1. Marcus Bleicher, Santiago de Compostela 2006 Particle number fluctuations and correlation Marcus Bleicher Institut für Theoretische Physik Goethe Universität Frankfurt Germany

2. Marcus Bleicher, Santiago de Compostela 2006 Outline of the talk Introduction Ratio fluctuations - D - scaled variance Baryon-strangeness correlations Summary

3. Marcus Bleicher, Santiago de Compostela 2006 Motivation At RHIC: look for signals of freely moving partons. At FAIR/SPS: look for the mixed phase and the onset of deconfinement E. Bratkovskaya, M.B. et al., PRC 2005

4. Marcus Bleicher, Santiago de Compostela 2006 Energy density fluctuations Hot spots in the ‘thermal’ energy density ‘Clusters’ of size ~ 5 fm 3 M. Bleicher et al, Nucl.Phys.A638:391,1998 X (fm) y (fm)  (GeV/fm 3 ) Pb(160AGeV)+Pb  z=1fm

5. Marcus Bleicher, Santiago de Compostela 2006 The tool UrQMD : Ultra-Relativistic Quantum Molecular Dynamics out-of-equilibrium transport model Particles interact via : - measured and calculated cross sections - string excitation and fragmentation - formation and decay of resonances Provides full space-time dynamics of heavy-ion collisions

6. Marcus Bleicher, Santiago de Compostela 2006 What can transport models do? Provide baseline calculations, including resonances, jets, flow,… Study energy/centrality dependence Provide a look “behind the curtain”, i.e. what is the origin of the observed effect Study acceptance effects, i.e. how does limited detector coverage and the trigger conditions influence the results

7. Marcus Bleicher, Santiago de Compostela 2006

8. Sources of fluctuations I Centrality determination - same volume? - same energy deposition? - same particle density? Number of (initial) collisions - elastic vs inelastic Collision energy spectrum of the individual collisions

9. Marcus Bleicher, Santiago de Compostela 2006 Fluctuations/Correlations II String mass: P(m 2 )~1/m 2  Multiplicity fluctuations at fixed E cm Fluctuations of string tension (A. Bialas 2000)  strangeness and p T fluctuations Resonance decays Flow Jets

10. Marcus Bleicher, Santiago de Compostela 2006 Ratio fluctuations proposed by Jeon, Koch, Mueller, Asakawa… (2000) E.g.

11. Marcus Bleicher, Santiago de Compostela 2006 The ‘famous’ D: The first smoking gun prediction Bleicher, Jeon, Koch, PRC (2000)

12. Marcus Bleicher, Santiago de Compostela 2006 Similar results from other models Zhang, Topor Pop, Jeon, Gale, hep-ph/0202057

13. Marcus Bleicher, Santiago de Compostela 2006 and why it doesn’t work Hadronization (quark recombination) destroys the fluctuation Finite acceptance might also destroy the signal (Zaranek et al.) qMD calculation by S. Scherrer

14. Marcus Bleicher, Santiago de Compostela 2006 Multiplicity fluctuations Extraction of the multiplicity distribution for every N par Note: Calculation is narrower than the data Pb+Pb (158 AGeV) in the NA49 acceptance (1.1<y CM <2.9)

15. Marcus Bleicher, Santiago de Compostela 2006 The fluctuation is quantified with the scaled variance : Enhanced fluctuations for mid- peripheral collisions are observed Multiplicity fluctuations at SPS: The problem    Similar results from HIJING, HSD and RQMD

16. Marcus Bleicher, Santiago de Compostela 2006 Multiplicity fluctuations at SPS: Not a problem? There seems not to be a problem in string cluster approaches.

