1. March 7, 2007S. Manly, University of Rochester1 Eccentric nuclear physics Steven Manly Univ. of Rochester University of Rochester March 7, 2007 steven.manly@rochester.edu http://hertz.pas.rochester.edu/smanly/ Full list of former/present UR PHOBOS Collaborators: Frank Wolfs, Inkyu Park, Wojtek Skulski, Robert Pak, Josh Hamblen, Pete Walters, Erik Johnson, Nazim Kahn, Adam Harrington, Ian Spitzer, Clifford Cheung, Jennifer Ellsworth, Alysse DeFranco, Garrett Mason, Yanting Wang Other PHOBOS groups at BNL, Maryland, INP Krakow, U. Ill. Chicago and MIT Today’s results: among others … SM, Pete Walters (UR), Mark Baker (BNL), Burak Alver (MIT) and Constantin Loizides (MIT), Richard Bindel (Maryland), Barbara Wosiek (INP, Krakow), Peter Steinberg (BNL), Gunther Roland (MIT)

2. March 7, 2007S. Manly, University of Rochester2 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 Eccentric nuclear physics

3. March 7, 2007S. Manly, University of Rochester3 Strong color field Energy grows with separation !!! E=mc 2 ! “white” proton quark quark-antiquark pair created from vacuum “white” proton (confined quarks) “white”  0 (confined quarks) Quantum Chromodynamics QCD distance energy density, temperature relative strength asymptotic freedom Similar to QED … except the gauge field carries the charge Thanks to Mike Lisa (OSU) for parts of this animation

4. March 7, 2007S. Manly, University of Rochester4 Generating a deconfined state Nuclear Matter (confined) Hadronic Matter (confined) Quark Gluon Plasma deconfined ! Present understanding of Quantum Chromodynamics (QCD) heating compression  deconfined matter !

5. March 7, 2007S. Manly, University of Rochester5

6. March 7, 2007S. Manly, University of Rochester6 The soup wars

7. March 7, 2007S. Manly, University of Rochester7 The phase diagram of QCD Temperature baryon density Neutron stars Early universe nuclei nucleon gas hadron gas colour superconductor quark-gluon plasma TcTc 00 critical point ? vacuum CFL

8. March 7, 2007S. Manly, University of Rochester8 Beamline Terminology: angles

9. March 7, 2007S. Manly, University of Rochester9 Beamline Terminology: angles Pseudorapidity =  = Lorentz invariant angle with repect to the beampipe 0 +1 +2 +3 -2 -3

10. March 7, 2007S. Manly, University of Rochester10 Terminology: angles  = azimuthal angle about the beampipe Beamline

11. March 7, 2007S. Manly, University of Rochester11 “Spectators” Zero-degree Calorimeter “Spectators” Paddle Counter peripheral collisions central collisions N ch N part 6% Terminology: centrality Thanks to P. Steinberg for parts of this slide “Participants”

12. March 7, 2007S. Manly, University of Rochester12 “Flow” = patterns in the energy, momentum, or particle density distributions that we use to ferret out clues as to the nature of the collision/matter To what extent is the initial geometric asymmetry mapped into the final state? View along beamline (Initial geometry)(particle density)(time)(physics of interaction) might reach hydro limit where given geometric asymmetry is converted into final state asymmetry as efficiently as possible

13. March 7, 2007S. Manly, University of Rochester13 (reaction plane) Flow quantified dN/d(  R ) = N 0 (1 + 2V 1 cos (  R ) + 2V 2 cos (2(  R ) +... ) View along beamline Fourier decomposition of the azimuthal multiplicity distribution Experimentally this is the azimuthal direction with the highest particle density, must correct for imperfect resolution

14. March 7, 2007S. Manly, University of Rochester14 (reaction plane) dN/d(  R ) = N 0 (1 + 2V 1 cos (  R ) + 2V 2 cos (2(  R ) +... ) Elliptic flow Flow quantified View along beamline

15. March 7, 2007S. Manly, University of Rochester15

16. March 7, 2007S. Manly, University of Rochester16 (PHOBOS : Normalized Paddle Signal) Hydrodynamic limit STAR: PRL86 (2001) 402 PHOBOS preliminary Hydrodynamic limit STAR: PRL86 (2001) 402 PHOBOS preliminary Thanks to M. Kaneta PRL 91 (2003) 182301 Non-viscous hydrodynamic models with QGP are successful in describing flow data at mid- rapidity for central events at low pt.

