1. The Structure of the Pomeron I. Y. Pomeranchuk 

2. Electroweak  Z 0, W +, W - Quantumchromodynamics 8 gluons Precision measurements and test of higher order corrections Excellent experimental confirmation Main assumptions experimentally verified Predictions so far are limited: QCD is too complicated for our present theoretical and mathematical methods --> limited areas of application Very much work is spendt to enlarge the areas where QCD can be applied.

3. Elements of QCD All particles with color charge participate: Quarks Antiquarks Gluons Gluons carry color charge. They interact with each other This is all the difference to QED!! Experimental Status: Gluons exist and carry spin 1 Gluons carry color charge: ‚tripel gluon vertex‘ exists There are 8 gluons (the gauge group is SU(3) C ) ss ss ss

4. coupling small for short distances (large scales) ‚hard processes‘ coupling rises strongly for large distances (≥. 2 fm) ‚soft processes‘ Perturbation theory works only for small distances, large scales (>1 GeV 2 ) ~1/r k*r V(r) r[fm] 1    GeV   1 10 100 ss no free quarks and gluons at large distances color string fragmentation Color dipoles pp r ~ 1/  

5. Protons and Predictions of QCD 1. bound state: proton is complicated state of three valence quarks, bound by gluon field (99.9% of mass!). QCD description: lattice theory p p 3. p-p scattering at high energies: total X-section and elastic scattering  tot ~ Im [ A el (t=0)] Very active new working area! None of the established methods works! 2. Parton-Parton scattering ‚hard processes with large scale‘: production of W‘s,Z 0,Top, Jets Successful description by perturbative QCD:  S << 1 p p needs parton distributions

6. Experimental facts of p-p scattering at high energies We observe a rather simple and universal picture! E cm [GeV]  tot 1. total cross sections rise at high energy with s=E cm 2    tot = a s -  + b s 1. Proton has diffuse edge (Gauß profile) 2. it becomes larger with s 3. it is grey!  = 0.0808 determines the rise at high energy d  /dt t[GeV 2 ] 2. differential X-section shows ‘diffraction’ picture d  /dt ~ s 2 e -bt E CM

7. The Pomeron high energy scattering is dominated by the exchange of ‚particles‘: ‚Regge trajectories = hadons and their rotational exitations‘  tot s [  (0)-1] = s -0.45 for ´Reggeon´  (t) =  (0) +  ´ t trajectory d  /dt ~ s 2[  (t) –1] describes fall of X-section at low energies E CM < 20 GeV p p X  f    rajectory (Reggeon) X J  No exhange particle is known for sure which could explain the rise of p-p scattering at high energy! It would carry the quantum numbers of the vacuum P=C = +1 and is colorless! artificial name : POMERON QCD: ´Pomeron´ must be composed of qq or gluon-gluon states! Pomeron C=P=+1 p p

8. The best experimental surrounding to study these questions are not offered by the Tevatron (as might be expected) but by the Electron-Proton Storage Ring HERA (DESY)

9. HERA e p 30 GeV 820 (920) GeV H1 ZEUS Start of construction 1984 Data taking: start 1992 end 30.06.2007 ca. 800 physicists at both e-p experiments construction cost HERA ~ 1.2 billion DM 2 experiments ~200 MDM e p √s =320 GeV in HH…. DESY

10. Deep Inelastic e-p Scattering: Measurement of Parton Structure p e e Spectators color string Scattering event at HERA (H1) Evidence for Scattering from pointlike partoncs ( colored quarks) Electron is scattered by large angle ~1/sin 4 (θ/2  ‚ Jets‘ in final state Hadrons in proton direction: a colored parton was scattered and left the proton color string

11. Snapshot of Parton Distribution with time resolution of ~1/Q << 1 fm Snapshot of Parton Distribution with time resolution of ~1/Q << 1 fm p e e  Hard scattering process t h ~ 1/Q << 1 fm fragmentation t F > 1 fm F 2 = Σe i 2 x[q i (x)+q i (x)] Q2Q2 x p p

12. Q 2 -Evolution of Strukturfunktionen Electrons scatter only from Quarks F 2 changes with Q 2, because resolution improves: the rise of F 2 at small x depends on the gluon density F 2 ep (x,Q 2 ) =  e f 2 x[ q f (x,Q 2 )+q f (x,Q 2 ) ]  dominant

