Gluons in the proton and exclusive hard diffraction

1. Gluons in the proton and exclusive hard diffraction • Introduction • data on exclusive vector meson electroproduction • sizes of gluon cloud • sizes of photon configurations • comparison to theory Aharon Levy Tel Aviv University Aharon Levy - Torino seminar

2. F2 parton densities. * ‘sees’ partons. parton density increases with decreasing x. • QCD based fits can follow the data accurately, yield parton densities. BUT: • many free parameters (18-30) (only know how parton densities evolve) • form of parameterisation fixed by hand (not given by theory) Aharon Levy - Torino seminar

3. all is not well … From Pumplin, DIS05 There are signs that DGLAP (Q2 evolution) may be in trouble at small x (negative gluons, high 2for fits). Need better data to test whether our parton densities are reasonable. The structure function FL will provide an important test. Can also get information on gluon density from exclusive hard processes. Aharon Levy - Torino seminar

4. Exclusive VM electroproduction (V0 =   DVCS) Aharon Levy - Torino seminar

5. g g IP ‘hard’ ‘soft’ soft to hard transition • Expect  to increase from soft (~0.2, from ‘soft Pomeron’ value) to hard (~0.8, from xg(x,Q2)2) • Expect b to decrease from soft (~10 GeV-2)to hard (~4-5 GeV-2) Aharon Levy - Torino seminar

6. soft  hard   s0.096 Below Q20.5 GeV2, see same energy dependence as observed in hadron-hadron interactions. Start to resolve the partons. Aharon Levy - Torino seminar

7. g g IP ‘hard’ ‘soft’ soft to hard transition • Expect  to increase from soft (~0.2, from ‘soft Pomeron’ value) to hard (~0.8, from xg(x,Q2)2) • Expect b to decrease from soft (~10 GeV-2)to hard (~4-5 GeV-2) Aharon Levy - Torino seminar

8. ingredients Use QED for photon wave function. Study properties of V-meson wf and the gluon density in the proton. Aharon Levy - Torino seminar

9. Mass distributions Aharon Levy - Torino seminar

10. Photoproduction process becomes hard as scale (mass) becomes larger. Aharon Levy - Torino seminar

11. (W) – ρ0 Fix mass – change Q2 Aharon Levy - Torino seminar

12. Proton dissociation MC: PYTHIA pdiss: 19± 2(st) ± 3(sys) % Aharon Levy - Torino seminar

13. (W) – ρ0,  Aharon Levy - Torino seminar

14. (W) - , J/,  Aharon Levy - Torino seminar

15.  (Q2+M2)- VM Aharon Levy - Torino seminar

16. Kroll + Goloskokov:  = 0.4 + 0.24 ln (Q2/4) (close to the CTEQ6M gluon density, if parametrized as xg(x)~x-/4) Aharon Levy - Torino seminar

17. 1 10 Q2(GeV2) (Q2) Fit to whole Q2 range gives bad 2/df (~70) Aharon Levy - Torino seminar

18. (Q2) (for Q2 > 1 GeV2) Aharon Levy - Torino seminar

19. IP IP Y Proton vertex factorisation p-dissociative elastic photoproduction proton vertex factorisation Similar ratio within errors for  and   proton vertex factorisation in DIS Aharon Levy - Torino seminar

20. Fit : b(Q2) – ρ0,  Aharon Levy - Torino seminar

21. g g ‘hard’ b(Q2+M2) - VM Aharon Levy - Torino seminar

22. Information on L and T Use 0 decay angular distribution to get r0400 density matrix element using SCHC  - ratio of longitudinal- to transverse-photon fluxes ( <> = 0.996) Aharon Levy - Torino seminar

23. R=L/T (Q2) When r0004 close to 1, error on R large and asymmetric  advantageous to use r0004 rather than R. Aharon Levy - Torino seminar

24. R=L/T (Q2) Aharon Levy - Torino seminar

25. R=L/T (Mππ) Why?? Aharon Levy - Torino seminar

26. R=L/T (Mππ) Possible explanation: example for =1.5 Aharon Levy - Torino seminar

27. Light VM: transverse size of ~ size of proton Heavy VM: size small  cross section much smaller (color transparency) but due to small size (scale given by mass of VM) ‘see’ gluons in the proton   ~ (xg)2  large  large kT small kT large config. small config. Photon configuration - sizes T: large sizesmall size strong color forcescolor screening large cross sectionsmall cross section *: *T, *L *T – both sizes, *L – small size Aharon Levy - Torino seminar

