCS Collab.
h = ±1 is the beam helicity
from P. Bertin, Baryon-07
t-slope close to 0, maybe even small negative

33. dashed – prediction for σL from VGG model using GPDs
Vanderhaeghen, Guichon, Guidal

34. Summary for existing measurements
New precise data on cross sections result in significantly
more stringent constraints on the models for GPDs
Results on DVCS promissing;
indication of scaling and handbag dominance in valence region
good agreement with NLO for HERA data
To describe present data on DVMP, both at large and small x,
including power corrections (or higher order pQCD terms) is essential
First experimental efforts to constrain GPD E and quark orbital momentum

35. Precision of DVCS unpolarized cross sections at eRHIC (1)
HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s pb-1/day
For one out of 6 W intervals (30 < W < 45 GeV)
eRHIC HE setup
σ(γ*p → γ p) [nb]
Lint = 530 pb-1
(2 weeks)
<W> = 37 GeV
Q2 [GeV2]
eRHIC measurements of cross section will provide significant constraints

36. Precision of DVCS unpolarized cross sections at eRHIC (2)
HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s pb-1/day
LE setup: e+/- ( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s pb-1/day
For one out of 6 Q2 intervals (8 < Q2 < 15 GeV2)
eRHIC
Lint = 530 pb-1
Lint = 180 pb-1
σ(γ*p → γ p) [nb]
<Q2> = 10.4 GeV2
W [GeV]
EIC measurements of cross section will provide significant constraints
also significantly extend the range towards small W

37. Towards 3D mapping of parton structure of the nucleon at EIC
(assumed for illustration)
α’ = GeV-2
Lint = 4.2 fb-1
simultaneous data in several (6) Q2 bins
Sufficient luminosity to do triple-differential measurements in x, Q2, t at EIC!

38. Lepton charge asymmetry at eRHIC
model of Belitsky, Mueller, Kirchner (2002) for GPDs at small xB
parameters of sea-quark sector fixed using H1 DVCS data (PL B517 (2001))
except magnetic moment κsea (-3 < κsea < 2), which enters Ji’s sum rule for Jq
BMK use ‘improved’ charge asymmetries ACcosφ and ACsinφ
HE setup, Lint = 530 pb-1 divided equally between e+ and e-
Q2 [GeV2]
W = 75 GeV , -t = 0.1 GeV2
W [GeV]
Q2 =4.5 GeV2 , -t = 0.1 GeV2
κsea = 2
κsea = -3
κsea = -3
κsea = 2
measurements of asymmetries at EIC sensitive tool to validate models of GPDs

39. Summary for DVCS at eRHIC
Wide kinematical range, overlap with HERA and COMPASS
1.5 ·10-4 < xB < sensitivity to quarks and gluons
1 < Q2 < 50 GeV sensitivity to QCD evolution
DVCS cross sections - significant improvement of precision wrt HERA
Intereference with BH - pioneering measurements for a collider
powerfull tool to study DVCS amplitudes
full exploratory potential, if e+ and e- available as well as longitudinaly and transversely polarized protons
Sufficient luminosity to do tripple-differential measurements in xB, Q2, t

40. Backup slide

41. A simulation of DVCS at eRHIC
HE setup: e+/- (10 GeV) + p (250 GeV) L = 4.4 · 1032 cm-2s pb-1/day
LE setup: e+/- ( 5 GeV) + p ( 50 GeV) L = 1.5 · 1032 cm-2s pb-1/day
diam. of the pipe cm, space for Central Detector: ≈ +/- 280 cm from IP
acceptance of Central Detector (improved ZDR) 2° < θlab < 178°
acceptance simulated by kinematical cuts
event generator: FFS (1998) parameterization with R=0.5, η = 0.4 and b = 6.2 GeV-2
Ee’ > Emin GeV Eγ > 0.5 GeV
2° < θe’ < 178° ° < θγ < 178°
Emin = 2 GeV (HE) or 1 GeV (LE)
DVCS + BH + INT cross section
kinematical smearing: parameterization of resolutions of H1 (SPACAL, LArCal) + ZEUS (θγ, φγ) + expected for LHC (θe’ , φe’ )
HE setup
LE setup
1 < Q2 < 50 GeV2
10 < W < 90 GeV
0.05 < |t| < 1.0 GeV2
due to acceptance and to ‘reasonably’ balance DVCS vs. BH following kinematical range chosen
1 < Q2 < 50 GeV2
0.05 < |t| < 1.0 GeV2
2.5 < W < 28 GeV