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Eccentric nuclear physics

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:

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Eccentric nuclear physics

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  1. 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) S. Manly, University of Rochester

  2. Eccentric nuclear physics • 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 S. Manly, University of Rochester

  3. quark-antiquark pair created from vacuum Quantum Chromodynamics QCD relative strength Similar to QED … except the gauge field carries the charge asymptotic freedom distance energy density, temperature quark Strong color field Energy grows with separation !!! “white” 0 (confined quarks) E=mc2 ! “white” proton (confined quarks) “white” proton S. Manly, University of Rochester Thanks to Mike Lisa (OSU) for parts of this animation

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

  5. S. Manly, University of Rochester

  6. The soup wars S. Manly, University of Rochester

  7. The phase diagram of QCD Early universe quark-gluon plasma critical point ? Tc Temperature colour superconductor hadron gas nucleon gas nuclei CFL r0 Neutron stars vacuum baryon density S. Manly, University of Rochester

  8. Terminology: angles Beamline S. Manly, University of Rochester

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

  10. Terminology: angles  = azimuthal angle about the beampipe Beamline S. Manly, University of Rochester

  11. peripheral collisions central collisions Terminology: centrality Nch “Spectators” “Participants” Zero-degreeCalorimeter 6% “Spectators” Paddle Counter Npart Thanks to P. Steinberg for parts of this slide S. Manly, University of Rochester

  12. “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 reachhydro limit where given geometric asymmetry is converted into final state asymmetry as efficiently as possible S. Manly, University of Rochester

  13. Flow quantified (reaction plane) Experimentally this is the azimuthal direction with the highest particle density, must correct for imperfect resolution View along beamline dN/d(f -YR ) = N0 (1 + 2V1cos (f-YR) + 2V2cos (2(f-YR) + ... ) Fourier decomposition of the azimuthal multiplicity distribution S. Manly, University of Rochester

  14. Flow quantified (reaction plane) Elliptic flow View along beamline dN/d(f -YR ) = N0 (1 + 2V1cos (f-YR) + 2V2cos (2(f-YR) + ... ) S. Manly, University of Rochester

  15. S. Manly, University of Rochester

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

  17. S. Manly, University of Rochester

  18. Paddle trigger Spectrometer arm Octagon Ring counter Vertex detector Average Flow in PHOBOS

  19. Average Flow in PHOBOS Correlate reaction plane determined from azimuthal pattern of hits in one part of detector Subevent A

  20. Average Flow in PHOBOS with azimuthal pattern of hits in another part of the detector Subevent B

  21. Average Flow in PHOBOS Or with tracks identified in the spectrometer arms Tracks

  22. Flow in PHOBOS • PHOBOS has made differential measurements of the average flow: • Centrality • pT • Pseudorapidity • Energy • Species

  23. Flow in PHOBOS Au+Au, A=197 Cu+Cu, A=63 In the most central events, 0 but v2 does not for Cu+Cu!

  24. 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

  25. 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.

  26. 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.)

  27. 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. x System size and eccentricity Standard eccentricity (standard) Centrality measure  Npart y 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

  29. Eccentricity - a representation of geometrical overlap y2 y2 x2 x2 σx2 Au-Au collision with Npart =64 Au-Au collision with Npart = 78

  30. 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

  31. Sample of Cu-Cu collisions Principal axis transformation y2 x2 y2 x2 Cu-Cu collision with Npart = 33 Cu-Cu collision with Npart = 28 Maximizes the eccentricity

  32. S. Manly, University of Rochester

  33. 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

  34. Standard Eccentricity Statistical errors only PHOBOS CollaborationPRL: nucl-ex/0610037 Cu+Cu 200 GeV Au+Au 200 GeV Scaling out the geometry Statistical errors only 200 GeV Au+Au 200 GeV Cu+Cu 200 GeV PRL: nucl-ex/0610037 PRC C72, 051901R (2005)

  35. Standard Eccentricity Statistical errors only PHOBOS CollaborationPRL: nucl-ex/0610037 Cu+Cu 200 GeV Au+Au 200 GeV Scaling out the geometry Statistical errors only 200 GeV Au+Au 200 GeV Cu+Cu 200 GeV Flow is huge in the smaller system! Particularly when the impact parameter goes to zero … What’s the air fare to Stockholm these days?? PRL: nucl-ex/0610037 PRC C72, 051901R (2005)

  36. Participant Eccentricity Statistical errors only Au+Au 200 GeV Cu+Cu 200 GeV Au+Au 200 GeV Cu+Cu 200 GeV PHOBOS CollaborationPRL: nucl-ex/0610037 PHOBOS CollaborationPRL: nucl-ex/0610037 Scaling out the geometry

  37. Au+Au at 200, 130, 62.4 and 19.6 GeV :PHOBOS CollaborationPRL 97, 012301 (2006) STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments Cu+Cu at 200, 62.4 GeV:PHOBOS CollaborationPRL: nucl-ex/0610037 Statistical errors only Cu+Cu at 22.4 GeV PHOBOS Preliminary

  38. Same area density (1/S)dN/dy and Scaled by epart Au+Au vs. Cu+Cu at 62.4 GeV Au+Au vs. Cu+Cu at 200 GeV Statistical errors only Statistical errors only Npart=82 Npart=80

  39. 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. 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. Elliptic flow develops event-by-event with respect to the participant ellipse

  42. Expected fluctuations from the part model Elliptic flow develops event-by-event with respect to the participant ellipse

  43. 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” v2 to “observed” v2. • Input different v2 distributions, convoluting them with the map and compare with data. Do max likelihood fit.

  44. A new event-by-event flow analysis from PHOBOS

  45. A new event-by-event flow analysis from PHOBOS Determine v2obs

  46. A new event-by-event flow analysis from PHOBOS Determine v2obs

  47. A new event-by-event flow analysis from PHOBOS Construct kernel

  48. A new event-by-event flow analysis from PHOBOS Determine dynamical fluctuations

  49. <v2> |η|<1 PRC 72, 051901 (2005) Number of participants Event-by-event mean v2 vs published results <v2>(|η|<1) = 0.5 x (11/12 <v2triangular> + <v2trapezodial>) Very good agreement of the event-by-event measured mean v2 with the hit- and tracked-based, event averaged, published results

  50. |η|<1 PHOBOS preliminary (90% C.L.) PHOBOS preliminary (90% C.L.) • <v2> • σv2 Au+Au 200 GeV Au+Au 200 GeV Number of participants Number of participants Elliptic flow fluctuations: <v2> and σv2 Dynamical flow fluctuations Mean elliptic flow |η|<1  Systematic errors: • Variation in η-shape • Variation of f(v2) • MC response • Vertex binning • Ф0 binning “Scaling” errors cancel in the ratio: relative fluctuations, σv2/<v2>

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