28. L and T same W dependence L  in small configuration T  in small and large configurations small configuration  steep W dep large configuration  slow W dep  large configuration seems to be suppressed L/tot(W) Aharon Levy - Torino seminar

29.  size of *L  *T  large configuration seems to be ssuppressed L/tot(t) Aharon Levy - Torino seminar

30. (W) - DVCS Final state  is real  T using SCHC  initial * is *T but W dep of  steep large *T configurations seem to be suppressed Aharon Levy - Torino seminar

31. Get effective Pomeron trajectory from d/dt(W) at fixed t Regge: Effective Pomeron trajectory ρ0photoproduction Aharon Levy - Torino seminar

32. g g ‘hard’ Effective Pomeron trajectory ρ0 electroproduction Aharon Levy - Torino seminar

33. Comparison to theory • All theories use dipole picture • Use QED for photon wave function • Use models for VM wave function – usually take a Gaussian shape • Use gluon density in the proton • Some use saturation model, others take sum of nonperturbative + pQCD calculation, and some just start at higher Q2 • Most work in configuration space, MRT works in momentum space. Configuration space – puts emphasis on VM wave function. Momentum space – on the gluon distribution. • W dependence – information on the gluon • Q2and R – properties of the wave function Aharon Levy - Torino seminar

34. ρ0 data (ZEUS) - Comparison to theory • Martin-Ryskin-Teubner (MRT) – work in momentum space, use parton-hadron duality, put emphasis on gluon density determination. Phys. Rev. D 62, 014022 (2000). • Forshaw-Sandapen-Shaw (FSS) – improved understanding of VM wf. Try Gaussian and DGKP (2-dim Gaussian with light-cone variables). Phys. Rev. D 69, 094013 (2004). • Kowalski-Motyka-Watt (KMW) – add impact parameter dependence, Q2 evolution – DGLAP. Phys. Rev. D 74, 074016 (2006). • Dosch-Ferreira (DF) – focusing on the dipole cross section using Wilson loops. Use soft+hard Pomeron for an effective evolution. Eur. Phys. J. C 51, 83 (2007). Aharon Levy - Torino seminar

35. ρ0 data (H1) - Comparison to theory • Marquet-Peschanski-Soyez (MPS): Dipole cross section from fit to previous ,  and J/ data. Geometric scaling extended to non-forward amplitude. Saturation scale is t-dependent. • Ivanov-Nikolaev-Savin (INS): Dipole cross section obtained from BFKL Pomeron. Use kt-unintegrated PDF and off-forward factor. • Goloskokov-Kroll (GK): Factorisation of hard process and proton GPD. GPD constructed from standard PDF with skewing profile function. Aharon Levy - Torino seminar

36. Q2 KMW – good for Q2>2GeV2 miss Q2=0 DF – miss most Q2 FSS – Gauss better than DGKP Aharon Levy - Torino seminar

37. Q2 Data seem to prefer MRST99 and CTEQ6.5M Aharon Levy - Torino seminar

38. W dependence KMW - close FSS: Sat-Gauss – right W-dep. wrong norm. MRT: CTEQ6.5M – slightly better in W-dep. Aharon Levy - Torino seminar

39. L/tot(Q2) Aharon Levy - Torino seminar

40. L/tot(W) All models have mild W dependence.None describes all kinematic regions. Aharon Levy - Torino seminar

41. L,T (Q2+M2) • Different Q2+M2 dependence of L and T (L0 at Q2=0) • Best description of L by GK; T not described. Aharon Levy - Torino seminar

42. Density matrix elements - ,  • Fair description by GK • r500 violates SCHC Aharon Levy - Torino seminar

43. VM/tot - ??? Aharon Levy - Torino seminar

44. Summary and conclusions • HERA data shows transition from soft to hard interactions. • The cross section is rising with W and its logarithmic derivative in W, , increases with Q2. • The exponential slope of the t distribution decreases with Q2 and levels off at about b = 5 GeV-2. Transverse size of gluon density (0.6 fm) inside the charge radius of the proton (0.8 fm). • Proton vertex factorisation observed also in DIS. • The ratio of cross sections induced by longitudinally and transversely polarised virtual photons increases with Q2, but is independent of W and t. The large configurations of the transversely polarised photon seem to be suppressed. • The effective Pomeron trajectory has a larger intercept and smaller slope than those extracted from soft interactions. • All these features are compatible with expectations of perturbative QCD. • None of the models which have been compared to the measurements are able to reproduce all the features of the data. • Precision measurements of exclusive vector meson electroproduction can help determine the gluon density in the proton. Aharon Levy - Torino seminar