1. Small-x and Diffraction at HERA and LHC Henri Kowalski DESY EDS Château de Blois 2005

2. ZEUSH1 Q 2 - virtuality of the incoming photon W - CMS energy of the incoming photon-proton system x - Fraction of the proton momentum carried by the struck quark x ~ Q 2 /W 2 Liquid Argon Calorimeter Uranium-Scintillator Calorimeter e 27 GeV p 920 GeV HERA – ep Collider

3. y – inelasticity Q 2 = sxy Infinite momentum frame Proton looks like a cloud of non-interacting quarks and gluons F 2 measures parton density in the proton at a scale Q 2

4. Gluon density Gluon density dominates F 2 for x < 0.01

5. Diffractive Scattering Non-Diffractive Event ZEUS detector Diffractive Event M X - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter

6. Dipole description of DIS equivalent to Parton Picture in perturbative region GBW – first Dipole Model only rudimentary evolution BGBK – DM with DGLAP Iancu, Itakura, Mounier (IIM) - CGC motivated ansatz Forshaw, Shaw (FS) - Regge type ansatz with saturation, CGC-inspired Mueller, Nikolaev, Zakharov  r  Q 2 ~1/r 2 Optical T

7. Comparison with Data FS model with/without saturation and IIM CGC model hep-ph/0411337. Fit F 2 and predict x IP F 2 D(3 ) F2F2 F2F2 FS(nosat) x CGC FS(sat)

8. Diffractive contribution of the total cross section  For larger M X,  diff has the similar W and Q 2 dependences as  tot. For the highest W bin (200<W<245 GeV),  diff (0.28<M X <35 GeV, M N <2.3 GeV) /  tot

9. Proton b – impact parameter Impact Parameter Dipole Saturation Model T(b) - proton shape Glauber-Mueller, Levin, Capella, Kaidalov… Kowalski Teaney

10. x < 10 -2 universal rate of rise of all hadronic cross-sections Total  * p cross-section

11. Dipole cross section determined by fit to F 2 Simultaneous description of many reactions Gluon density test? Teubner  * p -> J/  p IP-Dipole Model F 2 C IP-Dipole Model

12. GBW Model IP Dipole Model less saturation (due to IP and charm) strong saturation

13. Saturation scale HERA RHIC Q S RHIC ~ Q S HERA

14. Saturated state is partially perturbative   p cross-section exhibits the universal rate of growth

15. Absorptive correction to F 2 Example in Dipole Model F 2 ~ - Single inclusive pure DGLAP Diffraction

16. 2-Pomeron exchange in QCD Final States (naïve picture) 0-cut 1-cut 2-cut p   * p-CMS  YY detector p   * p-CMS  p  detector Diffraction

17. 0-cut 1-cut 2-cut 3-cut Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.

18. Note: AGK rules underestimate the amount of diffraction in DIS AGK rules in the Dipole Model

20. HERA Result Unintegrated Gluon Density Dipole Model Example from dipole model - BGBK Another approach (KMR) Active field of study at HERA: UGD in heavy quark production, new result expected from high luminosity running in 2005, 2006, 2007

21. Exclusive Double Diffractive Reactions at LHC  Diff = hard X-section × Gluon Luminosity factorization !!! f g – unintegrated gluon densities gg Jet+Jet gg Higgs low x QCD reactions : pp => pp + g Jet g Jet  ~ 1 nb for E T > 20 GeV, M(jj) ~ 50 GeV   ~ 0.5 pb for E T > 60 GeV, M(jj) ~ 200 GeV  JET | < 2 KMR Eur. Phys J. C23, p 311 x IP =  p/p, p T x IP ~ 0.2-1.5% pp => pp + Higgs   3) fb SM ~ O(100) fb MSSM 1 event/sec x IP =  p/p, p T x IP ~ 0.2-1.5%

22. t – distributions at HERA t – distributions at LHC with the cross-sections of the O(1) nb and L ~ 1 nb -1 s -1 => O(10 7 ) events/year are expected. For hard diffraction this allows to follow the t – distribution to t max ~ 4 GeV 2 For soft diffraction t max ~ 2 GeV 2 Saturated gluons Non-Saturated gluons t-distribution of hard processes should be sensitive to the evolution and/or saturation effects see: Al Mueller dipole evolution, BK equation, and the impact parameter saturation model for HERA data

