J. Roche Ohio University and Jefferson Laboratory Results shown are from the ”DVCS HALL A collaboration” (E and E03-106) First steps toward nucleon tomography using the Generalized Parton Distribution functions Carlos MUNOZ CEA/Saclay Alexandre CAMSONNE IN2P3/Clermont Malek MAZOUZ  IN2P3/Grenoble Pierre BERTIN IN2P3/Clermont Charles HYDE ODU/Clermont Ron RANSOMME Rutgers Franck SABATIE CEA/Saclay Eric VOUTIER IN2P3/Grenoble

Form factor In 1956, R. Hofstadter confirms that the proton is not a point like object But has a spatial extension that can be described in terms of form factors. Q 2 =-q 2 F 1 (Q 2 ),F 2 (Q 2 ) Lowest  order In 1972, with the discovery of the weak currents ( Z 0, W), the axial (     ) form factor G A (Q 2 ) and the pseudo-scalar form G p (Q 2 ) are introduced. Spin flip

In , the experiments at Stanford (R.Taylor et al.) showed that hadrons are made up of point like parts. These partons were identified to quarks and gluons predicted by theorists (M. Gellmann) in In these experiments an electron scatters inclusively off the nucleon With a large energy transferred to the target. These experiments Are know as “Deep Inelastic Scattering ” Extensively measured at SLAC, CERN, DESY,JLAB….. Beam: e,  polarized and non polarized Target : P,D,… polarized and non-polarized

q=(k-k’) k 0 -k’ 0 = Q 2 =-q 2 DEEP INELASTIC SCATTERING Note: There are two more structure functions corresponding to the weak exchange (Z 0,W) Structure functions X

Proton Particle Data Book

Photon flux before the target - photon flux after the target = all the photons that interacted Optical theorem X p k q The photon couples to a charge p p’ k k’ q q p=p’ k=k’

In the Bjorken’s limit (no transverse extension) The scattering happens off a parton (quark or antiquark) carrying a fraction x of the proton momentum  The structure functions F 1,2 (x,Q 2 ) ought to be independent of Q 2 : there is “scaling” This is wrong but one knows their evolutions through DGLAP The structure functions can be de-convoluted in flavor: Parton distributions PP K K q q PP K K q q

u d g/10 u,d x xf(x)

Polarized structure functions X e P Polarized electron Polarized target: transverse or longitudinal Neutron, proton….

Proton Deuteron Neutron (from 3 He) PDG

If not at the Bjorken’s limit  TWIST  Q     TWIST(1/Q 4 )+…. PP K K q q ++ …=

Sum rules Nucleon observables Parton distributionsObservables of the partons (charge, spin ….) + Charge Spin Consider the quarks only: Add the gluons:

The quarks orbit !! But around what ? ? Orbital momentum In order to determine L q, one needs to observe 2 partons interacting that is the correlations between partons.

To describe the waltz, one needs to count the number of dancers, their sexes, their race, their individual spin but none of that tells enough about the spinning of the whole dance group. Only a measure of the correlation between all the possible couples gives that information. DIS only measures the parton distributions and doesn’t give access to the correlations between the partons therefore doesn’t give access to the orbital momentum. The waltz

In 1996, D. Mueller, A. Radyushkin, and X. Ji generalized the parton distributions by breaking the handbag symmetry 4 functions per flavor Off Forward Parton Distributions Skewed Parton Distributions Generalized Parton Distributions x+  x-  t GPDs P P’ GPDs

Limits and sum rules Ji’s sum rule

There are many GPDs models In all cases, the models predictions are valid if the hand bag dominates Q 2, S >>M 2 et t << Q 2. The results presented today will be compared to the VGG (M. Vanderaghen, M. Guidal et P.A.M. Guichon ) model. x dependency is constrained by the form factors and the structure functions  dependency is constrained by mathematical conditions (positivity, polynomiality…) t dependency is factorized H q (x)=q(x) F 1 (t) inspired by the quark-soliton model is a code that you can use to do your plots… GPDs models

From theory to experiment Theory x+  x-  t GPDs Experiment   But nothing is that simple Handbag Diagram   Collins, Freund Physical process   This needs to be tested !!! Factorisation theorem : If one is close enough from the asymptotic limit then the handbag diagram is the main Contribution to DVCS. (leading twist) Q 2 and large with x B and t fixed

The GPDs enter in the DVCS amplitude as integrals over x GPDs appear in the real part through a Principal-value integral over x GPDs appear in the imaginary part along the line x=+/-  GPDs in the DVCS amplitude VGG model x-  x+ 

GPD observables Experimentaly, DVCS has the same final state than the Bethe-Heitler process. The BH is known if the form factors are known. With a longitudinaly polarized beam, the GPD observables are: At JLab energies, |T DVCS | 2 is small (?) P.Kroll, P.A.M. Guichon, M. Diehl, B. Pire, …

Parametrization of the cross sections Terms from the handbag (Twist 2) should dominate  and  Their dependence in Q 2 is predicted by the handbag and can be tested Belitsky, Mueller, Kirchner, Nucl. Phys. B629,323(2002) Decomposed the amplitudes in terms of angular harmonics and limited Fourier expansions Twist 2 Twist 3  azimuth between the virtual and real photon |DVCS| 2 Interference BH-DVCS C I ’s are linear combinations of the GPDs integrals and discrete values (x=  )

The Jlab/Hall A DVCS experiments The cross section is 4 times differential, so one needs to measure 4 variables: Q 2, x The Scattered electron Is detected in the Jlab/Hall A HRS: High precision determination of the quadri-vector of the  *  p/p~     rd t,  The outgoing real photon is detected in an high precision electromagnetic calorimeter: This allows an excelent determination of the direction of the real photon  = rd  

The Jlab/Hall A DVCS experiments Scattered electron The HRS acceptance Is well known (standard equipmennt) 1~2 % Emitted photon The calorimeter is a simple box e p → e (p)  The ‘matching’ of the two acceptances is perfect The virtual photon points To the center of the calorimeter **  One of the key strength of this experimental program is the excellent Knowledge of the acceptance which allow the extraction of cross sections.

