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 chyde@odu.edu Based on the work of A. Camsonne the DVCS Hall A Ph.D. students: M. Mazouz C. Munoz Camacho

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.

Experimental observables linked to GPDs q’ 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

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

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).

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.

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

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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%) 3.6 - 3.7 %

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

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!