1. Overview of low-x and diffraction at HERA Henri Kowalski DESY Rencontres de Moriond La Thuile, March 2006

2. F 2 is dominated by single ladder exchange ladder symbolizes a QCD evol. process ( DGLAP or others )

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

4. 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

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

6. Observation of diffraction indicates that single ladder may not be sufficient (partons produced from a single chain have exponentially suppressed rap. gaps) Inclusive DIS Hard Diffraction Optical T GBW – first Dipole Saturation Mode Golec-Biernat, Wuesthoff BGBK – DSM with DGLAP Bartels, Golec-Biernat, Kowalski IIM - BFKL-CGC motivated ansatz Iancu, Itakura, Munier FS – Regge ansatz with saturation Forshaw and Shaw Dipole Models equivalent to LO perturbative QCD for small dipoles Glauber Mueller

7. Impact Parameter Dipole Saturation Model KT - Kowalski Teaney KMW – Kowalski, Motyka, Watt proton shape

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

9. Inclusive Diffraction from fit to  tot predict  diff GBW, BGBK, …. -LPS

10. Dipole cross section determined by fit to F 2 Simultaneous description of many reactions F 2 C KMW KT

11. KMW

12. BGBG BGBG Description of the size of interaction region B D Modification by Bartels, Golec-Biernat, Peters proton size

13. Diffractive Di-jets Q 2 > 5 GeV 2 -RapGap Satrap

14. Saturation scale ( a measure of gluon density) HERA RHIC Q S RHIC ~ Q S HERA

15. Geometrical Scaling A. Stasto & Golec-Biernat J. Kwiecinski GS is an effective property of HERA data b-Dipole Model analysis: GS seen in the center of the proton Theoretical importance: property of non-linear evolution in QCD BK, JIMWLK

16. 2-Pomeron exchange in QCD Final States (naïve picture ) 0-cut 1-cut 2-cut Diffraction Multiple Interactions and Long Range Correlation

17. QCD diagrams

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

20. Exclusive Double Diffractive Reactions at LHC low x QCD reactions : pp => pp + g Jet g Jet  ~ 1 nb for M(jj) ~ 50 GeV   ~ 0.5 pb for M(jj) ~ 200 GeV  JET | < 1 x IP =  p/p, p T x IP ~ 0.2-1.5% High momentum measurement precision 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%

21. Absorptive corrections from BK equation Resummation of BFKL pomeron fan diagrams

22. Conclusions We are developing a very good understanding of inclusive and diffractive DIS interactions: F 2, F 2 D(3), F 2 c, Vector Mesons (J/Psi  HERA measurements suggests presence of Saturation phenomena Saturation scale determined at HERA agrees with RHIC Observation of diffraction indicates multi-gluon interaction effects -> Underlying events at LHC may be process dependent 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!!!! _____________________________________________________ Diffractive vector mesons scattering - an excellent probe of nuclear matter Ideal device: e-RHIC like machine with ~1/3 of HERA energy