The Jlab/Hall A experimental apparatus 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

The Jlab/Hall A experimental apparatus 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  t (ns) for 9-block around predicted « DVCS » block

E custom electronics and DAQ scheme 1. Electron trigger starts the game 2. Calorimeter trigger (350ns): - selects clusters - does a fast energy reconstruction - gives a read-out list of the modules which enter clusters over a certain threshold - gives the signal to read-out and record all the experiment electronics channels 3. Each selected electronics channel is digitized on 128ns by ARS boards t (ns) 4. Offline, a waveform analysis allows to extract reliable information from pile-up events

H(e,e’  )X H(e,e’  p) H(e,e’  )X - H(e,e’  ’)X' H(e,e’  )N  DVCS : exclusivity Good resolution : no need for the proton array Remaining  contamination 1.7% HRS+calorimeter ep -> ep  ep -> ep  0  0 ->  ep -> ep  0  ep -> ep  0 N  … HRS+calorimeter + proton array

E00-110: difference of cross-sections Corrected for real+virtual RC Corrected for efficiency Corrected for acceptance Corrected for resolution effects Checked elastic ~1% Twist-2 Twist-3 Extracted Twist-3 contribution small ! PRL97, (2006)

E00-110: Q 2 dependence and test of scaling =0.26 GeV 2, =0.36 No Q 2 dependence: strong indication for scaling behavior and handbag dominance Twist-2 Twist-3

 0 electro-production cross section: Dominance of twist 2 (isolation of leading twist) Sensitive to different linear combinations of GPDs than DVCS NEW: E : Jlab/Hall A 12 GeV experiment Q 2 variation: 2:1 range at each x Bj Accurate measurement of the twist-2 dominance x Bj variation (dependence): Precision data on variation of t-dependence with x Bj Study of transverse correlations t variation: 5 bins in 0 < t-t min < 1 GeV 2 Fourier-conjugate to the spatial distributions of quark as a function of their momentum fraction x Bj

E00-110: Total cross-sections Extracted Twist-3 contribution small ! PRL97, (2006) With these data, it is impossible to disentangle DVCS 2 from the interference term: they mix in the azimuthal analysis large

NEW: E07-007: Complete separation of the observables. Azimuthal analysis and 2 beam energies,the 2 contributions can be separated Rosenbluth type separation Goal 1: measure the total cross section d 4  using two beam energies at fixed x Bj =0.36 for three Q 2 =2.3, 1.9 and 1.5 GeV 2. E beam ranging from 3.5 to 6 GeV will provide a test of the scaling of the total cross section will allow to separated the interference BH-DVCS from DVCS 2 Goal 2: measure the 5 response functions of ep->ep  0 at Q 2 =2.3, 1.9, 1.5 GeV 2 –Separate  LT,  TT,  LT’ from  L +   T by azimuthal variation and  L from  T by Rosenbluth method –First test of factorization in this deep meson production channel –If scaling is observed can extract flavor information on GPDs

Some of the topics I did not talk about The same collaboration published results on the neutron (E03-106) got some electro-pion production data Other collaborations have published dedicated and non-dedicated DVCS data. DESY (HERMES and HERA) JLab/Hall B: large x and Q 2 data but asymmetry data only Many DVCS experiments have been approved to run in a near future: COMPASS: using  as beam JLab/Hall B Information about the structure of the nucleon can be obtained by measuring Deep Meson Production ( , , etc..)

The Jlab/Hall A DVCS collaboration has measured DVCS cross sections with high statistical and systematic precision using a HRS and a calorimeter both off the proton and the neutron Tests of the dominance of the handbag are positive The VGG model is too small by 30% The DVCS 2 cannot be neglected In summary The GPDs provide a new window on the nucleon structure that allow to study the correlation between its constituents BUT One needs to test the regime of applicability of the formalism (handbag dominance) The interpretability of the cross-section in term of GPDs is still in its infancy Many groups have and will continue to perform DVCS/GPD experiments. The Jlab/Hall A DVCS collaboration will study E07-007: complete separation of the cross section observables (DVCS 2 ) E : extended Q 2 and x ranges data coming up off proton, neutron (deuterium) on electro production of photon and  0 WANT TO JOIN US?

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n-DVCS is sensitive to Jd p-DVCS is sensitive to Ju Complementarity between neutron and proton measurements E results Model dependent extraction of J u and J d

E kinematics The calorimeter is centered on the virtual photon direction 50 days of beam time in the fall 2004, at 2.5  A intensity

Remaining contribution: ~1.7% (all non-  o electroproduction) Analysis – Looking for DVCS events MM 2 cut However: One needs to do a thorough  o subtraction if the only (e,  ) system is used to select DVCS events !!! (e,g,p) events

Testing the handbag dominance Symmetry around the virtual photon Broken by : the photon polarization the beam polarization If the handbag dominates in the case of a real photon virtual photon polarization longitudinal polarization of the beam There are 12 independant helicity amplitudes but only 5 observables in the case of a polarized beam and an unpolarized target. e -’  p e-e- ** hadronic plane leptonic plane 