1. Deep Virtual Compton Scattering at Jlab Hall A
Second Workshop on the
QCD Structure of the Nucleon
12-16 June 2006
Villa Mondragone, Italy
Deep Virtual Compton Scattering at Jlab Hall A
Charles E. Hyde-Wright
Old Dominion University, Norfolk VA
Based on the work of A. Camsonne
the DVCS Hall A Ph.D. students: M. Mazouz
C. Munoz Camacho

2. QCD, Confinement, and the Origin of Mass
We have a good understanding of the strong interaction at extreme short distance with perturbative QCD
We understand the long distance properties of the strong interaction in terms of Chiral Perturbation Theory
Confinement and the origin of ordinary mass (baryon mass) occurs at an intermediate distance scale.
Lattice QCD and many semi-phenomenological models give us a great deal of insight into the structure of hadrons at the confinement scale.
Nuclear binding (e.g. Bdeuteron=2.2 MeV, r-process nuclei…) are 1% effects or smaller of the ‘confinement’ scale ≈ 300 MeV/c.
We need experimental observables of the fundamental quark and gluon degrees of freedom of QCD, in coordinate space.
Forward parton distributions do not resolve the partons in space.
Elastic Electro-Weak Form Factors measure spatial distributions, but the resolution cannot be selected independent of momentum transfer.
Generalized Parton Distributions (GPD)!
x, momentum fraction variables
t=2.  Fourier Conjugate to impact parameter of quark or gluon.
Q2 = Resolution of probe.

3. Experimental observables linked to GPDsq’
q = k-k’ Q2 = q2>0 =q-q’ t=2
s = (k+p)2 xBj = Q2/(2p·q) W2 = (q+p)2
Using a polarized beam on an unpolarized target,
2 (actually 6) observables can be measured:
At JLab energies, |TDVCS|2 is small:
|TDVCS|2 / |TBH|2 ≈ -t xBj2 s2 / Q6
M. Diehl, yesterday

4. Into the harmonic structure of DVCS
|TBH|2
Interference term
e-’ j p e- g*
hadronic plane
leptonic plane g k k’ p p’ q’
BH propagators j dependence
Belitsky, Mueller, Kirchner

5. Tests of the handbag dominance
+ VdT(DVCS) + dTT(DVCS) cos(2)
+ VdLT’(DVCS) sin
Twist-2 terms should dominate s and Ds
Subject to ``reasonableness’’ of Twist-3 Matrix Elements
2. All coefficients have known Q2-dependence (Powers of -t/Q2 or (tmin-t)/Q2) which can be incorporated into analysis.
3. Angular Harmonic terms ci, si, are Q2-independent in leading twist (except for QCD evolution).

6. Designing a DVCS experiment
Measuring cross-sections differential in 4 variables requires:
Good identification of the experimental process, i.e. exclusivity
With perfect experimental resolution
H(e,e’)X
resonant or not
If the Missing Mass resolution is good enough, a tight cut removes the associated pion channels, but deep virtual po electroproduction still must be be subtracted with a statistical sample.

7. e p → e (p) g Hall A DVCS philosophy
Precision measurement of kinematics
Precision knowledge of the acceptance
High Resolution Spectrometer (HRS) for electron
Simple, high performance 11x13 element (3x3x19cm3) PbF2 Calorimeter
Waveform digitizing
Low resolution detection of proton direction
e p → e (p) g
Scattered electron
The HRS acceptance
is well known
Emitted photon
The calorimeter has a simple
rectangular acceptance
R-function
cut g
Acceptance matching by design !
Virtual photon « acceptance » placed at center of calorimeter g*
Simply:
t: radius
j: phase

8. Digital trigger on calorimeter and fast digitizing-electronics
1. HRS Trigger
5. Digitize Waveform
2. ARS Stop
6. Pulse fit In
1GHz Analog Ring Sampler
(ARS)
t (ns)
4. Validate or Fast Clear (500ns)
3. S&H 60ns gate 
FPGA Virtual Calorimeter
PbF2 blocks
Z>>50
Fast Digital Trigger
4. Find 2x2 clusters>1GeV

9. E00-110 experimental setup and performances
5x20 block plastic scintillator array
15cm LH2 target
Left Hall A HRS with electron package
75% polarized 2.5uA electron beam
75% polarized 2.5uA electron beam
15cm LH2 target
Left Hall A HRS with electron package
11x12 block PbF2 electromagnetic calorimeter
5x20 block plastic scintillator array
11x12 block PbF2 electromagnetic calorimeter
Pbeam=75.32% ± 0.07% (stat)
Vertex resolution
1.2mm
Dt (ns) for 9-block
around predicted
« DVCS » block

