1. Explicit DVCS amplitudes Trento, Jan. 4, 2010 L. Jenkovszky (BITP, Kiev) in collaboraton with S. Fazio, R. Fiore and A. Lavorini (Calabria)

2. Items discussed: • Inclusive (DIS) and exclusive (DVCS, VMP,…); • Dipole approach (?); σ~xg(x,Q^2) (Brodsky; Ryskin et al.); • Factorization (in QCD and Regge); • Geometry (b~1/m^2?); • Regge pole models; where is BFKL? • How “hard” is DVCS and VMP? • From DVCS and VMP to GPD • From JLab via COMPASS to HERA

3. Recent history: 1. A. Donnachie, P.V. Landshoff, Excluusive Vector photoproduction…, Phys. Lett.B 478 (2000) 145; D-L.,Successful description of vector meson electroproduction, hep-ph/0803.0686; 2. M.Ryskin, Yu.M. Shabelski, and A.G.Shuvaev, t-dependeces…, hep-ph/9803434; 3. F. Cano, J.-M. Laget, hep-ph, 0111146, 0209362, 0208213;,… 4. D. Mueller, Pomeron dominance in DVCS,… htp-ph/0605013. 5. K. Kumerički, D. Mueller, and K. Passek- Kumerički, Nucl. Phys. B794 (2008) 244; 6. M. Capua, R. Fiore, S. Fazio, L. Jenkovszky, and F. Paccanoni, Phys. Letters, B 645 (2007) 161. 7. A.B.Kaidalov et al. (unitarity)

4. -t 0

5. DIS X The proton is smashed (completely destroyed)

6. DIS Reconstruction of the DVCS amplitude from DIS or ?

8. DVCS kinematics

9. Diagrams of DVCS (a) and VMP (b) amplitudes and their Regge-factorized form (c)

10. High-energy DVCS (or VMP): the sum of a “soft” and a “hard” pomeron exchante is approcimated by an “effective” Pomeron

11. Effective trajectory • W dependence s ~ W d d = 4 (a(t) – 1) a(t) = a(0) + a’ t • shrinkage of diffractive peak W – t correlation t dependence as a function of W W dependence as a function of t P. Marage Exclusive hard diffraction at HERA (DVCS and VM) EDS’09 – CERN 29/06-03/07/2009

13. elast. p. diss. DVCS (LPS) r f DVCS (p. diss.) t dependences P. Marage Exclusive hard diffraction at HERA (DVCS and VM) EDS’09 – CERN 29/06-03/07/2009

14. b slopes elastic p. dissoc. optical model - b decrease with dipole size (Q2, mq) - universal scale dependence for m2 > 5 GeV2m2 = (Q2 + M2)/4 for VM m2 = Q2 for DVCS - b(r, f at large Q2) -> b (J/y) -> small room for VM form factor bVM P. Marage Exclusive hard diffraction at HERA (DVCS and VM) EDS’09 – CERN 29/06-03/07/2009

16. GS in DVCS?

17. Matching soft and hard physics (combining Regge pole models and DGLAP evolution) P. Desgrolard, L.J., and F. Paccanoni, Interpolating between soft and hard dynamics in DIS, EPJ, 7 (1999) 263; A. Donnachie and P.V. Landshoff, Perturbative QCD and Regge poles: closing the circle. hep-ph/0111427, 9 Apr. 2002; L. Csernai, L. J., J. Kontros, and A. Magas, Paccanoni, From Regge behavior to DGLAP evolution, Eur. Phys. J. C24 (2002) 205-211. A similar solution for exclusive reactions (e.g. DVCS) is highly desirable!

19. The sub-process γ*p γp in a Regge-factorized form: A(s,t, )~

20. The DVCS amplitude can be written as

22. Hence the scattering amplitude, with the correct signature, becomes

23. Photoproduction- and DIS limits (a consistency check)

32. DVCS at HERA

33. DVCS at HERA

34. DVCS at HERA

35. DVCS at HERA

36. ρ meson electroproduction at HERA

37. ρ meson eletctroproduction at HERA

38. ρ meson eletctroproduction at HERA

41. J/Ψ electroproduction at HERA

42. J/Ψ electroproduction at HERA

43. J/Ψ electroproduction at HERA

46. Ratio of the longitudinal to transverse cross sections for J/Ψ electroproduction at HERA

47. Ratio of the longitudinal to transverse cross sections for φ electroproduction at HERA

49. Fitted values of the “hardness” measure: parameter h

50. The “hardness parameter” h as function of the energy W