1. NE X US hep-ph/0007198 Physics Reports 350 (2001) 93-289 Guideline: theoretical consistency hep-ph/0102194 Phys. Rev. Lett. 86 (2001) 3506 Hajo Drescher, Fuming Liu Sergej Ostapchenko, Tanguy Pierog Klaus Werner

2. 1 Parton-based Gribov-ReggeTheory Aim: connecting properly parton model and Gribov-Regge Theory Extending work by Gribov, Kaidalov, Capella...

3. Reminder (Basic QM)

4. Symbols: full and dashed line  elastic and cut diagram Very useful for nucleus-nucleus

5. soft hardsemihard (one of three) The elastic amplitude: Soft: parameterization - hard: pQCD - semihard: convolution soft/hard

6. Inelastic scattering in pp: Amplitude: Squared amplitude => interference terms: => Symbolic notation

7. Inelastic scattering in AB: Squaring amplitude  sum over many interference terms expressed via cut and uncut elementary diagrams full energy conservation!! (Elastic and inelastic elem. Interactions)

8. We sum all terms in a class =>  (K). The inelastic cross section is a sum over classes: Symbol b = impact parameter + nuclear coordinates - Number of cut diagrams for kth NN pair - Momentum fractions of elementary interactions Classes of interference terms:

9. Interpretation: One can show: with

10.  serves clearly as basis to calculate (topological) cross sections but also particle production conserving energy in both cases !! (the only model which does so) Consistency problem solved !!

11. Pomeron number distribution narrower than in conv. appr. Considerably less multiplicity fluctuations in pp comparison with data: not so great Comparing with conventional approach Dashed: conventional Full: new approach

12. 2 Pomeron-Pomeron Interactions Shadowing Saturation Diffraction Screening Increasing mult. fluctuations Solving F 2 -  tot puzzle One additional parameter: triple Pomeron coupling. Fixed from HERA diffractive data 

13. Parton language: Consider a cut Pomeron as a succession of parton emissions = parton cascade At high energies, more and more parton cascades contribute They overlap and interact

14. Energy dependence With increasing energy, higher and higher orders have to be considered We fix a maximal energy (so far LHC) and consider all contributing orders

15. Cutting diagrams

16. Elastic scattering: Cut diagrams: Reduces increase of cross section with energy (screening) Increases multiplicity fluctuations Some consequences

17. No effect on inclusive spectra: relative weight of diagrams 1 : -4 : 2  the three contributions cancel Inclusive spectra The diagrams do not cancel. The middle one is dominant.  negative contribution  softening of inclusive spectra

18. Consider the different contributions to inclusive particle production in pp scattering at given rapidity (  )  factorizable non-factorizable Contribution zero (complete cancellation)  inclusive cross section is factorizable

19. The different contributions to F 2 in deep inelastic scattering (DIS) are as well factorizable: So does this mean one can hide all these complicated diagrams in a simple measurable function f ? with the same function f as in pp scattering 

20. YES - if one is only interested in inclusive spectra NO - if one is interested in total cross sections:  tot = factorizable + non-factorizable diagrams Very important! NO - if one is interested in Monte Carlo applications topological cross sections = factorizable + non-factorizable diagrams Very important!

21. Structure function F 2 Red: complete calculation Blue: calculation without Pomeron-Pomeron interactions Little difference !!!! because of many cancellations

22. Total and elastic cross section in pp Red: complete calculation Blue: calculation without Pomeron-Pomeron interactions Big difference!!! Important contributions from nonfactorizable diagrams

23. 3 NE X US + Hydro Nucleus-nucleus collisions: particle densities are too high for independent string fragmentation Use NEXUS for the initial stage (  0 ) Calculate energy density and velocity field at  =  0 Apply hydro evolution for  0 (event by event!) Efficient hydro code = SPHERIO C.E. Aguiar, T. Kodama U.F. Rio de Janeiro T. Osada,Y. Hama U. São Paulo Coupling: O. Socolowski, KW Nantes

24. Summary Final stage: hydro-evolution Considerable improvement of the GRT approach by considering energy conservation properly Pomeron-Pomeron interactions are crucial but contribute differently for inclusive spectra and cross sections (eikonal approach does not work)