17. March 7, 2007S. Manly, University of Rochester17

18. S. Manly – U. Rochester March 7, 200718 Average Flow in PHOBOS Ring counter Octagon Spectrometer arm Paddle trigger Vertex detector

19. S. Manly – U. Rochester March 7, 200719 Correlate reaction plane determined from azimuthal pattern of hits in one part of detector Subevent A Average Flow in PHOBOS

20. S. Manly – U. Rochester March 7, 200720 with azimuthal pattern of hits in another part of the detector Average Flow in PHOBOS Subevent B

21. S. Manly – U. Rochester March 7, 200721 Or with tracks identified in the spectrometer arms Average Flow in PHOBOS Tracks

22. S. Manly – U. Rochester March 7, 200722 PHOBOS has made differential measurements of the average flow:  Centrality  p T  Pseudorapidity  Energy  Species Flow in PHOBOS

23. S. Manly – U. Rochester March 7, 200723 Au+Au, A=197 Cu+Cu, A=63 In the most central events,  0 but v 2 does not for Cu+Cu! Flow in PHOBOS

24. S. Manly – U. Rochester March 7, 200724 Bridging experiment and geometry Since experiments cannot measure the underlying geometry directly, models remain a necessary evil. multiplicity, etc. models centrality impact parameter number of participants eccentricity Models are also needed to connect fundamental geometric parameters with each other Experiment Geometry

25. S. Manly – U. Rochester March 7, 200725 Modeling Geometry Glauber’s formalism for the scattering of a particle off of a nuclear potential. Historically, this model involved integrating the nuclear overlap function of two nuclei with densities given by the Woods-Saxon distribution. Nucleons proceed in a straight line, undeflected by collisions Irrespective of previous interactions, nucleons interact according to the inelastic cross section measured in pp collisions. Glauber Assumptions

26. S. Manly – U. Rochester March 7, 200726 A different application of the Glauber formalism is a Monte Carlo technique, in which the average over many simulated events takes the place of an integration. Au+Au Collisions with the same N part (64 participants) (cross section, shape, impact parameter, number of participating nucleons, etc.) This has been a very successful tool at RHIC in relating various geometric properties

27. S. Manly – U. Rochester March 7, 200727 The nuclei are offset by an impact parameter generated randomly from a linear distribution (vanishing small at b=0) Nucleons are treated as hard spheres. Their 2D projections are given an area of  NN (taken from pp inelastic collisions) The nuclei are “thrown” (their x-y projections are overlapped), and opposing nucleons that touch are marked as participants.

28. S. Manly – U. Rochester March 7, 200728 Standard eccentricity (  standard ) x System size and eccentricity Expect the geometry, i.e., the eccentricity, of the collision to be important in comparing flow in the Au-Au and Cu-Cu systems Centrality measure  N part   Paddle signal, ZDC, etc. MC simulations y

29. S. Manly – U. Rochester March 7, 200729 x2x2 Au-Au collision with Npart =64 y2y2 x2x2 y2y2 Au-Au collision with Npart = 78 x2x2 Eccentricity - a representation of geometrical overlap

30. S. Manly – U. Rochester March 7, 200730 Sample of Cu-Cu collisions Cu-Cu collision with Npart = 33Cu-Cu collision with Npart = 28 Yikes! This is a negative eccentricity! y2y2 x2x2 y2y2 x2x2

31. S. Manly – U. Rochester March 7, 200731 Cu-Cu collision with Npart = 33Cu-Cu collision with Npart = 28 Principal axis transformation Maximizes the eccentricity Sample of Cu-Cu collisions y2y2 x2x2 x2x2 y2y2

32. March 7, 2007S. Manly, University of Rochester32

33. S. Manly – U. Rochester March 7, 200733 System size and eccentricity Au-Au Cu-Cu PHOBOS-Glauber MC preliminary Mean eccentricity shown in black S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031

34. S. Manly – U. Rochester March 7, 200734 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

35. S. Manly – U. Rochester March 7, 200735 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 Flow is huge in the smaller system! Particularly when the impact parameter goes to zero … What’s the air fare to Stockholm these days??

