1. Studies of hard exclusive processes at CLAS
Harut Avakian
Jefferson Lab
GPD2006 Workshop , Trento, June 8, 2006
Introduction
Exclusive processes
Photons (DVCS)
Pseudoscalar mesons
Vector mesons
Summary
* In collaboration with V.Burkert and L.Elouadrhiri

2. Physics Motivation
Describe the complex nucleon structure in terms of quark and gluon degrees of freedom.
hard gluon
DVCS
DVMP
longitudinal photons
hard vertices
DVCS – for different polarizations of beam and target provide access to different combinations of GPDs H, H, E
DVMP for different mesons is sensitive to flavor contributions (r0/r+ select H, E, for u/d flavors, p, h, K select H, E) ~
Study the asymptotic regime and guide theory in describing HT.

3. Electroproduction Kinematicsg e q p
g*->g require a finite longitudinal momentum transfer defined by the generalized Bjorken variable x
Longitudinal and transverse polarizations mix by qg

4. Asymmetry in DVCS Experiments
dQ2dxBdtd
~ |TDVCS + TBH|2
GPD
CLAS at 4.3 GeV
HERMES 27 GeV
A(f) = asinf + bsin2f
S. Stepanyan et al. Phys. Rev. Lett. 87 (2001)
A. Airapetian et al. Phys. Rev. Lett. 87 (2001)

5. f-dependent amplitudeBH
5.7 GeV
f=0
f=45
f=90
DVCS
x=0.25
Strong dependence on kinematics of prefactor f-dependence, at y≈ycol,P1(f)→0
Fraction of pure DVCS increases with t and f

6. GPDs from ep->e’p’g
Requirements for precision (<15%) measurements of GPDs from DVCS SSA:
Define the procedure to extract GPDs from ALU
effect of finite bins (prefactor variations) ~10%
other moments
Define background corrections
pion contamination ~10%
radiative background
ADVCS
A complete simulation of the whole chain from particle detection to GPD extraction, including the DVCS and background (counts, asymmetries) as well as extraction procedure (averaging over kinematic factors) required to ensure the reliability of measured GPDs.

7. The CLAS Detector ~ 200 physicists 37 institutions Q2
High luminosity, polarized CW beam
Wide physics acceptance, including exclusive, semi-inclusive processes, current and target fragmentation
Wide geometric acceptance, allowing detection of multi-particle final states
~ 200 physicists
37 institutions Q2
Forward CALO

8. DVCS event samples Angular cut most efficient in separating p0
3 event samples with W>2 (after data quality cuts)
epg(DVCS)
epX photons in CLAS (~2M events)
tight cuts on PID,missing mass MX, no other tracks
2) epg photon in Calorimeter (~ events)
cut on the direction qgX<0.015,
3) epgg photon(p0) in Calorimeter (~70000 events)
cut on the direction qpX<0.02,
epg(p0)
Angular cut most efficient in separating p0
Kinematic coverage of 5.75 GeV(red) and 5.48(blue) CLAS data sets

9. DVCS and p0 MC vs Data epp0 epg pg
Exclusive photon production simulated using a realistic MC(based on Korotkov’s code)
Exclusive p0 production simulated using a realistic MC (based on PDFs, fitted to CLAS data)
Kinematic distributions in x,Q2 and t for p0 tuned to describe the CLAS data (b=1)

10. g MC vs Data
Region where BH totally dominates (small t, small photon qLAB)
Negligible DVCS x-section, small p0 contamination
Rapidly changing prefactors, mainly small f, hard to detect photons
Large angles
Uniform coverage in angle f, photon measurement less challenging
DVCS x-section non negligible introduce some model dependence)
p0 dominates the single photon sample (in particular at low Q2 and large t )
MC Kinematic distributions in x,Q2,t consistent with the CLAS data

11. p0 contamination in epg-sample
CLAS forward Calo g
single photons from p0 p0
BH-DVCS g
(photon lab. angle)
At large angles detected photon can be used as veto (epX-sample).
Cut on the direction of the measured photon (require detection of proton) significantly reduce the contamination (epg-sample).

