1. Deeply Virtual ω Production Michel Garçon & Ludyvine Morand (SPhN-Saclay) for the CLAS collaboration MENU 2004, Beijing e-e- e -’ pp’ ω **

2. Which picture prevails at high Q 2 ? Meson and Pomeron (or two-gluon) exchange … … or scattering at the quark level ? π, f 2, P ρ0ρ0 σ, f 2, P ω π, f 2, P Φ P Flavor sensitivity of DVMP on the proton: ω ρ0ρ0 2u+d, 9g/4 ω 2u-d, 3g/4 Φ s, g ρ+ρ+ u-d γ* L ωLωL (Photoproduction) (SCHC)

3. CLAS: high luminosity run at 5.75 GeV First JLab experiment with GPDs in mind (october 2001 – january 2002) - polarized electrons, E = 5.75 GeV - Q 2 up to 5.5 GeV 2, -Integrated luminosity: 30 fb -1 - W up to 2.8 GeV W = 2.8 2.4 2 1.8 GeV e - p  e - p ω π + π - π 0

4. Identification of channel e - p  e - p ω π + π - π 0 m2m2 (2m  ) 2  -   0 n    +… 00   Separation of :    +  -  0 (M = 783 MeV,  = 8 MeV)  0   +  - (M = 770 MeV,  = 151 MeV) through missing mass

5. Determination of CLAS efficiency in 4D Analysis Code CLAS GEANT simulation Event Generator NgenNacc For each 4D bin : eff = Nacc/Ngen 4 kinematical variables => 4D efficiency table Q 2, x B, t,  eff ~ 5% Q 2 (GeV 2 ) xBxB 28 millions events 20 days through simulation

6. x B from 0.16 to 0.70 Q 2 from 1.6 to 5.6 GeV 2 + binning in  or t Background subtraction

7. Extraction of σ γ*p->pω   *p  p  (  b) Q 2 (GeV 2 ) 0.16 < x B < 0.220.22 < x B < 0.280.28 < x B < 0.34 0.58 < x B < 0.640.52 < x B < 0.580.46 < x B < 0.520.40 < x B < 0.46 0.34 < x B < 0.40 Q 2 (GeV 2 ) Bin to bin syst. errors included = 15-18% Main sources : background subtraction = 8 or 12% efficiency calculation = 8%

8. Comparison with previous data  Compatibility with DESY data (1977)  Disagreement with Cornell data (1981) Q 2 range much extended with our data

9.  (deg) d  /d  (  b/rd) Differential cross sections in  => First indication of helicity non conservation in s-channel  TT et  TL (  b) 0.40 < x B < 0.46 0.22 < x B < 0.280.28 < x B < 0.34 0.46 < x B < 0.520.52 < x B < 0.580.58 < x B < 0.64 0.16 < x B < 0.220.34 < x B < 0.40 Q 2 (GeV 2 )

10. Differential cross sections in t Large t range, up to 2.7 GeV 2. Small t : diffractive regime (d  /dt  e bt ) Large t : cross sections larger than anticipated

11. Comparison with JML model Model includes exchange of π 0, f 2, P p p’ ω ** π0π0 Small |t| ** ω pp’ Large |t| THIS WORK (J.-M. Laget, to be published in Phys. Rev. D)

12. Second part of data analysis: study of ω decay ω channel identification Determination of CLAS efficiency in 6D Study of ω decay Angular distribution of ω decay products (study of e - pπ + π - X final state)  Determination of ω polarization  Test of s-channel helicity conservation (SCHC) 6D efficiency table Q 2, x B, t, , θ N, φ N eff ~ 0,5% 00 

13. Study of ω decay (2)

14. ω decay study : φ N dependence => other indication of non conservation of helicity in the s-channel Determination of

15. Contribution of  L from VGG (GPDs) and JML (Regge) models VGG model: M. Vanderhaeghen, P. Guichon, M. Guidal = 2.1 GeV = 2.8 GeV  L  T +  L

16. Conclusions and perspectives Precise measurements of the e - p  e - p  reaction at high Q 2 and over a wide range in t Exclusive reactions are measurable at high Q 2 (even with the current « modest » CEBAF energy) First significant analysis of  decay in electroproduction Cross sections larger than anticipated at high t SCHC does not hold for this channel Evidence for unnatural parity exchange   0 exchange very probable even at high Q 2 What do we learn ?

