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

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NE X US

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

  2. 1Parton-basedGribov-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. The elastic amplitude: soft hard semihard (one of three) Soft: parameterization - hard: pQCD - semihard: convolution soft/hard

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

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

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

  9. Interpretation: with One can show:

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

  12. 2 Pomeron-Pomeron Interactions  • Diffraction • Screening • Shadowing • Saturation • Increasing mult. fluctuations • Solving F2-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. Some consequences Elastic scattering: Reduces increase of cross section with energy (screening) Cut diagrams: Increases multiplicity fluctuations

  17. Inclusive spectra No effect on inclusive spectra: relative weight of diagrams 1 : -4 : 2  the three contributions cancel 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 ()  non-factorizable Contribution zero (complete cancellation) factorizable  inclusive cross section is factorizable

  19. The different contributions to F2 in deep inelastic scattering (DIS) are as well factorizable: with the same function f as in pp scattering  So does this mean one can hide all these complicated diagrams in a simple measurable function f ?

  20. 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! YES - if one is only interested in inclusive spectra

  21. Structure function F2 Little difference !!!! because of many cancellations Red: complete calculation Blue: calculation without Pomeron-Pomeron interactions

  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. Nucleus-nucleus collisions: particle densities are too high for independent string fragmentation 3 NEXUS + Hydro • 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 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) Final stage: hydro-evolution

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