12. p0 contamination
Main unknown in corrections of photon SSA are the p0 contamination and its beam SSA.
Extract from epp0 MC the ratio of single to double photon detection probability
MC the ratio for 0 g
1.0<Q2<2.0,
0.1<x<0.3 MC
Use epp0 MC and data to estimate the contribution of p0 in the epg and epX samples
Contamination from p0 photons increasing at large t and x .

13. Beam SSA after correction for p0 contamination
epg
VGG with TM correction
before
Open symbols raw asymmetry
Filled symbols asymmetry corrected for p0
after
Subtract p0 contribution for each f bin
Two data sets (e16 at 5.7 GeV,e1f at 5.5 GeV) with different torus field (different kinematic coverage) and beam energy are consistent.

14. GPD extraction from Beam SSA:MC
corrected for p0
GPDs: MC-input
epg
H+x(F1+F2)H +kF2E
raw asymmetry
0.3<x<0.4
only H
2<Q2<3
Divide the ALU by the kinematic factor cLU extracted from event by event sum
Extraction procedure tested with GEANT based MC with realistic x-sections for DVCS and pions recover input GPDs ~

15. GPD extraction from Beam SSA:Data
ALU corrected for p0 (bin by bin)
H → ratio of the ALU and prefactor cLU calculated for all events in a bin (averaged over f)
VGG with TM
BMK*
GPD sums (H) extracted for two non-overlapping data sets epX(ep0g) and epg consistent

16. DVCS SSA kinematic dependences at 5.7 GeV
PRELIMINARY
-t<0.5 GeV2
Fine binning allows to observe the x and Q2 dependence
Preliminary data for fully exclusive epg is consistent with the ep data and consistent with GPD base predictions
Need realistic GPD models to perform fits

17. Calorimeter and superconducting magnet within CLAS torusγ
Dedicated CLAS DVCS experiment
→ Dedicated detection of 3 particles e, p and γ in final state
→ Large kinematical coverage in xB and t
p0 e1DVCS
More in F.-X. Girod’s talk
Calorimeter and superconducting magnet within CLAS torus
Improves significantly the epg and in particular the epgg samples at low t
p0 e1DVCS
p0 e16/e1f
424 PbWO4 crystals
CLAS PRELIMINARY
Significant beam SSA measured for p0
dedicated calorimeter (IC) detect photons from 5o

18. Target Spin Asymmetry (LTSA): t- Dependence from CLAS
Unpolarized beam, longitudinal target:
DsUL ~ sinfIm{F1H+x(F1+F2)(H +.. }
DsLL ~ cosfRe{F1H+x(F1+F2)(H +.. } ~
Kinematically suppressed g p0
First data available(5 CLAS days), more(60 days) to come at 6 GeV
Measurements with polarized target will constrain the polarized GPDs and combined with beam SSA measurements would allow precision measurement of unpolarized GPDs.

19. / Ratio p/h= MX Mgg Eides,Frankfurt,Strikman 1998
g/p h r/w
Eides,Frankfurt,Strikman 1998
W >2 GeV
5.75GeV (0<t<1)
Q2>1.5GeV2 MX p0 h
Mgg /
Ratio p/h=
Requires separation of longitudinal and transverse contributions

20. Exclusive p+p- and p+p0 e p e p  e- p  e- nr+ π+ π- π+π0
Provide access to different combinations of orbital momentum contributions Ju,Jd
r0 -> 2Ju + Jd, r+ -> Ju - Jd

21. Exclusive 2 pion production: MX (epX)
CLAS (5.75 GeV)
D++ ,N* f2 f0 r
Significant background from exclusive 2 pion production

