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

1. Small-x and Diffraction atHERAand LHCHenri KowalskiDESY EDS Château de Blois 2005

2. HERA – ep Collider H1 ZEUS e 27 GeV p 920 GeV Liquid Argon Calorimeter Uranium-Scintillator Calorimeter Q2 - 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 ~ Q2/W2

3. y – inelasticity Q2 = sxy Infinite momentum frame Proton looks like a cloud of non-interacting quarks and gluons F2 measures parton density in the proton at a scale Q2

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

5. Diffractive Scattering Non-Diffractive Event ZEUS detector Diffractive Event MX - 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 er<<1 Q2~1/r2 Optical T Mueller, Nikolaev, Zakharov 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

7. Comparison with Data FS modelwith/without saturation and IIMCGC model hep-ph/0411337. Fit F2 and predict xIPF2D(3) FS(nosat) F2 CGC FS(sat) F2 x

8. Diffractive contribution of the total cross section • For larger MX, sdiff has the similar W and Q2 dependences as stot. • For the highest W bin (200<W<245 GeV), • sdiff(0.28<MX<35 GeV, MN<2.3 GeV) /stot

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

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

11. Dipole cross section determined by fit to F2 Simultaneous description of many reactions F2 C Gluon density test? Teubner IP-Dipole Model g*p -> J/y p g*p -> J/y p IP-Dipole Model

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

13. Saturation scale HERA RHIC QSRHIC ~ QSHERA

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

15. Absorptive correction to F2 Example in Dipole Model - F2 ~ Diffraction Single inclusive pure DGLAP

16. 2-Pomeron exchange in QCD Final States (naïve picture) detector Diffraction 0-cut DY g* p g*p-CMS <n> 1-cut g* p g*p-CMS detector <2n> 2-cut g* p g*p-CMS

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

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

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 xIP = Dp/p, pT xIP ~ 0.2-1.5% xIP = Dp/p, pT xIP ~ 0.2-1.5% 1 event/sec low x QCD reactions: pp => pp + gJet gJets ~ 1 nb for ET > 20 GeV , M(jj) ~ 50 GeV s ~ 0.5 pb for ET > 60 GeV , M(jj) ~ 200 GeV hJET| < 2 KMR Eur. Phys J. C23, p 311 sDiff = hard X-section × Gluon Luminosity factorization !!! gg Jet+Jet gg Higgs pp => pp + Higgs s ~ O(3) fb SM ~ O(100) fb MSSM fg – unintegrated gluon densities

22. t – distributions at LHC with the cross-sections of the O(1) nb and L ~ 1 nb-1 s-1 => O(107) events/year are expected. For hard diffraction this allows to follow the t – distribution to tmax ~ 4 GeV2 For soft diffraction tmax ~ 2 GeV2 t – distributions at HERA 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 Saturated gluons

23. Survival Probability S2 Soft Elastic Opacity t – distributions at LHC Effects of soft proton absorption modulate the hard t – distributions Khoze Martin Ryskin Dipole form double eikonal t-measurement will allow to disentangle the effects of soft absorption from hard behavior single eikonal

24. F2 Gluon Luminosity Exclusive Double Diffraction Dipole Model L. Motyka, HK preliminary QT2 (GeV2)

25. Conclusions We are developinga very good understanding of inclusive and diffractive g*p interactions: F2 , F2D(3) , F2c , 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. The behavior of the rise with Q2 universal rate of rise of all hadronic cross-sections Smaller dipoles  steeper rise Large spread ofleffcharacteristic for IP Dipole Models

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

29. Unintegrated Gluon Densities Dipole Model Exclusive Double Diffraction Note: xg(x,.) and Pgg drive the rise of F2 at HERA and Gluon Luminosity decrease at LHC

30. Saturation Model Predictions for Diffraction

31. Absorptive correction to F2 Example in Dipole Model F2 ~ - Diffraction Single inclusive pure DGLAP

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

35. 2-Pomeron exchange in QCD Final States (naïve picture) detector Diffraction 0-cut DY g* p g*p-CMS <n> 1-cut g* p g*p-CMS detector <2n> 2-cut g* p g*p-CMS

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

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

38. Problem of DGLAP QCD fits to F2 CTEQ, MRST, …., IP-Dipole Model at small x valence like gluon structure function ? Remedy: Absorptive corrections? MRW Different evolution? BFKL, CCSS, ABFT

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

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

41. Density profile grows with diminishing x and r approaches a constant value Saturated State - Color Glass Condensate S – Matrix => interaction probability Saturated state = high interaction probability S2 => 0 multiple scattering rS - dipole size for which proton consists of one int. length

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

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

44. RHIC

45. Conclusions We are developinga very good understanding of inclusive and diffractive g*p interactions: F2 , F2D(3) , F2c , 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 MX - 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. Diffractive Signature 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 note : DY ~ log(W2 / M 2X)

49. 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) Rise of sgptot with W is a measure of radiation intensity Diffraction is similar to the elastic scattering: replace the outgoing photon by the diffractive final state r , J/Y or X = two quarks