17. JML model (Regge) : Good agreement when introducing a t dependence in the  form factor  suggests coupling to a « point » object at high t (hep-ph/0406153) VGG model (GPDs) : Direct comparison not possible since  L not measured Nevertheless  handbag diagram contributes only about 1/5 of measured cross sections  no incompatibility → ω most challenging/difficult channel to access GPD Explore physical significance of high t behaviour Systematic study of other processes (e - p  e - p  0, ,  ) in view of an interpretation in terms of GPDs Measurements feasible up to Q 2 =8-9 GeV 2 with CEBAF@12 GeV Perspectives Comparison to models

18. linear saturation Regge theory applied to vector meson production α(t) t (Jean-Marc Laget et al., see also talk of Marco Battaglieri) Regge trajectories exchange in t channel 00   parameters = coupling constants g ij Extension to electroproduction case *  add a parameter = electromagnetic form factor  0 exchange dominance at W ~ few GeV in ω photoproduction

19. FACTORIZATION GPD formalism for vector mesons In the Bjorken regime : Collins et al. t small Amplitude: e-e- p p p+  q q-  x+  x-  e-e- p M ** L L MM H, E z t=  2 Cross section: Scaling law =  0, ,  (see talk by Michel Guidal)

20. Kinematical domain explored Resonances W=1,8 W=M Inelastic x B = 0,1 x B = 0,8 valence quarks ν (GeV) 0,1110100 Q 2 (GeV 2 ) 0,1 1 10 M1,8 Elastic pQCD Regge gluons sea quarks Elastic Resonances Deep inelastic W (GeV) M1,8

21. Electron identification e-e- 10 RL 6 RL OUT IN Information from DC + CC + EC e-e- -- Pion rejection Electron selection

22. Hadron identification Information from DC + SC DC  SC  ++ p

23. Identification of channel e - p  e - p ω π + π - π 0 through missing mass 00   m2m2  0  

24. Background subtraction  Event weighting : w=1/eff(Q 2,x B,t,  ) y(m) = Skewed Gaussian + Pol2 (peak + radiative tail) (background)  Fit of M X [e - pX] with :  Subtraction of y(m).  Integration of event number between 720 and 850 MeV.

25. Determination of CLAS efficiency in 6D 6 kinematical variables => 6D efficiency table Q 2, x B, t, , θ N, φ N 118 millions events 63 days through simulation For each 6D bin : eff = Nacc/Ngeneff ~ 0,5% Analysis Code GPPGSIM Event Generator NgenNacc

26. Phase space (1)

27. Phase (2)

28. Experimental Q 2, x B, t, , … distributions e-p+-Xe-p+-X e-p+Xe-p+X

29. CLAS system efficiency 4D 6D

30. Formalism for ω decay Decay angular distribution : elements of ω spin density matrix ε parameter of virtual photon polarization R = σ L /σ T (Rp :  =  T +  L ) Deduce : ω polarization via SCHC test : (necessary condition) If SCHC, then  separation σ L, σ T Test of hypothesis of natural parity exchange in the t-channel (NPE) : (necessary condition) 0 -, 1 +  UNPE 0 +,1 -  NPE pp’ ω ** i, j   meson helicity   virtual photon polarization

31. Study of ω decay (2) Determination of

32. ω decay study (4) …  exchange of unnatural parity particle in the t-channel Method of moments :2 Determination of 15 parameters which should vanish if SCHC holds combinaison which should vanish if NPE holds

33.  decay study (cont.) But : and If SCHC then : and

34. R extraction 0 if SCHC 1 if SCHC  SCHC Theory : Observation : So one can’t extract R. Same helicity amplitudes than the ones that come into play in 

35. R extraction (cont.) Suppose SCHC holds, then : One has found : Then : But : So :

37.  0 meson production and JML model

38. Comparison with JML model (cont.) = 2.1 GeV = 2.8 GeV Within this model,  Data still favor a t-dependent πγ ω form factor.  π 0 exchange dominant for the whole Q 2 range.  σ T dominant for the whole Q 2 range.

39. Form Factors => transverse position Q 2 = -t Exclusive elastic reactions e-e- e-e- pp Motivations High Q 2 reactions give access to internal dynamics of the nucleon Deep inclusive reactions Parton Distributions  longitudinal momentum fraction  quarks contribution to nucleon spin x = x B e-e- e-e- p X Deep exclusive reactions Generalized Parton Distributions  correlations !  quark angular momentum e-e- e-e- pp  ou M x, t, ξ e-e- e-e- **

40. Link with FF and PD  0  access to correlations, x,  dependence  quark longitudinal impulsion t dependence  quark transverse impulsion Ji sum rule : GPD formalism (cont.)

41. VGG (GPDs) model x,t,  dependence parametrization: 2 parameters : b valence et b sea Corrections to leading order: In fact Q 2 non infinite In pratice : non perturbative effects at small Q 2 averaged by « frozing » the strong coupling constant  S to 0.56

42. Contribution of  L from VGG (GPDs) model (cont.)

44.  * p  p  b) Q 2 (GeV 2 ) x B =0.31 x B =0.38 x B =0.45 x B =0.52  0 meson results at 4.2 GeV (Regge) C. Hadjidakis et al.

45.  0 meson results at 4.2 GeV (GPDs) x B =0.31 x B =0.38 x B =0.45 x B =0.52 Q 2 (GeV 2 )  * L p  p  L  b) C. Hadjidakis et al.

47. G parity definition