22. Exclusive ρ meson production: g*p → pρ0
CLAS (5.75 GeV)
GPD formalism (beyond leading order) describes approximately data for xB<0.4, Q2 >1.5 GeV2
Analysis in progress
GPD
(MG-MVdh)
Decent description in pQCD framework already at moderate Q2

23. Exclusive r0 production on transverse target
2D ┴(Im(AB*))/p
AUT = -
|A|2(1-x2) - |B|2(x2+t/4m2) - Re(AB*)2x2
A ~ 2Hu + Hd
B ~ 2Eu + Ed r0
A ~ Hu - Hd
B ~ Eu - Ed r+ r0
Eu, Ed needed for
angular momentum
sum rule.
K. Goeke, M.V. Polyakov,
M. Vanderhaeghen, 2001
Asymmetry is a more appropriate observable for GPD studies at JLab energies as possible corrections to the cross section are expected to cancel

24. CLAS12 High luminosity polarized (~80%) CW beam
Wide geometric acceptance
Wide physics acceptance
Provides new insight into
- quark orbital angular momentum contributions
- 3D structure of the nucleon’s interior and correlations
- quark flavor polarization

25. CLAS12 - DVCS/BH Target Asymmetry
e p epg
Transversely polarized target
Sample kinematics
E = 11 GeV
Q2=2.2 GeV2, xB = 0.25, -t = 0.5GeV2
DsUT ~ sinfIm{k1(F2H – F1E) +…}df
AUTx Target polarization in scattering plane
AUTy Target polarization perpendicular to
scattering plane
Asymmetry highly sensitive to the u-quark contributions to the proton spin.

26. Summary
DVCS beam spin asymmetries was extracted from two different CLAS data sets and for two different samples and was used to study GPDs.
DVCS target spin asymmetry was extracted and compared with GPD based predictions (in publication) .
Studies of the exclusive p0 background performed. Beam and target SSA extracted.
High luminosity, polarized CW beam, wide kinematic and geometric acceptance allow studies of exclusive meson production in hard scattering kinematics, providing data needed to study GPDs.
And here is the summary.
I’ll just add that one week ago the CD1 (stands for critical decision step 1) was approved
Giving a green light for 12 GeV upgrade to proceed
CLAS12 Full acceptance, general purpose detector for high luminosity electron scattering experiments, is essential for high precision measurements of 3D PDFs in the valence region.

27. support slides…

28. Deeply Virtual Compton Scattering ep→e’p’g
Interference responsible for SSA, contain the same lepton propagator P1(f) as BH
The DVCS SSA appeared to be very different compared to more familiar pion
SSA and the main difference is due to BH propagators. The Interference
And BH terms have the same prefactor and are both increasing in the region
Where the Propagator is small.
A detailed structure of the beam SSA is shown here and as we can see the measurement
Of the combination of GPDs is starit forward in the region where the DVCS cros section is negligible
And requires only the knowledge of the BH moments.
GPD combinations accessible as azimuthal moments of the total cross section.
Way to access to GPDs

29. g MC vs Data All single photons DVCS data DVCS MC
From the comparison of reconstructed data and MC for exclusive pi0,
You can see that we have a pretty good control over the pi0 background.
Shown here are distributions for exclusive pi0, for pion energy,…..
Exclusive photon production simulated using a realistic MC(based on S.Korotkov’s code)
Kinematic distributions in x,Q2,t consistent with the CLAS data

30. Target Spin Asymmetry: t- Dependence
Unpolarized beam, longitudinal target:
DsUL ~ sinfIm{F1H+x(F1+F2)(H +.. }
DsLL ~ cosfRe{F1H+x(F1+F2)(H +.. } ~
Kinematically suppressed
Target SSA measurements for the DVCS (Deeply Virtual Compton Scattering) process,
Providing acces to a different combination of H and H~ compared to the beam SSA measurements
In DVCS.
Some data is already available to constrain the GPD H~ both from HERMES and CLAS.
CLAS projections correspond to 60 days of running at
same conditions as for the SIDIS experiment (simultaneous measurements).
First data available(5 CLAS days), more(60 days) to come at 6 GeV
Measurements with polarized target will constrain the polarized GPDs and combined with beam SSA measurements would allow precision measurement of unpolarized GPDs.

