1. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20061 The eccentricities of flow S. Manly University of Rochester International Workshop on Hadron Physics and Properties of High Baryon Density Matter Xi’An, China November 23, 2006 Direct evidence for color strings?

2. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20062 ec·cen·tric·i·ty ( k s n-tr s -t ) n. pl. ec·cen·tric·i·ties The quality of being eccentric. Deviation from the normal, expected, or established. An example or instance of eccentric behavior. Physics. The distance between the center of an eccentric and its axis. Mathematics. The ratio of the distance of any point on a conic section from a focus to its distance from the corresponding directrix. This ratio is constant for any particular conic section. From American Heritage Dictionary The eccentricities of flow

3. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20063 Burak Alver, Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel, Wit Busza (Spokesperson), Vasundhara Chetluru, Edmundo García, Tomasz Gburek, Joshua Hamblen, Conor Henderson, David Hofman, Richard Hollis, Roman Hołyński, Burt Holzman, Aneta Iordanova, Chia Ming Kuo, Wei Li, Willis Lin, Constantin Loizides, Steven Manly, Alice Mignerey, Gerrit van Nieuwenhuizen, Rachid Nouicer, Andrzej Olszewski, Robert Pak, Corey Reed, Christof Roland, Gunther Roland, Joe Sagerer, Peter Steinberg, George Stephans, Andrei Sukhanov, Marguerite Belt Tonjes, Adam Trzupek, Sergei Vaurynovich, Robin Verdier, Gábor Veres, Peter Walters, Edward Wenger, Frank Wolfs, Barbara Wosiek, Krzysztof Woźniak, 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 The PHOBOS Collaboration

4. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20064 I offer a humble apology for some repetition to those of you who saw the PHOBOS talks in Shanghai …

5. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20065 Average Flow in PHOBOS Ring counter Octagon Spectrometer arm Paddle trigger Vertex detector

6. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20066 Correlate reaction plane determined from azimuthal pattern of hits in one part of detector Subevent A Average Flow in PHOBOS

7. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20067 with azimuthal pattern of hits in another part of the detector Average Flow in PHOBOS Subevent B

8. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20068 Or with tracks identified in the spectrometer arms Average Flow in PHOBOS Tracks

9. S. Manly – U. Rochester Xi’an, China, Nov. 23, 20069 Separation of correlated subevents typically large in  Average Flow in PHOBOS

10. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200610 PHOBOS has made differential measurements of the average flow:  Centrality  p T  Pseudorapidity  Energy  Species Flow in PHOBOS I will give you an update of ongoing work on understanding how flow scales from species to species and a new event-by-event measurement of fluctuations in v 2

11. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200611 Elliptic Flow: new results for Cu-Cu at 22.4 GeV Au+Au Au+Au: PHOBOS Collaboration PRL. 94 (2005) 122303 Cu+Cu: PHOBOS Collaboration PRL: nucl-ex/0610037 Cu+Cu Preliminary

12. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200612 Au+Au: PHOBOS Collaboration PRL 97, 012301 (2006) Cu+Cu at 200, 62.4 GeV: PHOBOS Collaboration PRL: nucl-ex/0610037 Statistical errors only Elliptic Flow: new results for Cu-Cu at 22.4 GeV

13. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200613 Preliminary Au+Au 0-20%20-40% Cu+Cu Track-based method 0 <  < 1.6 Elliptic Flow: Au+Au and Cu+Cu v 2 vs p t comparison

14. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200614 Statistical errors only Standard Eccentricity PHOBOS Collaboration PRL: nucl-ex/0610037 Au+Au 200 GeV Cu+Cu 200 GeV Statistical errors only 200 GeV PRL: nucl-ex/0610037 Au+Au 200 GeV Cu+Cu 200 GeV PRC C72, 051901R (2005) Scaling out the geometry

15. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200615 Participant Eccentricity PHOBOS Collaboration PRL: nucl-ex/0610037 Au+Au 200 GeV Cu+Cu 200 GeV Statistical errors only PHOBOS Collaboration PRL: nucl-ex/0610037 Cu+Cu 200 GeV Au+Au 200 GeV Scaling out the geometry

16. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200616 It has been suggested that v 2 may scale as instead of - Bhalerao, Ollitrault – PLB 641, 260 (2006) - Ollitrault – private communications (2006) In Collaboration with Ulrich Heinz 2 part ε ε PHOBOS MC The difference between is as small as our estimate of the robustness of the calculation … will ignore for now. What is the appropriate form of the eccentricity scaling?

17. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200617 STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments Statistical errors only Au+Au at 200, 130, 62.4 and 19.6 GeV : PHOBOS Collaboration PRL 97, 012301 (2006) Cu+Cu at 200, 62.4 GeV: PHOBOS Collaboration PRL: nucl-ex/0610037 Cu+Cu at 22.4 GeV PHOBOS Preliminary

18. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200618 Similar area density (1/S)dN/dy Statistical errors only Similar area density (1/S)dN/dy and scaled by  part Statistical errors only

19. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200619 Au+Au vs. Cu+Cu at 200 GeV Au+Au vs. Cu+Cu at 62.4 GeV Same area density (1/S)dN/dy and Scaled by  part Statistical errors only N part =80N part =82

20. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200620 Scaled by  part Same centrality (40%) Same centrality (40%) Scaled by  part Same area density (1/S)dN/dy Same area density (1/S)dN/dy Statistical errors only PHOBOS

21. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200621 Elliptic flow develops event-by-event with respect to the participant ellipse

22. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200622 Expected fluctuations from the  part model Elliptic flow develops event-by-event with respect to the participant ellipse

23. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200623 A new event-by-event flow analysis from PHOBOS

24. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200624 A new event-by-event flow analysis from PHOBOS Determine v 2 obs

25. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200625 A new event-by-event flow analysis from PHOBOS Determine v 2 obs

26. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200626 A new event-by-event flow analysis from PHOBOS Construct kernel

27. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200627 A new event-by-event flow analysis from PHOBOS Determine dynamical fluctuations

28. S. Manly – U. Rochester Xi’an, China, Nov. 23, 2006 Event-by-event mean v 2 vs published results |η|<1 PRC 72, 051901 (2005) Number of participants Very good agreement of the event-by-event measured mean v 2 with the hit- and tracked-based, event averaged, published results (|η| + )

29. S. Manly – U. Rochester Xi’an, China, Nov. 23, 2006 Elliptic flow fluctuations: and σ v 2 Au+Au 200 GeV Number of participants |η|<1 PHOBOS preliminary (90% C.L.) Au+Au 200 GeV Number of participants PHOBOS preliminary (90% C.L.) σ v 2 |η|<1 “Scaling” errors cancel in the ratio: relative fluctuations, σ v 2 / Mean elliptic flow Dynamical flow fluctuations Systematic errors: Variation in η-shape Variation of f(v 2 ) MC response Vertex binning Ф 0 binning

30. S. Manly – U. Rochester Xi’an, China, Nov. 23, 2006 Number of participants PHOBOS preliminary (90% C.L.) σ v 2 / |η|<1 Au+Au 200 GeV Elliptic flow fluctuations: σ v 2 /

31. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200631 Elliptic flow fluctuations: σ v 2 / Number of participants PHOBOS preliminary (90% C.L.) σ v 2 / |η|<1 Au+Au 200 GeV Number of participants PHOBOS preliminary (90% C.L.) σ v 2 / |η|<1 Au+Au 200 GeV MC with no fluctuations

32. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200632 Number of participants PHOBOS preliminary (90% C.L.) σ v 2 / |η|<1 Au+Au 200 GeV MC with no fluctuations Participant eccentricity model prediction Elliptic flow fluctuations: σ v 2 /

33. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200633 Things to consider and naïve questions How seriously should we take this Glauber- driven participant eccentricity model? Number of participants Allows us to make sense of both the system size scaling and fluctuations in the data Really need Cu-Cu fluctuations measurement where the eccentricity fluctuations will be larger … let’s hope the measurements can be made

34. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200634 Things to consider and naïve questions How seriously should we take this Glauber- driven participant eccentricity model? Number of participants PHOBOS fluctuations analysis depends on MC … things not yet in the MC used to determine the kernel (such as short range correlations) can show up as fluctuations Fortunately, the wonderful and complementary STAR measurement (P. Sorensen – QM2006) provides a consistency check. Data-driven and independent. Agrees well. Measurement will likely hold up

35. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200635 Things to consider and naïve questions How seriously should we take this Glauber- driven participant eccentricity model? Number of participants Participant eccentricity model calculation has proven to be robust during studies that followed its introduction at QM2005 It seems we should take it seriously Should we be bothered that we don’t have much room for other sources of fluctuations?

36. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200636 Things to consider and naïve questions If we take the participant eccentricity model seriously, what do we learn? Whatever the form of the matter in the early stage of the collision, it seems the relevant interactions that drive the flow signal are initially localized transversely in a way similar to the participant nucleons. Inconsistent with any picture where the initial state is driven by a large number of low-x partons that fill the nuclear transverse area.

37. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200637 Things to consider and naïve questions It seems we are seeing transversely localized parton production with a granularity not so different from the interacting nucleons! Something like color strings? Is this telling us something about the reality of some models vs. others? This seems rather fundamental … are there other measurements that show “stringiness” so directly? If we take the participant eccentricity model seriously, what do we learn?

38. S. Manly – U. Rochester Xi’an, China, Nov. 23, 200638 Perhaps it seems obvious that this might happen, but it is incredibly cool to see it … and it contradicts the naïve view many of us might have had (well, me anyway) of a densely packed initial transverse distribution