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The simple geometric scaling of flow – perhaps it’s not so simple after all

The simple geometric scaling of flow – perhaps it’s not so simple after all. Steven Manly (Univ. of Rochester) For the PHOBOS Collaboration. Burak Alver , Birger Back, Mark Baker, Maarten Ballintijn, Donald Barton, Russell Betts, Richard Bindel ,

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The simple geometric scaling of flow – perhaps it’s not so simple after all

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  1. The simple geometric scaling of flow – perhaps it’s not so simple after all Steven Manly (Univ. of Rochester) For the PHOBOS Collaboration S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  2. 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 Collaboration meeting, BNL October 2002 Collaboration meeting in Maryland, 2003 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  3. Paddle trigger Spectrometer arm Octagon Ring counter Vertex detector Flow in PHOBOS S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  4. Flow in PHOBOS Correlate reaction plane determined from azimuthal pattern of hits in one part of detector Subevent A S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  5. Flow in PHOBOS with azimuthal pattern of hits in another part of the detector Subevent B S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  6. Flow in PHOBOS Or with tracks identified in the spectrometer arms Tracks S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  7. Flow in PHOBOS Separation of correlated subevents typically large in  S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  8. Probing collisions with flow • Differential flow has proven to be a useful probe of heavy ion collisions: • Centrality • pT • Pseudorapidity • Energy • System size • Species S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  9. Elliptic flow – Cu-Cu results • Differential flow has proven to be a useful probe of heavy ion collisions: • Centrality • pT • Pseudorapidity • Energy • System size • Species S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  10. Elliptic flow – Cu-Cu results Hit based 200 GeV PHOBOS preliminary Cu-Cu, h± Track based 200 GeV Hit based 62.4 GeV PHOBOS preliminary Cu-Cu, h± S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 • Cu flow is large • Track- and hit-based results agree (200 GeV) • ~20-30% rise in v2 from 62.4 to 200 GeV S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  11. Elliptic flow – Cu-Cu results PHOBOS preliminary Cu-Cu, 62.4 GeV, h± 0-40% centrality PHOBOS preliminary Cu-Cu, 200 GeV, h± 0-40% centrality S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 Au-Au Cu-Cu v2(η) shape reminiscent of Au-Au S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  12. Au-Au '=||-ybeam Elliptic flow – Cu-Cu results S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 v2 Cu-Cu collisions also exhibit extended longitudinal scaling PHOBOS preliminary Cu-Cu, h± statistical errors only PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303 Longitudinal scaling reminiscent of Au-Au S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  13. models Bridging experiment and geometry Since experiments cannot measure the underlying geometry directly, models remain a necessary evil. Geometry Experiment • centrality • impact parameter • number of participants • eccentricity multiplicity, etc. Models are also needed to connect fundamental geometric parameters with each other S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  14. Modeling Geometry Glauber’s formalism for the scattering of a particle off of a nuclear potential. Glauber Assumptions • 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. Historically, this model involved integrating the nuclear overlap function of two nuclei with densities given by the Woods-Saxon distribution. S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  15. 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 Npart(64 participants) This has been a very successful tool at RHIC in relating various geometric properties (cross section, shape, impact parameter, number of participating nucleons, etc.) S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  16. GlauBall is the PHOBOS implementation of a Glauber MC Nucleons are distributed randomly based on an appropriately chosen Woods-Saxon radial density and arbitrary polar coordinates. An internucleon separation can be introduced at this step Subsequently, only the x and y (transverse) nucleon positions are used, so the nuclei can be thought of as 2 dimensional projections S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  17. 