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Models for RHIC and LHC: New Developments

Presently used models for the initial stage are inconsistent Main problem: energy conservation not done properly Big effects. ==> New ideas are needed ( H. Drescher, S. Ostapchenko, T. Pierog, K. W. ). Models for RHIC and LHC: New Developments.

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Models for RHIC and LHC: New Developments

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  1. Presently used models for the initial stage are inconsistent Main problem: energy conservation not done properly Big effects ==> New ideas are needed ( H. Drescher, S. Ostapchenko, T. Pierog, K. W. ) Models for RHIC and LHC:New Developments Klaus WERNER, Nantes

  2. Multiple scattering approach (parallel i.a.) Elementary interaction = Pomeron Ignoring energy sharing: simple formulas Open Problems(Gribov-Regge Approach and Parton Model) Gribov Regge Theorie K. Werner

  3. Model: Pomeron = cylinder Doubles scattering: double cylinder => chains of hadrons Full energy conservation BUT: Energy conservation is not at all considered in cross section calculations Wrong by itself And inconsistent with particle production Particle production: K. Werner

  4. Inclusive cross section as convolution of parton distributions with parton-parton cross section ... QCD … but how to deal with multiple scattering? Via the eikonal approach => same formula as in GRT (no energy conservation) Parton Model Same problems K. Werner

  5. Formulate (topol.) cross section calculations and particle production within one consistent approach Respect energy conservation in a rigorous way This is a MUST, dictated by theoretical consistency Increases predictive power enormously What to Do? K. Werner

  6. hep-ph/0007198 (213 pages) to be published in Physics Reports H. Drescher, S. Ostapchenko, T. Pierog, K. Werner Solution: Parton-based Gribov-Regge Theorie Guideline: theoretical consistency K. Werner

  7. Reminder (Basic QM) K. Werner

  8. Successive parton emissions Ordered virtualities down to some minimum value Below: soft physics (?) Structure of the Nucleon Deep inelastic scattering (photon-nucleon scattering): K. Werner

  9. Mass of the soft object emitting the first parton: x being the momentum fraction of the parton if sea quark  distribution 1/x  large mass !!! if valence quark  distribution 1/  small mass Emission of the first (softest) parton: K. Werner

  10. Valence: Sea: Two contributions: Large mass object soft Pomeron K. Werner

  11. Straightforward generalization of photon-nucleon hard scattering in the middle successive parton emission towards both ends at each end: valence (v) or sea (s)  four contributions (ss,vs,sv,vv) ss,vs,sv -- semihard vv -- hard In addition: purely soft contribution Elementary Interaction in NN K. Werner

  12. The elastic amplitude: soft hard semihard (one of three) Soft: parameterization - hard: pQCD - semihard: convolution soft/hard K. Werner

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

  14. Multiple Scattering (AB or pp) Define model via elastic amplitude Basic version: parallel inter- actions Full energy conservation Inelastic scattering: deduced in a self-consistent way K. Werner

  15. Amplitude: Squared amplitude => interference terms: Inelastic scattering in pp: => Symbolic notation K. Werner

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

  17. Probability distribution  We define classes K of interference terms and sum all terms in a class => (K) => Symbol b = impact parameter + nuclear coordinates - Number of cut diagrams for kth NN pair - Momentum fractions of elementary interactions is probability distribution for these variables K. Werner

  18.  serves clearly as basis to calculate (topological) cross sections but also particle production conserving energy in both cases !! Consistency problem solved !! K. Werner

  19. Pomeron number distribution narrower than in conv. appr. Considerably less multiplicity fluctuations in pp pp multiplicity distributions much narrower than data pp total cross section increases too fast with energy PbPb multiplicity too high Comparing with conventional approach: Comparing with data: Nothing to do about due to considerably reduced parameter space !! K. Werner

  20. The cure: Pomeron-Pomeron interactions Elastic scattering: Reduces increase of cross section with energy (screening) Interference terms (cut diagrams): Increases multiplicity fluctuations K. Werner

  21. Present Status (= NEXUS 2) • Only lowest oder (Y diagrams) with effective coupling (improves pp considerably)see poster T. Pierog • no nuclear effects yet (but very soon). This should reduce multiplicity (screening) • many results in hep-ph/0007198 K. Werner

  22. It is possible to cure this problem and formulate multiple scattering consistently (proper energy conservation) But: too narrow multiplicity distributions, too fast increase of total cross section Presently used models (initial stage) are inconsistent Summary • Solution: Y diagrams (screening) • So far only lowest order • Final remark: we have to be more concerned about the theoretical content of model -- an ill-defined model which fits the data is quite useless ... K. Werner

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