13. Quark und Gluon Densities in the Proton Gluon density is determined from the observed scaling violations or directly from 2-jet cross sections gluon Quark densities are directly measured: 50% of proton momentum! x Gluon- Momentum distribution ~ x – g F 2 (x) ~ x – at small x huge

14. QCD universality: the parton densities are valid for all hard scattering processes, (after corrections for higher order effects in  S ) Example: 2 -Jet cross section in pp collisions is predicted! Universality of Parton distributions: a triumph of QCD  LHC x~0.03 x~0.3 Tevatron

15. Hadron-Hadron Scattering at HERA? Infinite momentum frame Q2Q2 x p e x= Q 2 /y*s (momentum fraction of parton) Electrons as probes for quark Structure -- parton densities, scaling violations.. Q 2 steers the transition from hard collisions ( perturbative QCD) to soft hadron physics. We can ‘engineer’ our hadron! F 2 (x, Q 2 ) = F 2 (W 2, Q 2 ) ≈ 4π  2 Q 2 * σ  *p (W 2,Q 2 ) Proton rest frame r T ~2/Q ( size of dipole) rTrT L ~ 1/x ~ 50 fm! ~ 1 .01 fm At low x a color dipole of variable size 2/Q interacts with the proton at high CM energy s=W 2 (  p) ≈ Q 2 /x ≈ 1000 ÷ 90000 GeV 2 Low x = high energy scattering!  *p

16. the  * p cross section at high energies Another look at deep inelastic scattering: proton rest system   p (W 2 )~ F 2 (W 2,Q 2 )/Q 2 ~ W 2 =0.08 =0.35 W2W2 low x soft Pomeron (p-p) intercept slope depends on Q ~ 1/r: there can be no universal Pomeron!

17. diffractive scattering 1. elastically scattered Proton! (would be best ) 2. no ‚forward energy‘ (rapidity gap event ) ca. 10% of all events xPxP q  Rapidity gap DIS gap p Large Q  e Events first seen by ZEUS

18. Electron Scattering from the Pomeron we measure the diffractive structure function F 2 D ( , Q 2, x P ) in inclusive scattering: Quark structure of the Pomeron e xPxP q  Rapidity gap Experimental Facts: 1. F 2 D ( , Q 2, x P ) = x P -2[  (t)-1] *F 2 D (  Q 2 ) Pomeron flux * Quark distribution of Pomeron 2.  = 1.16±.03 = 1.08 ! ( not soft Pomeron) 2. We scatter from pointlike partons - scaling - Jets Resolved Pomeron Model: -The wave function of the Protons contains a ‚Pomeron‘ component. -The electron scatters from the quarks in the ‚Pomeron‘. -The Pomeron flux factor is not described by the soft Pomeron!

19. Diffractive Parton Distributions approximate scaling  F2DQ2)F2DQ2)   QCD analysis of scaling violations: dominated by The Pomeron is dominated by Gluons Gluons (~75 % of Pomeron momentum ) Gluons have high average momenta  but badly known at high  Quark distribution is directly measured

20. Direct Measurement of the Pomeron Gluon Distribution -jet 2-Jet  events measure gluons in the Pomeron! Factorisation? Are diffractive parton distributions universal for all diffractive processes? Do we get the same gluon distribution?

21. 2-Jet cross section shows same Pomeron flux with  (0)=1.2 and agrees with resoved Pomeron model. Gluon density is in agreement with F 2 D but only with Fit B  2-jets discriminate between solutions Pomeron is dominated by gluons qqg fluctuationen in the Photon dominate QCD factorisation is valid for Diffractive Deep Inelastic Scattering this is required by QCD -> Collins 222-Jet cross section in diffractive DIS NLO QCD prediciton based on factorisation ß ß

22. 22Diffractive Parton Distributions (best set) Combinded QCD analysis of F 2 D and 2-jet X-cross sections assuming factorisation z =  can we use them?