17. Marcus Bleicher, Santiago de Compostela 2006 Where is the problem? Pb+Pb (158 AGeV) in the NA49 acceptance (1.1<y CM <2.9) mean value correctly reproduced Variance reproduced for central and very peripheral events Failure for mid-peripheral events

18. Marcus Bleicher, Santiago de Compostela 2006 Analysis of different windows the normalized variance : flat in the projectile hemisphere larger in the mirror acceptance even larger in 4  maximum around N p =40

19. Marcus Bleicher, Santiago de Compostela 2006 The number of participants  ’       

20. Marcus Bleicher, Santiago de Compostela 2006 Fluctutions in target region the fluctuation has a maximum around N p =25 introduces an asymetry between projectile and target participants leads to an increase of the multiplicity fluctuation in the target hemisphere

21. Marcus Bleicher, Santiago de Compostela 2006 Correlation length in rapidity Rapidity window dependence : correlation length of the order of 1 unit of rapidity  target and projectile hemisphere are independent in hadron-string models

22. Marcus Bleicher, Santiago de Compostela 2006 Mixing and fluctuations   I.e. the trigger condition ‘marks’ projectile and target participants This allows to study the degree of mixing of the matter produced in HIC Data suggest strong mixing of hemispheres  Hints to expanding initial fireball in contrast to string dynamics

23. Marcus Bleicher, Santiago de Compostela 2006 Baryon-Strangeness Correlations Definition: Idea: Strangeness and baryon number carriers are different in QGP and hadron gas. First suggested by V. Koch et al., 2005 HG: strangeness is decoupled from baryon number (mesons)  small C BS correlation QGP: strangeness is fixed to baryon number (strange quark)  large C BS correlation

24. Marcus Bleicher, Santiago de Compostela 2006 Lattice estimate of C BS C BS can be obtained from lattice simulations : - calculate off-diagonal susceptibilities - vanishing chemical potential - quenched approximation (no quarks of the sea) with  ss /T 2 =0.53 and  us +  ds =0,  C BS ~1 consistent with a weakly interacting QGP R.V. Gavai and S.Gupta Phys. Rev. D 67/65 A. Majumder, V. Koch, J. Randrup arXiv:nucl-th/0510037

25. Marcus Bleicher, Santiago de Compostela 2006 Baryon-Strangeness Correlations 2 Limiting cases for C BS : Large  B : C BS  3/2 large acc. window: C BS  0 Explored with help of increasing rapidity window in Au+Au reaction at RHIC Present models yield similar results for small rapidity window Different handling of the fragmentation region/spectators influences results at large rapidities Haussler, Stoecker, Bleicher, hep-ph/0507189

26. Marcus Bleicher, Santiago de Compostela 2006 Baryon-Strangeness Correlations 3 Energy dependence of C BS allows to study the onset of deconfinement transition Note that the QGP result is for  Here |y max |<0.5 Deviations from the HG are expected around high SPS energy region, due to QGP onset. Haussler, Stoecker, Bleicher, hep-ph/0507189

27. Marcus Bleicher, Santiago de Compostela 2006 Baryon-Strangeness Correlations 4 Centrality dependence of C BS allows to study the critical volume needed for QGP formation. Note that the QGP result is for  |y max |<0.5, E cm =200AGeV Hadron-string transport models predict no centrality dependence of CBS A QGP transition leads to a strong centrality dependence Haussler, Stoecker, Bleicher, hep-ph/0507189, PRC in print

28. Marcus Bleicher, Santiago de Compostela 2006 Summary The D puzzle is solved: hadronization destroys all initial state correlations Hadron-string models fail to reproduce the measured multiplicity fluctuations  might indicate that the matter at CERN SPS is ‘mixed’ Baryon-strangeness correlations allow to pin down the onset of the QGP transition. Fluctuations and correlations are valuable tools to study heavy ion reactions. However, the interpretation is usually difficult.

29. Marcus Bleicher, Santiago de Compostela 2006 Thanks Elena Bratkovskaya Manuel Reiter Sascha Vogel Xianglei Zhu Horst Stoecker Diana Schumacher Hannah Petersen Stephane Haussler Diana Schumacher