10. ARS system in a high-rate environment
5-20% of events require a 2-pulse fit
Maintain Energy & Position Resolution independent of pile-up events
Optimal timing resolution
10:1 True:Accidental ratio at L=1037/(cm2 s) unshielded calorimeter
Dt (ns)
HRS-Calo
coincidence
st=0.6 ns
2ns beam structure

11. E00-110 kinematics The calorimeter is centered
on the virtual photon direction.
Acceptance: < 150 mrad
50 days of beam time in the fall 2004, at 2.5mA intensity

12. Analysis – Looking for DVCS events
HRS: Cerenkov, vertex, flat-acceptance cut with R-functions).
Calo: 1 cluster in coincidence in the calorimeter above 1.2GeV.
Coincidence: subtract accidentals, build missing mass of H(e,g)X system.
Generate estimate of 0 H(e,eY events from measured H(e,e)Y events.
H(e,e’)X: MX2
kin3
Exclusive DVCS events
H(e,e’) Y
H(e, e’ N 
Threshold

13. H(e,e’) Exclusivity [ H(e,e’)X - H(e,e’)Y ]: Missing Mass2
H(e,e’p
H(e,e’…
H(e,e’p) sample
<2% in estimate of
H(e,e)N…
below threshold MX2<(M+m)2
H(e,e’p) simulation,
Normalized to data

14. Analysis – Extraction of observables
Re-stating the problem (difference of cross-section):
Observable
Kinematic
factors
GPD !!!

15. Analysis – Calorimeter acceptance
The t-acceptance of the calorimeter is uniform at low tmin-t:
Xcalo (cm)
Ycalo (cm)
Calorimeter
5 bins in t:
Min Max Avg
-0.40
-0.35
-0.37
-0.30
-0.33
-0.26
-0.28
-0.21
-0.23
-0.12
-0.17
Large-t
j dependence

16. d Difference: Extraction of observables
Averaged over t
<-t>=0.23 GeV2, <xB>=0.36

17. Analysis – Difference of counts – 2 of 4 bins in t
Twist-3 contribution is small
po contribution is small
po is Twist-3 (dLT’)
Acceptance
effects
included in fit

18. Total cross section and GPDs
| |
Interesting !
Only depends on H and E
with

19. Tests of scaling yield positive results
Conclusion at 6 GeV
High luminosity (>1037) measurements of DVCS cross sections are feasible using trigger + sampling system
Tests of scaling yield positive results
No Q2 dependence of CT2 and CT3
Twist-3 contributions in both Ds and s are small
Note: DIS has small scaling violation in same x, Q2 range.
In cross-section difference, accurate extraction of Twist-2 interference term
High statistics extraction of cross-section sum.
Models must calculate Re[BH*DVCS]+|DVCS|2
 = [d(h=+) + d(h=-) ] ≠ |BH|2
Relative Asymmetry contains DVCS terms in denominator.

20. Hall A at 11 GeV (in preparation for PAC30
HALL A: H(e,e’)
3,4,5 pass beam: k = 6.6, 8.8, 11 GeV
Spectrometer: HRS: k’≤4.3 GeV
Calorimeter 1.5 x larger
Similar MX2 resolution at each setup.
Same 1.0 GHz Digitizer for PbF2
Calorimeter trigger improved
( better p0 subtraction)
Luminosity x Calo acceptance/block = 2x larger.
Same statistic (250K)/setup
100 Days

21. JLab12: Hall A with 3, 4, 5 pass beam
Absolute measurements: d(e=±1)
250K events/setup
H(e,e’)p
Unphysical
Twist 2 & Twist 3 separation.
Im{DVCS*BH}+DVCS2
Re{DVCS*BH} +’DVCS2
100 days

22. Projected Statistics: Q2=9.0 GeV2, xBj = 0.60
250K exclusive DVCS events total

23. What systematic errors?
For the future experiments
At this day (June 2006):
3% HRS+PbF2 acceptance +luminosity + target
3% H(e,e’g)Xg p0 background
2% Inclusive H(e,e’g)Np
2% Radiative Corrections
2% Beam polarization measurement
2% X
1% X
1% X
Total (quadratic sum)= 5.1% (5.6%) %

25. DVCS on the neutron and the deuteron - Preliminary
Q2= 1.9 GeV2
<t>= -0.3 GeV2
Mx2 upper cut
2nd cut
1st cut
It is clear that there are two contributions with different sign : DVCS on the neutron and DVCS on the deuteron

26. 0 Electroproduction & Background Subtraction
H(e, e’ )X {
M
Minimum angle in lab = 4.4° (E00110)
Asymmetric decay: One high energy forward cluster… mimics DVCS MX2!