23. Diffractive Parton Densities in p-p Collisions (Tevatron) p p pp jet Faktor 10 gap  Predicted cross section using diffractive parton Densities from HERA Diffractive X-sections in pp do not factorise! ??????? Diffractive processes in hadron reactions are more difficult to describe. What destroys factorisation?  study HERA  p (controversial..) Several models on the market to explain this fact: Multiple interactions including ‚spectator partons destroy the rapidity gap or color neutralisation by soft gluons depends on parton final state and CM energy

24. Central diffractive particle production at pp Colliders Central Higgs production at LHC?Test at Tevatron: central 2-jet  CDF

25. Main experimental results 1.‚Pomeron‘ is (dominantly) a gluon state rise of γ*p cross section is not universal but depends on Q 2 The diffractive gluon density is universal for DIS It cannot be applied directly to Hadron-Hadron scattering These facts must be reproduced by any theoretical description! Next: Theoretical models which try to describe more aspects of diffractive scattering - flux factors - parton densities resp. σ γ*p

26. Could Pomeron be a Regge trajectory which is exchanged in diffractiven processes? The bound states on this trajectory could be glueballs! Model of Donnachie und Landshoff soft Pomeron:  S (t) = 1.008 + 0.25 * t Phenomenological description of total X-sections by Pomeron trajectory glueball candidates J=2 Soft Pomeron E xperiment: intercept  (0) of the ‚trajectory‘ changes with Q 2 resp. the size of the hadrons. There can be no universal Pomeron trajectory! Model describes data rather well and is economic! hard Pomeron:  H (t) = 1.44 + 0.10 * t   p (W 2,Q 2 ) at high Q 2 (98): Use 2 Pomeron trajectories

27. from hard to soft physics: do we see saturation? We measure high energy scattering of a color dipole with the proton We can choose the transverse size of the dipole via Q 2 The only unknown in principle is the dipole-p cross section which depends on: x ~ 1/t the transverse size of the dipole the distribution profile of the gluons in the proton can it be calculated? r~1/Q dipole-p cross- section dipole WF in the photon (calc.) diffraction (F 2 D ) F2F2 σ  *p (x,Q 2 )~ F 2 (x,Q 2 )/Q 2 σ T,L diffr B

28. the dipole –p cross section: the saturation model r~2/Q R 0 (x)  qq perturbative QCD predicition for small dipole sizes ~r 2 R 0 (x) ~ (1/x) λ : average gluon distance at which saturation sets in. Depends also on transverse gluon profile T(b). ~r 2 (perturbative) saturation simplest version: Golec-Biernat, Wüsthoff 99 : R 0 (x)= (x/x 0 ) λ * 1 GeV 2 improvements: + Bartels, Kowalski proton Ψ diffractive Ψ production describable by 2-gluon exchange (LO only so far) Ψ confront to data: Fits to F 2 at x<10 -2 to determine free parameters:  x 0 = 3 10 -4, λ= 0.15, describes transition to soft physics!  

29. successes of dipole saturation model τ = Q 2 * R 0 2 (x) 1. describes F 2 at small x and moderate Q 2 2. predicts ‘geometric scaling’ of F 2 at small x F 2 (x,Q 2 ) = F 2 ( Q 2 * R 0 2 (x) ) eqiv. σ  *p = σ  *p (Q 2 *R 0 2 (x) ) 3. predicts the ratio DIS diffractive/ DIS = constant vs. energy  this was one of the simple messages of the data which are not easily explained 4. detailed predictions concerning diffractive processes (needs more theoretical work) This is of course no proof of saturation but several disconnected effects are successfully predicted…  very appealing though not compelling

30. soft color interaction:,calculation‘ of dipole cross section in ‘semiclassical model’ The qq color dipole is scattered from the color field of the Proton and is neutralized statistically. How does the gluon field look like in the proton ?

31. Free parameters (few) are determined by a fit of the predictions to F 2 (x,Q2)  Diffractive distributions are predicted. description of F 2 D is ‘acceptable’

32. Models exhibit approximate factorisation of Pomeron flux Normalisation off by factors 2 BUT: only leading order (no progress recently) Diffractive 2-Jet events Models with color neutralisation by soft gluons (non pertubative) Color dipole models: 2gluon-exchange and ‚saturation‘ 2gluon Res. Pomeron saturation

33. S= E cm 2 edge area increases due to the evolution of soft gluons which become visible (active) at high energy proton gets blacker and inceases its size with increasing CM energy b_ ‚ black‘ example: model of Pirner, Shoshi, Steffen ‚2002 HERA energy how does the proton look like at high energy? Profile function LHC could be consolidated much better by HERA measurements and their theoretical interpretation