E p = 920 GeV, E e = 27.5 GeV, # bunches = 189 I p = 110 mA, I e = 40 mA

1. Small-x and Diffraction in DIS atHERAIHenri KowalskiDESY 12thCTEQ Summer School Madison - Wisconsin June 2004

2. H1 detector ZEUS detector Ep = 920 GeV, Ee = 27.5 GeV, # bunches = 189 Ip = 110 mA, Ie = 40 mA Linst= 2 x 1031 cm-2 s-1

3. ZEUS detector Q2 ~ 2 –100 GeV2 Q2 ~ 0.05-0.6 GeV2 Q2 - virtuality of the incoming photon W - CMS energy of the incoming photon-proton system x- Fraction of the proton momentum carried by struck quark x ~ Q2/W2

4. y – inelasticity Q2 = sxy Infinite momentum frame Proton looks like a cloud of noninteracting quarks and gluons F2 measures parton density in proton at scale Q2 F2 = f e2f x q(x,Q2)

5. there is a change of slope at small-x, near Q2 = 1 GeV2

6. Gluon density Gluon density dominates F2 for x < 0.01

7. Gluon density known with good precision at larger Q2. For Q2 ~1 GeV2 gluons tends to go negative. NLO, so not impossible BUT – cross sections such as L also negative !

8. MX - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton

9. Diffractive Signature DY ~ log(W2 / M 2X) diff Non- diff Non-Diffraction Diffraction - Rapidity uniform, uncorrelated particle emission along the rapidity axis => probability to see a gap DY is ~ exp(-<n>DY) <n> - average multiplicity per unit of rapidity dN/ dM 2X ~ 1/ M 2X => dN/dlog M 2X ~ const

10. Slow Proton Frame incoming virtual photon fluctuates into a quark-antiquark pair which in turn emits a cascade-like cloud of gluons Transverse size of the quark-antiquark cloud is determined by r ~ 1/Q~ 2 10-14cm/ Q (GeV) Diffraction is similar to the elastic scattering: replace the outgoing photon by the diffractive final state r , J/Y or X = two quarks Rise of sgptot with W is a measure of radiation intensity

11. Radiation process emission of gluons is ordered in rapidities QCD Toy Model: integrals over transverse momenta are independent of each other Rise of sgptot with W is a measure of radiation intensity

12. Dipole description of DIS

13. Q2~1/r2 exp(-mq r)

14. GBW Model K. Golec-Biernat, M. Wuesthoff Scaling in Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski Parameters fitted to DIS F2 data: s0 = 23 mb l = 0.29 x0 = 0.0003

15. Parameters fitted to HERA DIS data: c2 /N ~ 1 s0 = 23 mb l = 0.29 x0 = 0.0003

16. Saturation Model Predictions for Diffraction

17. Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski

18. GBW model, in spite of its compelling success has some obvious shortcomings: The treatment of QCD evolution is only rudimentary remedy => incorporate DGLAP into dipole cross-section J. Bartels, K. Golec-Biernat, H. Kowalski The dipole cross section is integrated over the transverse coordinate although the gluon density is expected to be a strongly varying function of the impact parameter. Recently: BFKL motivated Ansatz proposed by Iancu, Itakura, Munier

19. Impact Parameter Dipole Saturation Model H. Kowalski D. Teaney hep-ph/0304189 Proton b – impact parameter well motivated: Glauber Mueller Levin Capella Kaidalov T(b) - proton shape

20. Derivation of the GM dipole cross section probability that a dipole at b does not suffer an inelastic interaction passing through one slice of a proton S2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton <= Landau-Lifschitz

21. t-dependence of the diffractive cross sectionsdetermines the b distribution

22. Q2 > 0.25 GeV2 mu = 0.05 GeV mc = 1.30 GeV Fit parameters lg= -0.12 C= 4.0 Q02 = 0.8 GeV2 c2/N = 0.8 x < 10-2

23. GBW Model IP Saturation Model

24. ----- universal rate of rise of all hadronic cross-sections Smaller dipoles  steeper rise Large spread of leff characteristic for Impact Parameter Dipole Models

25. Saturation region -------------------------------------------------------------------------------------------------------

26. All quarks Charmed quark

27. Gluon density Charm structure function

28. Photo-production of Vector Mesons

29. Absolute values of cross sections are strongly dependent on mc

33. Absorptive correction to F2 from AGK rules • Martin • M. Ryskin • G. Watt Example in Dipole Model F2 ~ - Single inclusive pure DGLAP Diffraction

34. Fit to diffractive data using MRST Structure Functions A. Martin M. Ryskin G. Watt

35. A. Martin M. Ryskin G. Watt

36. Density profile grows with diminishing x and r approaches a constant value Saturated State - Color Glass Condensate S2 -probability that a dipole does not suffer an inelastic interaction passing through the entire proton Saturated state = = high interaction probability S2 => 0 multiple scattering rS - dipole size for which proton consists of one int. length

37. Saturation scale= Density profile at the saturation radius rS lS = 0.25 lS = 0.15

38. Saturation in the un-integrated gluon distribution kT factorisation formula dipole formula

39. GBW - - - - - - - - - - - - - - - - - - - - - x = 10-6 BGBK ___________________________________ x = 10-2 GBW - - - - - - - - - - - - - - - - - - - - - x = 10-4 BGBK ___________________________________ x = 10-2 - numerical evaluation

40. _ Diffractive production of a qq pair

42. Inclusive Diffraction LPS - Method

43. END of Part I