Gluons in the proton and exclusive hard diffraction

1. Gluons in the proton and exclusive hard diffraction • Introduction • soft, hard interactions • gluons • data on exclusive vector meson electroproduction • sizes of gluon cloud • sizes of photon configurations • effective Pomeron trajectory • comparison to theory Aharon Levy Tel Aviv University and MPI Aharon Levy - Hosza seminar

2. Aharon Levy - Hosza seminar

3. LHeC Aharon Levy - Hosza seminar

4. Deep Inelastic kinematics Spin [20 fb-1 /point] Aharon Levy - Hosza seminar

5. e p r b HERA Kinematics Ee=27.5 GeV EP=920 GeV s=(k+P)2 = (320 GeV)2 Transverse distance scale: McAllister, Hofstadter Ee=188 MeV rmin=0.4 fm Bloom et al. 10 GeV 0.05 fm CERN, FNAL fixed target 500 GeV 0.007 fm HERA 50 TeV 0.0007 fm where tis the square of the 4-momentum transferred to the proton Impact parameter: Aharon Levy - Hosza seminar

6. Proton  momentum frame Partons frozen during time of interaction. Virtual photon samples the quark distribution. Assume that partons form incoherent beam. The parton density distributions are meant to be universal quantities. Aharon Levy - Hosza seminar

7. e p r b Photon fluctuates into , , ….. states, which interact with the proton. r large  interaction soft, r small  interaction hard. Proton rest-frame soft and hard – studied by W (or x~1/W2) dependence of the cross section. Aharon Levy - Hosza seminar

8. soft Donnachie and Lanshoff– universal behavior of total hadron-hadron cross section : high energy behaviortot  s0.08 Aharon Levy - Hosza seminar

9. IP - Pomeron Regge trajectories Aharon Levy - Hosza seminar

10. at small x hard DIS: The rise of F2 with decreasing x is strongly dependent on Q2. Aharon Levy - Hosza seminar

11.   s0.08 soft  hard Below Q20.5 GeV2, see same energy dependence as observed in hadron-hadron interactions. Start to resolve the partons. Aharon Levy - Hosza seminar

12. 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 - Hosza seminar

13. 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 - Hosza seminar

14. Exclusive VM electroproduction (V0 =   DVCS) Aharon Levy - Hosza seminar

15. 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 - Hosza seminar

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

17. Mass distributions Aharon Levy - Hosza seminar

18. Photoproduction process becomes hard as scale (mass) becomes larger. Aharon Levy - Hosza seminar

19. (W) – ρ0 Fix mass – change Q2 Aharon Levy - Hosza seminar

20. (W) - , J/,  Aharon Levy - Hosza seminar

21.  (Q2+M2)- VM Aharon Levy - Hosza seminar

22. 1 10 Q2(GeV2) (Q2) Fit to whole Q2 range gives bad 2/df (~70) Aharon Levy - Hosza seminar

23. Fit : b(Q2) – ρ0,  Aharon Levy - Hosza seminar

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

25. DVCS Kornelija Passek-Kumaricki - EDS07 Frankfurt - Strikman Aharon Levy - Hosza seminar

26. 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 - Hosza seminar

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

28. 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 - Hosza seminar

29. 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 is suppressed L/tot(W) Aharon Levy - Hosza seminar

30.  size of *L  *T  large configuration suppressed L/tot(t) Aharon Levy - Hosza seminar

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

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

33. Effective Pomeron trajectory ρ0 electroproduction Aharon Levy - Hosza seminar

34. 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 - Hosza seminar

35. ρ0 data - 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 - Hosza seminar

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

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

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

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

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

41. 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). • 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 are 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 - Hosza seminar