23. Dipole form double eikonal single eikonal Khoze Martin Ryskin t – distributions at LHC Effects of soft proton absorption modulate the hard t – distributions t-measurement will allow to disentangle the effects of soft absorption from hard behavior Survival Probability S 2 Soft Elastic Opacity

24. L. Motyka, HK preliminary Gluon Luminosity Q T 2 (GeV 2 ) Dipole Model F2F2 Exclusive Double Diffraction

25. Conclusions We are developing a very good understanding of inclusive and diffractive g * p interactions: F 2, F 2 D(3), F 2 c, Vector Mesons (J/Psi)…. Observation of diffraction indicates multi-gluon interaction effects at HERA HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with RHIC HERA determined properties of the Gluon Cloud Diffractive LHC ~ pure Gluon Collider => investigations of properties of the gluon cloud in the new region Gluon Cloud is a fundamental QCD object - SOLVE QCD!!!!

27. Smaller dipoles  steeper rise Large spread of eff characteristic for IP Dipole Models universal rate of rise of all hadronic cross-sections The behavior of the rise with Q 2

28. GBW Model KT-IP Dipole Model less saturation (due to charm) strong saturation

29. Unintegrated Gluon Densities Exclusive Double Diffraction Note: xg(x,.) and P gg drive the rise of F 2 at HERA and Gluon Luminosity decrease at LHC Dipole Model

30. Saturation Model Predictions for Diffraction

31. Absorptive correction to F 2 Example in Dipole Model F 2 ~ - Single inclusive pure DGLAP Diffraction

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

33. A. Martin M. Ryskin G. Watt

34. AGK Rules The cross-section for k-cut pomerons: Abramovski, Gribov, Kancheli Sov.,J., Nucl. Phys. 18, p308 (1974) 1-cut 2-cut QCD Pomeron F (m) – amplitude for the exchange of m Pomerons

35. 2-Pomeron exchange in QCD Final States (naïve picture) 0-cut 1-cut 2-cut p   * p-CMS  YY detector p   * p-CMS  p  detector Diffraction

36. 0-cut 1-cut 2-cut 3-cut Feynman diagrams QCD amplitudes J. Bartels A. Sabio-Vera H. K.

37. Probability of k-cut in HERA data Dipole Model

38. Problem of DGLAP QCD fits to F 2 CTEQ, MRST, …., IP-Dipole Model at small x valence like gluon structure function ? Remedy: Absorptive corrections? MRW Different evolution? BFKL, CCSS, ABFT

39. BFKL ------ from Gavin Salam - Paris2004 LO DGLAP --- at low x Next to leading logs NLLx -----

40. from Gavin Salam - Paris 2004 Ciafalloni, Colferai, Salam, Stasto Similar results by Altarelli, Ball Forte, Thorn

41. Density profile grows with diminishing x and r approaches a constant value Saturated State - Color Glass Condensate multiple scattering S – Matrix => interaction probability Saturated state = high interaction probability S 2 => 0 r S - dipole size for which proton consists of one int. length

42. Saturation scale = Density profile at the saturation radius r S S = 0.15 S = 0.25

43. Saturated state is partially perturbative cross-sectiom exhibits the universal rate of growth

44. RHIC

45. Conclusions We are developing a very good understanding of inclusive and diffractive  * p interactions: F 2, F 2 D(3), F 2 c, Vector Mesons (J/Psi)…. Observation of diffraction indicates multi-gluon interaction effects at HERA Open problems: valence-like gluon density? absorptive corrections low-x QCD-evolution HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with the RHIC one HERA+NMC data => Saturation effects are considerably increased in nuclei

47. Diffractive Scattering Non-Diffractive Event ZEUS detector Diffractive Event M X - invariant mass of all particles seen in the central detector t - momentum transfer to the diffractively scattered proton t - conjugate variable to the impact parameter

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

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