Particle number fluctuations and correlation

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

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

3. 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 Marcus Bleicher, Santiago de Compostela 2006

4. Energy density fluctuations Pb(160AGeV)+Pb • Hot spots in the ‘thermal’ energy density • ‘Clusters’ of size ~ 5 fm3 e (GeV/fm3) X (fm) y (fm) Dz=1fm M. Bleicher et al, Nucl.Phys.A638:391,1998 Marcus Bleicher, Santiago de Compostela 2006

5. 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 Marcus Bleicher, Santiago de Compostela 2006

6. 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 Marcus Bleicher, Santiago de Compostela 2006

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 Marcus Bleicher, Santiago de Compostela 2006

9. Fluctuations/Correlations II • String mass: P(m2)~1/m2Multiplicity fluctuations at fixed Ecm • Fluctuations of string tension (A. Bialas 2000)strangeness and pT fluctuations • Resonance decays • Flow • Jets Marcus Bleicher, Santiago de Compostela 2006

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

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

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

13. 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 Marcus Bleicher, Santiago de Compostela 2006

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

15. Multiplicity fluctuations at SPS:The problem • The fluctuation is quantified with the • scaled variance : • Enhanced fluctuations for mid- • peripheral collisions are observed Similar results from HIJING, HSD and RQMD Note : - for a poisson distribution, w=1 Marcus Bleicher, Santiago de Compostela 2006

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

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

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

19. The number of participants Calorimeter : measure of the energy deposited by the projectile spectators TPC’s : measure of the particles multiplicities In the UrQMD, the number of participant spectators is determined with a rapidity cut on the nucleons Marcus Bleicher, Santiago de Compostela 2006

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

21. 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 Marcus Bleicher, Santiago de Compostela 2006

22. 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 M. Gazdzicki and M. Gorenstein:arXiv:hep-ph/0511058 Marcus Bleicher, Santiago de Compostela 2006

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

24. Lattice estimate of CBS CBS can be obtained from lattice simulations : - calculate off-diagonal susceptibilities - vanishing chemical potential - quenched approximation (no quarks of the sea) with css/T2=0.53 and cus+ cds=0, CBS~1consistent 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 Marcus Bleicher, Santiago de Compostela 2006

25. Baryon-Strangeness Correlations 2 • Limiting cases for CBS: • Large mB: CBS3/2 • large acc. window: CBS0Explored with help of increasing rapidity window inAu+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 Marcus Bleicher, Santiago de Compostela 2006

26. Baryon-Strangeness Correlations 3 Energy dependence of CBS allows to study the onset of deconfinement transition Note that the QGP result is for m=0 Here |ymax|<0.5 • Deviations from the HG are expected around high SPS energy region, due to QGP onset. Haussler, Stoecker, Bleicher,hep-ph/0507189 Marcus Bleicher, Santiago de Compostela 2006

27. Baryon-Strangeness Correlations 4 Centrality dependence of CBS allows to study the critical volume needed for QGP formation. Note that the QGP result is for m=0 |ymax|<0.5, Ecm=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 Marcus Bleicher, Santiago de Compostela 2006

28. 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. Marcus Bleicher, Santiago de Compostela 2006

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