31. Target Spin Asymmetry: t- Dependence
Unpolarized beam, longitudinal target:
DsUL ~ sinfIm{F1H+x(F1+F2)(H +.. }
DsLL ~ cosfRe{F1H+x(F1+F2)(H +.. } ~
Kinematically suppressed
CLAS 5.7
CLAS+IC
Target SSA measurements for the DVCS (Deeply Virtual Compton Scattering) process,
Providing acces to a different combination of H and H~ compared to the beam SSA measurements
In DVCS.
Some data is already available to constrain the GPD H~ both from HERMES and CLAS.
CLAS projections correspond to 60 days of running at
same conditions as for the SIDIS experiment (simultaneous measurements).
First data available(5 CLAS days), more(60 days) to come at 6 GeV
Measurements with polarized target will constrain the polarized GPD and combined with beam SSA measurements would allow precision measurement of unpolarized GPDs.

32. g MC vs Data
Exclusive photon production simulated using a realistic MC(based on S.Korotkov’s code)
From the comparison of reconstructed data and MC for exclusive pi0,
You can see that we have a pretty good control over the pi0 background.
Shown here are distributions for exclusive pi0, for pion energy,…..
Exclusive photon production simulated using a realistic MC(based on S.Korotkov’s code)
Kinematic distributions in x,Q2,t consistent with the CLAS data

33. p0 contamination Main unknown in corrections of photon SSA
are the p0 contamination and its beam SSA.
Use epgg to estimate the contribution of p0 in the ep and epg samples
1.0<Q2<2.0, 0.1<x<0.3
1.0<Q2<2.0, 0.1<t<0.45
Here you can see the pio contamination in the DVCS sample for a certain beam x,Q2 and x (ratio of
Number of photons from pi0 to the total number of photons) as a function of the azimuthal angle.
The right plot shows the beam SSA extracted from the CLAS data.
The contamination is increasing at large t.
Contamination from p0 photons increasing at large t and x and also at large f.
Significant SSA measured for exclusive p0s also should be accounted

34. pion SSA from r(p+p-/p+p0) r+
PYTHIA at 5.7 GeV r0
Larger fraction of p+ from r at low x and large z
p+ SSA at large z may also have a significant (~20%) contribution from r
Exclusive r (higher twist for SIDIS) crucial for pX and ppX studies

35. GPD extraction from Beam SSA:MC
GPDs: MC-input
corrected for p0
epg
epX
0.3<x<0.4
2<Q2<3
only H
Here you can see the pio contamination in the DVCS sample for a certain beam x,Q2 and x (ratio of
Number of photons from pi0 to the total number of photons) as a function of the azimuthal angle.
The right plot shows the beam SSA extracted from the CLAS data.
The contamination is increasing at large t.
Divide the ALU by the kinematic factor extracted on event by event sum (filled symbols: MC, empty: data)
Statistics enough to separate H and H+x(F1+F2)H +kF2E (blue line) ~

36. correcting for p0 contamination
Here you can see the pio contamination in the DVCS sample for a certain beam x,Q2 and x (ratio of
Number of photons from pi0 to the total number of photons) as a function of the azimuthal angle.
The right plot shows the beam SSA extracted from the CLAS data.
The contamination is increasing at large t.
Denominator corrected for the pion contamination for each bin