36. S. Manly – U. Rochester March 7, 200736 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

37. S. Manly – U. Rochester March 7, 200737 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

38. S. Manly – U. Rochester March 7, 200738 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

39. S. Manly – U. Rochester March 7, 200739 Data seems to indicate that it is the participant eccentricity rather than the standard eccentricity that characterizes the relevant azimuthal asymmetry that drives elliptic flow Hot zone formed by participating nucleons rather than some sea of low-x partons?

40. S. Manly – U. Rochester March 7, 200740 Fluctuating ellipse shape seems to reconcile data from different systems. Within a single system (i.e., Au+Au) does the elliptic flow signal fluctuate? If so, does the fluctuation signal agree with expectations from the participant eccentricity fluctuations?

41. S. Manly – U. Rochester March 7, 200741 Elliptic flow develops event-by-event with respect to the participant ellipse

42. S. Manly – U. Rochester March 7, 200742 Expected fluctuations from the  part model Elliptic flow develops event-by-event with respect to the participant ellipse

43. S. Manly – U. Rochester March 7, 200743 A new event-by-event flow analysis from PHOBOS (Cliff Note or Spark Note version)  Use full detector (need statistics for event-by-event sensitivity)  Full detector is complicated. So, use MC to create map for “input” v 2 to “observed” v 2.  Input different v 2 distributions, convoluting them with the map and compare with data. Do max likelihood fit.

44. S. Manly – U. Rochester March 7, 200744 A new event-by-event flow analysis from PHOBOS

45. S. Manly – U. Rochester March 7, 200745 A new event-by-event flow analysis from PHOBOS Determine v 2 obs

46. S. Manly – U. Rochester March 7, 200746 A new event-by-event flow analysis from PHOBOS Determine v 2 obs

47. S. Manly – U. Rochester March 7, 200747 A new event-by-event flow analysis from PHOBOS Construct kernel

48. S. Manly – U. Rochester March 7, 200748 A new event-by-event flow analysis from PHOBOS Determine dynamical fluctuations

49. S. Manly – U. Rochester March 7, 200749 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| + )

50. S. Manly – U. Rochester March 7, 200750 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 

51. S. Manly – U. Rochester March 7, 200751 Number of participants PHOBOS preliminary (90% C.L.) σ v 2 / |η|<1 Au+Au 200 GeV Elliptic flow fluctuations: σ v 2 /

52. S. Manly – U. Rochester March 7, 200752 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

53. S. Manly – U. Rochester March 7, 200753 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 /

54. March 7, 2007S. Manly, University of Rochester54 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

55. March 7, 2007S. Manly, University of Rochester55 Things to consider and naïve questions How seriously should we take this Glauber- driven participant eccentricity model? Number of participants There is a wonderful and complementary STAR measurement (P. Sorensen – QM2006) which provides a consistency check. Data-driven and independent. Agrees well.

56. March 7, 2007S. Manly, University of Rochester56 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?

57. March 7, 2007S. Manly, University of Rochester57 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.

58. March 7, 2007S. Manly, University of Rochester58 Things to consider and naïve questions It seems we are seeing transversely localized matter production with a granularity not so different from the interacting nucleons! Something like color strings? This contradicts the naïve view many of us might have had (well, me anyway) of a densely packed initial transverse distribution. If we take the participant eccentricity model seriously, what do we learn?

59. March 7, 2007S. Manly, University of Rochester59 Of course, the international fashion industry is always way ahead of the rest of us. Where there are strings, there are clothes …