3 Remarks on Fluctuations in Hadron Production at RHIC

1. New Results from the PHOBOS Collaboration 3 Remarks on Fluctuations inHadron Production at RHIC Gunther Roland Massachusetts Institute of Technology

2. PHOBOS Collaboration Burak Alver, Birger Back,Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Zhengwei Chai, Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Kristjan Gulbrandsen, Clive Halliwell, Joshua Hamblen, Ian Harnarine, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Jay Kane,Piotr Kulinich, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Eric Richardson, Christof Roland, Gunther Roland, Joe Sagerer, Iouri Sedykh, Chadd Smith, Maciej Stankiewicz, Peter Steinberg, George Stephans, Andrei Sukhanov, Artur Szostak, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Donald Willhelm, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, Shaun Wyngaardt, Bolek Wysłouch ARGONNE NATIONAL LABORATORY BROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER

3. RHIC Heavy Ion Collision

4. PHOBOS Experiment

5. Charged Hadron dN/d 19.6 GeV 62.4 GeV 130 GeV 200 GeV centrality preliminary PHOBOS Au+Au preliminary preliminary Cu+Cu Au+Au : PRL 91, 052303 (2003) d+Au : PRL 93, 082301 (2004) d+Au

6. 1st Remark To good approximation ( 10-4), all events are “the same”

7. Raw dN/d seen by PHOBOS Search for unusual events: I. Multiplicity Fluctuations  Integral II. Shape Fluctuation 2 of single-event vs average

8. Unusual Events in Au+Au Total Multiplicity Fluctuations Shape Fluctuations 2M Events Frequency of events 200 Events Multiplicity distribution and 2 (shape)distribution shows distinct tails - O(10-4)

9. Possible Explanation Total Multiplicity Fluctuations Shape Fluctuations Rate of unusual events correlates with ‘luminosity’ - Consistent with collision-pileup as source of rare events

10. 2nd Remark Hadrons are not produced one-by-one, but in “clusters”

11. N P N (Impact parameter) P+N P-N (Partitioning) P Analysis Concept Forward/backward multiplicity fluctuations RMS used to determine σC

12. Clusters and σ2C P N Forward/backward correlations give access to cluster structure of particle production

13. Cluster-size from F/B fluctuations 40-60% peripheral 0-20% central PHOBOS 200 GeV Au+Au preliminary PHOBOS 200 GeV Au+Au preliminary Forward/backward correlations suggest effective cluster size of  2-2.5 for 200 GeV Au+Au

14. Clusters in p+p UA5: Phys.Lett.B123:361,1983 Keff P+N 546 GeV Reminiscent of results from p+p

15. 3rd Remark Initial state shape fluctuations drive expansion dynamics

16. “Elliptic Flow” Non-central collision: Initial state eccentricity

17. Time Transverse Plane Azimuthal Angle (rad) “Elliptic Flow” 2*v2 Non-central collision: Initial state eccentricity Elliptic Flow: Final state anisoptropy

18. PHOBOS 200 GeV Statistical errors only PHOBOS 200 GeV h± Statistical errors only Au+Au preliminary Cu+Cu preliminary Elliptic Flow vs Npart v2 near mid-rapidity v2 for Au+Au follows initial state eccentricity

19. PHOBOS 200 GeV Statistical errors only PHOBOS 200 GeV h± Statistical errors only Au+Au preliminary Cu+Cu preliminary Elliptic Flow vs Npart v2 near mid-rapidity Substantial v2 even for most central bin in Cu+Cu

20. Standard Eccentricity Nucleus 1 y Nucleus 2 b x Participant Region Eccentricity Calculation Au+Au Au+Au Cu+Cu

21. Standard Eccentricity Participant Eccentricity x Nucleus 1 Nucleus 1 y Nucleus 2 y Nucleus 2 b b x Participant Region Participant Region Au+Au Au+Au Cu+Cu Eccentricity Calculation Au+Au Au+Au Cu+Cu

22. Density Scaling Standard Eccentricity Cu+Cu Au+Au Low Density Limit: STAR, PRC 66 034904 (2002) Voloshin, Poskanzer, PLB 474 27 (2000) Heiselberg, Levy, PRC 59 2716, (1999)

23. Participant Eccentricity Au+Au Cu+Cu Density Scaling Standard Eccentricity Cu+Cu Au+Au “Participant Eccentricity” allows v2 scaling from Cu+Cu to Au+Au Low Density Limit: STAR, PRC 66 034904 (2002) Voloshin, Poskanzer, PLB 474 27 (2000) Heiselberg, Levy, PRC 59 2716, (1999)

24. Summary To good approximation ( 10-4), all events are “the same”  Hadrons are not produced one-by-one, but in “clusters”  Initial state shape fluctuations drive expansion dynamics

25. Backup Raw data  

26. Standard Eccentricity Participant Eccentricity PHOBOS 200 GeV PHOBOS 200 GeV Cu+Cu preliminary Cu+Cu preliminary Au+Au Au+Au Backup “Participant Eccentricity” allows v2 scaling from Cu+Cu to Au+Au

27. Au+Au Cu+Cu L~A1/3 Backup “Participants” PHOBOS Glauber MC Au+Au Npart/2 ~ A Cu+Cu Ncoll= # of NN collisions: ~A4/3 “Collisions”

28. Au+Auvs Cu+Cu Interplay of initial geometry and initial density Test ideas of early thermalization and collectivity Nucleus 1 y Nucleus 2 PHOBOS Glauber MC x Participant Region Backup Au+Au Cu+Cu wrt reaction plane

29. Backup PHOBOS preliminary h± PHOBOS preliminary h± 0-50% centrality 0-50% centrality PHOBOS preliminary h± 0-50% centrality Eccentricity difference is important for same centrality selection. V2(pT) for Cu-Cu is similar v2(pT) for Au-Au when scaled by part

30. Cu+Cu preliminary Au+Au Backup Au+Au: PRL 94, 082304 (2005), PLB 578, 297 (2004)