37. GPDs from ep->e’p’g
Requirements for precision (<10%) measurements of GPDs from DVCS SSA:
Define the procedure to extract GPDs from ALU
effect of finite bins ~10%
Define background corrections
pion contamination ~10%
radiative background
VGG-99
p0 dominates the single photon sample at low Q2 in the kinematics where BH is small
Precision measurements of GPDS require a detailed understanding of possible
Background. In addition to the BH DVCS and there interference there are other processes
Giving contributions to the observed exclusive photon sample, like pi-0 production and so called associated DVCS.
So far the data was always plotted as the beam spin asymmetry,
While the relevant quantity is the corresponding sin\phi moment.
Typically the data was fitted by a simple sum of sin\phi and sin2\phi terms asumming
No other moments play any role. For precision analysis, in particular for the sin2\phi moment other moments may play a significant role.
Because of the rapidly changing prefactor, finite binning in x,Q^2 and phi introduces
Terms with propagators which canceled in theory the ratio of Interference term and the BH contribution
does not exactly cancel out in ratio of averages.
Different procedures were applied to eliminate the pi0 background. For precision measurements
Understanding of the background will be important and a possible approach will be to correct for pi0
Contribution instead of trying to eliminate it.

38. CLAS/DVCS (ep → epX) at 5.75 GeV
VGG
PRELIMINARY
(not for circulation)
0.15 < xB< 0.4
1.50 < Q2 < 4.5 GeV2
-t < 0.5 GeV2 ~
DsLU ~ sinfIm{F1H + x(F1+F2)H +kF2E}
DVCS beam SSA consistent with GPD based predictions
No significant sin2f observed
The final state photon was not detected and p0 contamination estimate relies on MC

39. SSA in exclusive pion production
Target SSA at 27.5 GeV
Beam SSA ALU at 6GeV
ep->e’p+n
HERMES
W2>4GeV2, Q2>1.5GeV2
CLAS PRELIMINARY -
Beam SSA and longitudinally pol. target SSA provide information on HT ( 0 at leading order)

40. Contributions to ep->e’p’gBH
f=0
f=45
f=90
DVCS
M. Vanderhaeghen et al. Phys.Rev.D60:094017,1999

41. BH cosf moment BH cosf moment can generate ~3% sin2f in the ALU
Another factor are other azimuthal moments in the cross section, in particular
The BH cos\phi, which can be as large as 20%. This is known precisely and
Was included in our analysis.
BH cosf moment can generate ~3% sin2f in the ALU

42. p0 beam SSA cross section
Main unknown in corrections of photon SSA
are the p0 contamination and its beam SSA.
Use epgg to estimate the contribution of p0 in the ep and epg samples
1.6<Q2<2.6, 0.22<x<0.32
CLAS 5.7 GeV
Here you can see the pio contamination in the DVCS sample for a certain beam x,Q2 and x (ratio of
Number of photons from pi0 to the total number of photons) as a function of the azimuthal angle.
The right plot shows the beam SSA extracted from the CLAS data.
The contamination is increasing at large t.
Contamination from p0 photons increasing at large t and x and also at large f.
Significant SSA measured for exclusive p0s also should be accounted

43. Hall A at 6 GeV, future ideas
Extend current configuration to xBj=0.6, Q2=4.0 GeV2
Add magnetic field near target to suppress Møller electrons. Increase luminosity to 1038/cm2/sec:
H,D (e,e’g)X : s(MX2)  0.2 GeV2 < (M+mp)2-M2
Add Magnetic field and tracking detectors in front of calorimeter sufficient to identify charge of e+e- pairs:
H(e,e’e+e-)p at small e+e- mass  [GPD/x]x=x
(Suppress p0 Dalitz decay by missing mass).