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. S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  18. x System size and eccentricity Standard eccentricity (standard) Centrality measure  Npart MC simulations MC simulations Paddle signal, ZDC, etc. Expect the geometry, i.e., the eccentricity, of the collision to be important in comparing flow in the Au-Au and Cu-Cu systems What is the relevant eccentricity for driving the azimuthal asymmetry? S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  19. Eccentricity - a representation of geometrical overlap y2 y2 x2 x2 σx2 Au-Au collision with Npart =64 Au-Au collision with Npart = 78 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  20. Sample of Cu-Cu collisions Yikes! This is a negative eccentricity! y2 y2 x2 x2 Cu-Cu collision with Npart = 33 Cu-Cu collision with Npart = 28 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  21. Sample of Cu-Cu collisions Gives negative eccentricity Principal axis transformation y2 x2 y2 x2 Cu-Cu collision with Npart = 33 Cu-Cu collision with Npart = 28 Maximizes the eccentricity S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  22. x x System size and eccentricity Standard eccentricity (standard) Participant eccentricity (part) Two possibilities Fluctuations in eccentricity are important for small A. S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  23. System size and eccentricity S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 Mean eccentricity shown in black Au-Au Cu-Cu PHOBOS-Glauber MC preliminary PHOBOS-Glauber MC preliminary Cu-Cu Au-Au PHOBOS-Glauber MC preliminary PHOBOS-Glauber MC preliminary S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  24. System size and eccentricity Fluctuations in eccentricity are important for the Cu-Cu system. Must use care in doing Au-Au to Cu-Cu flow comparisons. Eccentricity scaling depends on definition of eccentricity. S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  25. Elliptic flow – v2 scaling 1 statistical and systematic errors added in quadrature h± h± • Expect v2/~ constant for system at hydro limit. • Note the importance of the eccentricity choice. S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  26. Elliptic flow – v2 scaling 1 statistical and systematic errors added in quadrature h± h± Given other similarities between Au-Au and Cu-Cu flow, perhaps this is evidence that part is (close to) the relevant eccentricity for driving the azimuthal asymmetry S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  27. Elliptic flow – v2 scaling Red is data from Cu-Cu collisions,blue is data from Au-Au collisions Expect in “low density limit”. S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  28. Elliptic flow – v2 scaling Red is data from Cu-Cu collisions,blue is data from Au-Au collisions • Caution: we used part for PHOBOS data. Important for Cu-Cu, less critical for Au-Au. • Scale v2() to ~v2(y) (10% lower) • Scale dN/d to be ~dN/dy (15% higher) Scaling observed to be similar between systems if participant eccentricity is used. S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  29. Elliptic flow – v2 scaling Red is data from Cu-Cu collisions,blue is data from Au-Au collisions • Caution: we used part for PHOBOS data. Important for Cu-Cu, less critical for Au-Au. • Scale v2() to ~v2(y) (10% lower) • Scale dN/d to be ~dN/dy (15% higher) Points for STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments Scaling observed to be similar between systems if participant eccentricity is used. S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  30. Elliptic flow – system dependence 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 to v2(pT) for Au-Au when scaled by part S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  31. Elliptic flow – system dependence PHOBOS 62.4 GeV h± 0-40% centrality PHOBOS 200 GeV h± 0-40-% centrality preliminary preliminary Statistical errors only Statistical errors only v2 for Cu-Cu is ~20% smaller than v2 for Au-Au plotted 0-40% centrality. Drops another ~20% if scaled by ratio S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031 S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  32. Conclusions • Cu-Cu elliptic flow large. Similar in shape to Au-Au. Hit based 200 GeV PHOBOS preliminary Cu-Cu, 200 GeV, h± 0-40% centrality Track based 200 GeV PHOBOS preliminary Cu-Cu, h± S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  33. v2 PHOBOS preliminary Cu-Cu, h± '=||-ybeam Conclusions • The Cu-Cu systems exhibits extended longitudinal scaling. statistical errors only S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  34. Conclusions • Eccentricity calculated in standard way from Glauber model is not robust and potentially misleading for small systems. S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  35. Conclusions • Eccentricity definition very important for small systems. 1 statistical and systematic errors added in quadrature h± h± S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  36. Conclusions • Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for part may imply that part (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry. S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

  37. Conclusions • Cu-Cu elliptic flow large. Similar in shape to Au-Au. • The Cu-Cu systems exhibits extended longitudinal scaling. • Eccentricity calculated in standard way is not robust and potentially misleading for small systems. • Eccentricity definition very important for small systems. • Similarity of Au-Au to Cu-Cu flow and the fact that scaling seems to work for part may imply that part (or something close to it) is the relevant geometric quantity for generating the azimuthal asymmetry. S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire

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