S' Manly U' Rochester Gordon Conf' 2006, New London, New Hampshire

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The simple geometric scaling of flow perhaps
its not so simple after all
Steven Manly (Univ. of Rochester) For the
PHOBOS Collaboration
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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 Holynski,
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 Wozniak,
Shaun Wyngaardt, Bolek Wyslouch 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
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Flow in PHOBOS
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Flow in PHOBOS
Correlate reaction plane determined from
azimuthal pattern of hits in one part of detector
Subevent A
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Flow in PHOBOS
with azimuthal pattern of hits in another part of
the detector
Subevent B
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Flow in PHOBOS
Or with tracks identified in the spectrometer arms
Tracks
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Flow in PHOBOS
Separation of correlated subevents typically
large in ?
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Probing collisions with flow

• Differential flow has proven to be a useful probe
  of heavy ion collisions
• Centrality
• pT
• Pseudorapidity
• Energy
• System size
• Species

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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

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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

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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(?) shape reminiscent of Au-Au
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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
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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
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Modeling Geometry
Glaubers 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.
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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.
AuAu 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.)
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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
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The nuclei are offset by an impact parameter
generated randomly from a linear distribution
(vanishing small at b0) 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.
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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?
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Eccentricity - a representation of geometrical
overlap
?y2
?y2
?x2
?x2
sx2
Au-Au collision with Npart 64
Au-Au collision with Npart 78
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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
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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
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System size and eccentricity
Participant eccentricity (?part)
Standard eccentricity (?standard)
Two possibilities
Fluctuations in eccentricity are important for
small A.
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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
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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
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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
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
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
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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
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
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
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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
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
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Conclusions

• The Cu-Cu systems exhibits extended longitudinal
  scaling.

statistical errors only
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Conclusions

• Eccentricity calculated in standard way from
  Glauber model is not robust and potentially
  misleading for small systems.

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Conclusions

• Eccentricity definition very important for small
  systems.

1? statistical and systematic errors added in
quadrature
h
h
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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.

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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.