44. CLAS12 - DVCS/BH Beam Asymmetry
e p epg
DsLU~sinfIm{F1H+..}df
Sensitive to GPD H
L = 1x1035
T = 2000 hrs
ALU
E=4.3 GeV
Now we turn to exclusive measurements with CLAS-12 which is one of main driving forces of the JLAB upgrade to 12 GeV.
First DVCS beam SSA. Left plot shows published CLAS data, which is integrated over all t,x,Q^2 bins.
Right plot shows projections of the same asymmetry in tiny bins in x,Q^2
(\Delta Q2 = 1 GeV2, \Delta x = 0.05) as a function of t.
S. Stepanyan et al. Phys. Rev. Lett. 87 (2001)

45. Collinearity kinematics
HERMES
CLAS-5.7
Strong dependence of collinearity kinematics changes region of enhanced t as afunction of beam energy

46. CLAS12 - DVCS/BH Target Asymmetry
e p epg
L = 2x1035 cm-2s-1
T = 1000 hrs
DQ2 = 1GeV2
Dx = 0.05
E = 11 GeV
Longitudinally polarized
target ~
Ds~sinfIm{F1H+x(F1+F2)H...}df
CLAS preliminary
AUL
E=5.75 GeV
This slide shows target SSA for DVCS. Left plot existing data and right future projections.
<Q2> = 2.0GeV2
<x> = 0.2
<-t> = 0.25GeV2

47. Meson production in GPD framework
Only longitudinal photons
GPDs
GPDs
Different final state mesons filter out different combinations of unpolarized (H,E) and polarized (H,E) GPDs.
2. Studies needed to define on how far is the asymptotic regime and guide theory in describing HT. ~ ~

48. [ ] ò Quark Angular Momentum Sum Rule ½ = ½ (Du+Dd+Ds) + Lq + Jg
GPDs Hu, Hd, Eu, Ed provide access to total quark
contribution to proton angular momentum.
Proton’s spin
½ = ½ (Du+Dd+Ds) + Lq + Jg
J q [ ] ò - x +
- J G = = 1 ) , q( 2 E H
xdx
J q
X. Ji, Phy.Rev.Lett.78,610(1997)
One of the most exciting features of GPDs as pointed out by ..
Is the direct link with elusive orbital momentum the main focus of this workshop.
So the goal will be to measure the GPDs in accessible kineamtics, extrapolate to inaccessible and
Calculate the orbital momentum.
Large x contributions important.

49. Form Factor Studies Sachs Form Factors ~9 0% GE(t)=F1(t)+t/4M2*F2(t)
GM(t)=F1(t)+F2(t) n
It was shown that Formfactors measured at large t-can provide important imformation
On the x-dependence of GPDs as the integrals at higher t are more sensitive to large
X-behaviour of GPDs relevant for the OAM sum rule.
This plots show fits to data, at high t coming from Jlab experiments on Electric (recoil pol. Technique)
and magnetic FFs of proton and neutron(double polarization he3, and deuteron elastic).
New experiments will extend proton Ge/Gm to 9(14) and neutron to 3.4(7)
More data expected in 2006/2007

50. Form Factor Studies
Use various parameterizations for GPDs to fit the existing form factor data
A.Afanasev hep-ph/
Diehl et al, Eur.Phys.J c39 (2005)
M.Guidal et al PRD (2005)
Different parameterizations yield different contributions for quarks to the OAM
A)Large Ld and small Lu
B)Sum of Lu and Ld small
Different groups inclusing Andrei afanasev, Diehl and Guidal with collaborators
used different parameterizations for GPDs to fit the data on FFs.
The main issue here is that different realistic fits produce different values for contributions of
U and d quark to the total orbital momentum as fits were done at large t requiring further extrapolations.
The table I borrowed from Afanasev’s paper Shows spread for 3 different parameterizations.
It is clear that more observables are needed, with more sensitivity at small t and large x.
DVCS is one of the cleanest processes providing info on GPDs.
Issues: different realistic fits to FFs produce different values for Lq
fits done at high t, need to be extrapolated to t→0
More observables needed for detailed studies of GPDs and the
OAM (RCS,DVCS,DVMP)

51. Transversity GPDs with exclusive r,r+
hard
Large momentum
transfer, large rapidity gap
Virtual photon replaced with 2 gluons
hard
(courtesy M. Vanderhaeghen)
GPD
Smaller rapidity gap
r+ selects quark antiquark exchange with the nucleon.
Long distance part described by GPD HT
Ivanov et al. hep-ph/

