1. Gunther Roland - MITPHOBOS ISMD’05 3 Remarks on Fluctuations in Hadron Production at RHIC Gunther Roland Massachusetts Institute of Technology New Results from the PHOBOS Collaboration

2. Gunther Roland - MITPHOBOS ISMD’052 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 LABORATORYBROOKHAVEN NATIONAL LABORATORY INSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOWMASSACHUSETTS INSTITUTE OF TECHNOLOGY NATIONAL CENTRAL UNIVERSITY, TAIWANUNIVERSITY OF ILLINOIS AT CHICAGO UNIVERSITY OF MARYLANDUNIVERSITY OF ROCHESTER PHOBOS Collaboration

3. Gunther Roland - MITPHOBOS ISMD’053 RHIC Heavy Ion Collision

4. Gunther Roland - MITPHOBOS ISMD’054 PHOBOS Experiment

5. Gunther Roland - MITPHOBOS ISMD’055 centrality Au+Au : PRL 91, 052303 (2003) d+Au : PRL 93, 082301 (2004) 19.6 GeV62.4 GeV130 GeV 200 GeV preliminary Cu+Cu d+Au Au+Au PHOBOS Charged Hadron dN/d 

6. Gunther Roland - MITPHOBOS ISMD’056 1st Remark To good approximation (  10 -4 ), all events are “the same”

7. Gunther Roland - MITPHOBOS ISMD’057 Raw dN/d  seen by PHOBOS Search for unusual events: I. Multiplicity Fluctuations  Integral II. Shape Fluctuation   2 of single-event vs average

8. Gunther Roland - MITPHOBOS ISMD’058 Unusual Events in Au+Au Multiplicity distribution and  2 (shape) distribution shows distinct tails - O(10 -4 ) 200 Events Total Multiplicity FluctuationsShape Fluctuations 2M Events Frequency of events

9. Gunther Roland - MITPHOBOS ISMD’059 Possible Explanation Rate of unusual events correlates with ‘luminosity’ - Consistent with collision-pileup as source of rare events Shape FluctuationsTotal Multiplicity Fluctuations

10. Gunther Roland - MITPHOBOS ISMD’0510 2nd Remark Hadrons are not produced one-by-one, but in “clusters”

11. Gunther Roland - MITPHOBOS ISMD’0511 Analysis Concept RMS used to determine σ C P-N P N P+N (Impact parameter) (Partitioning) PN Forward/backward multiplicity fluctuations

12. Gunther Roland - MITPHOBOS ISMD’0512 Clusters and σ 2 C P N Forward/backward correlations give access to cluster structure of particle production

13. Gunther Roland - MITPHOBOS ISMD’0513 Cluster-size from F/B fluctuations 40-60% peripheral0-20% 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. Gunther Roland - MITPHOBOS ISMD’0514 Clusters in p+p 546 GeV P+N UA5: Phys.Lett.B123:361,1983 K eff Reminiscent of results from p+p

15. Gunther Roland - MITPHOBOS ISMD’0515 3rd Remark Initial state shape fluctuations drive expansion dynamics

16. Gunther Roland - MITPHOBOS ISMD’0516 “Elliptic Flow” Non-central collision: Initial state eccentricity

17. Gunther Roland - MITPHOBOS ISMD’0517 “Elliptic Flow” Time Transverse Plane Azimuthal Angle (rad) Non-central collision: Initial state eccentricity Elliptic Flow: Final state anisoptropy 2*v 2

18. Gunther Roland - MITPHOBOS ISMD’0518 preliminary PHOBOS 200 GeV h ± Statistical errors only Cu+Cu preliminary Au+Au PHOBOS 200 GeV Statistical errors only v 2 for Au+Au follows initial state eccentricity v 2 near mid-rapidity Elliptic Flow vs N part

19. Gunther Roland - MITPHOBOS ISMD’0519 preliminary PHOBOS 200 GeV h ± Statistical errors only Cu+Cu preliminary Au+Au PHOBOS 200 GeV Statistical errors only Substantial v 2 even for most central bin in Cu+Cu v 2 near mid-rapidity Elliptic Flow vs N part

20. Gunther Roland - MITPHOBOS ISMD’0520 Standard Eccentricity x y Nucleus 2 Nucleus 1 Participant Region b Au+Au Cu+Cu Au+Au Eccentricity Calculation

21. Gunther Roland - MITPHOBOS ISMD’0521 Standard Eccentricity x y Nucleus 2 Nucleus 1 Participant Region b Au+Au Cu+Cu Au+Au Nucleus 1 Nucleus 2 Participant Region x y Participant Eccentricity b Au+Au Cu+Cu Au+Au Eccentricity Calculation

22. Gunther Roland - MITPHOBOS ISMD’0522 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) Density Scaling

23. Gunther Roland - MITPHOBOS ISMD’0523 Standard Eccentricity Cu+Cu Au+Au Participant 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) Density Scaling “Participant Eccentricity” allows v 2 scaling from Cu+Cu to Au+Au

24. Gunther Roland - MITPHOBOS ISMD’0524 Summary  Initial state shape fluctuations drive expansion dynamics  To good approximation (  10 -4 ), all events are “the same”  Hadrons are not produced one-by-one, but in “clusters”

25. Gunther Roland - MITPHOBOS ISMD’0525 Backup Raw data  

26. Gunther Roland - MITPHOBOS ISMD’0526 Backup Standard Eccentricity Cu+Cu preliminary Au+Au PHOBOS 200 GeV “Participant Eccentricity” allows v 2 scaling from Cu+Cu to Au+Au Participant Eccentricity PHOBOS 200 GeV Au+Au Cu+Cu preliminary

27. Gunther Roland - MITPHOBOS ISMD’0527 L~A 1/3 N coll = # of NN collisions: ~A 4/3 N part /2 ~ A “Participants” “Collisions” PHOBOS Glauber MC Au+Au Cu+Cu Au+Au Cu+Cu Backup

28. Gunther Roland - MITPHOBOS ISMD’0528 Backup PHOBOS Glauber MC Au+Au vs Cu+Cu –Interplay of initial geometry and initial density –Test ideas of early thermalization and collectivity wrt reaction plane x y Nucleus 2 Nucleus 1 Participant Region Au+Au Cu+Cu

29. Gunther Roland - MITPHOBOS ISMD’0529 Backup Eccentricity difference is important for same centrality selection. V 2 (p T ) for Cu-Cu is similar v 2 (p T ) for Au-Au when scaled by  part PHOBOS preliminary h ± 0-50% centrality PHOBOS preliminary h ± 0-50% centrality PHOBOS preliminary h ± 0-50% centrality

30. Gunther Roland - MITPHOBOS ISMD’0530 Au+Au: PRL 94, 082304 (2005), PLB 578, 297 (2004) Cu+Cu preliminary Au+Au Backup