52. Hard Exclusive Meson Production(HMP)
Belitsky hep-ph/ (ep->e’p+n)
Q2=4 GeV2 ~
Corrections applied
Im H
Q2=10 GeV2
D2=-0.3GeV2 ~ E ~
ReH
No significant variations in SSA “precocious scaling”
Only longitudinal cross sections
Large power correction to cross section

53. Physics Motivation
Describe the complex nucleon structure in terms of quark and gluon degrees of freedom.
parton distributions
angular momentum
gluon polarization
hard
Exclusive production of photons and hadrons in hard scattering kinematics.
test QCD based predictions (assuming factorization) for different observables and measure underlying GPDs.
studies of applicability of partonic picture in exclusive reactions
GPDs
The main goal is to study the nucleon structure in terms of partonic degrees of freedom.
From three main ingredients, JLab program is focused on parton distributions and in particular
Observables related to angular momentum of quarks. From 8 GPDs
Describing the nucleon structure we have relatively clear understanding how to access first 4,
And we hope that in future we may be able to probe transversity GPDs using their relations
With TMDs. the Boer-Mulders.
Main processes of interest are exclusive production of photons and hadrons in hard scattering
Kinematics. While photon production is already proved to be a clean tool to acces GPDs, work is also going on with
Pseudoscalar and vector mesons to study the applicability of partonic picture in exclusive reactions

54. Ratio p/h= / Eides,Frankfurt,Strikman 1998 CLAS Preliminary
Requires separation of longitudinal and transverse contributions

55. Flavor Separation and Helicity-Dependent GPDs
Ok now we turn to mesons where things are less clear.
As it was already discussed mesons if the GPD formalism will work will
Provide important information on flavor dependence.
Vector and pseudoscalar meson production allows to separate flavor and isolates the helicity-dependent GPDs.

56. DVCS Experiments CLAS at 4.3 GeV HERMES 27 GeV A(f) = asinf + bsin2f
Published dvcs experiments on DVCS.
This was a big step. The data was enough to demonstrate the existence of
The signal, it was to few to plot any significant kinematic dependences.
Since then a lot more data was accumulated many groups are doing analysis.
So what are the main problems we try to overcome?
A(f) = asinf + bsin2f
S. Stepanyan et al. Phys. Rev. Lett. 87 (2001)
A. Airapetian et al. Phys. Rev. Lett. 87 (2001)

57. Deeply Virtual Compton Scattering ep->e’p’g
dQ2dxBdtd
~ |TDVCS + TBH|2
DVCS BH
GPD
TBH : given by elastic form factors
TDVCS: determined by GPDs
Polarized beam, unpolarized target: ~
DsLU ~ sinfIm{F1H + x(F1+F2)H +kF2E}
DVCS
Kinematically suppressed BH
Unpolarized beam, longitudinal target: ~
DsUL ~ sinfIm{F1H+x(F1+F2)(H +.. }
With unpolarized and polarized targets the single photon production cross section
Has contributions from DVCS itself from Bete-Heitler and from their interference.
The plot shows contributions from BH (red line) DVCS (blue line) and total for
CLAS, HERMES and COMPASS energies as a function of momentum transfer to proton (t=(p1-p2)^2).
Corresponding contributions from the interference term \sigma_LU, \sigma_UL and \sigma_UT are sensitive
To different combinations of GPDs H, H~ and E.
Measurements of corresponding azimuthal moments will allow separation of different contributions
and extraction of underlying GPDs. Measurement of both GPDs H~ and E~ require a good knowledge of
H, so the measurement of H is the main focus.
Kinematically suppressed
x = xB/(2-xB ),k = t/4M2
Unpolarized beam, transverse target:
Different GPD combinations accessible as azimuthal moments of the total cross section.
DsUT ~ sinfIm{k1(F2H-F1E ) +.. }
Kinematically suppressed