s. manly – u. rochester gordon conf. 2006, new london, new hampshire1 the simple geometric scaling...
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S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 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
Collaboration meeting, BNL October 2002
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 LABORATORYINSTITUTE OF NUCLEAR PHYSICS PAN, KRAKOW MASSACHUSETTS INSTITUTE OF TECHNOLOGY
NATIONAL CENTRAL UNIVERSITY, TAIWAN UNIVERSITY OF ILLINOIS AT CHICAGOUNIVERSITY OF MARYLAND UNIVERSITY OF ROCHESTER
Collaboration meeting in Maryland, 2003
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 3
Flow in PHOBOS
Ring counter
Octagon
Spectrometer arm
Paddle trigger
Vertex detector
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 4
Correlate reaction plane determined from azimuthal pattern of hits in one part of detector
Flow in PHOBOS
Subevent A
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 5
with azimuthal pattern of hits in another part of the detector
Flow in PHOBOS
Subevent B
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 6
Or with tracks identified in the spectrometer arms
Flow in PHOBOS
Tracks
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 7
Separation of correlated subevents typically large in
Flow in PHOBOS
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 8
Differential flow has proven to be a useful probe of heavy ion collisions:
CentralitypT
PseudorapidityEnergySystem sizeSpecies
Probing collisions with flow
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 9
Differential flow has proven to be a useful probe of heavy ion collisions:
CentralitypT
PseudorapidityEnergySystem sizeSpecies
Elliptic flow – Cu-Cu results
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 10
Elliptic flow – Cu-Cu results
Cu flow is large
Track- and hit-based results agree (200 GeV)
~20-30% rise in v2 from 62.4 to 200 GeV
PHOBOS preliminary Cu-Cu, h±
PHOBOS preliminary Cu-Cu, h±
Hit based 62.4 GeV
Hit based 200 GeV
Track based 200 GeV
S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 11
Elliptic flow – Cu-Cu results
Cu-Cu v2(η) shape reminiscent of Au-Au
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
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 12
Elliptic flow – Cu-Cu results
Longitudinal scaling reminiscent of Au-Au
PHOBOS preliminary Cu-Cu, h±
v 2
'=||-ybeam
Cu-Cu collisions also exhibit extended longitudinal scaling statistical errors only
Au-Au
S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031
PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 13
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
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.
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
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)
(cross section, shape, impact parameter, number of participating nucleons, etc.)
This has been a very successful tool at RHIC in relatingvarious geometric properties
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 generatedrandomly from a linear distribution (vanishing small at b=0)
Nucleons are treated as hard spheres. Their 2D projectionsare 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
22
22
xy
xy
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 Npart
Paddle signal, ZDC, etc.
MC simulations
What is the relevant eccentricity for driving the azimuthal asymmetry?
MC simulations
22y
22x
yyσ
xxσ
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 19
x2
Au-Au collision with Npart =64
y2
x2
y2
Au-Au collision with Npart =
78
x2
22
22
xy
xy
Eccentricity - a representation of geometrical overlap
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 20
Sample of Cu-Cu collisions
Cu-Cu collision with Npart = 33 Cu-Cu collision with Npart = 28
Yikes! This is a negative eccentricity!
y2
x2 y
2
x2
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 21
Cu-Cu collision with Npart = 33 Cu-Cu collision with Npart = 28
Gives negative eccentricity Principal axis transformation
Maximizes the eccentricity
Sample of Cu-Cu collisions
y2
x2
x2y
2
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 22
Fluctuations in eccentricity are important for small A.
22
22
xy
xy
System size and eccentricity
Participant eccentricity (part)
x
Standard eccentricity (standard)
x
Two possibilities
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 23
System size and eccentricity
Au-Au
Au-Au
Cu-Cu
Cu-Cu
PHOBOS-Glauber MC preliminary
PHOBOS-Glauber MC preliminary
PHOBOS-Glauber MC preliminary
PHOBOS-Glauber MC preliminary
Mean eccentricity shown in blackS. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 24
Fluctuations in eccentricity are important for the Cu-Cu system.
System size and eccentricity
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
Expect v2/ ~ constant for system at hydro limit.
Note the importance of the eccentricity choice.
h±
1 statistical and systematic errors added in quadrature
h±
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
h±
1 statistical and systematic errors added in quadrature
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 asymmetryS. 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
dy
dN
s
1v2 Expect in “low density limit”.
S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031
Red is data from Cu-Cu collisions, blue is data from Au-Au collisions
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 28
Elliptic flow – v2 scaling
Scaling observed to be similar between systems if participant eccentricity is used.
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)
S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031
Red is data from Cu-Cu collisions, blue is data from Au-Au collisions
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 29
Elliptic flow – v2 scaling
Points for STAR, NA49 and E877 data taken from STAR Collaboration, Phys.Rev. C66 (2002) 034904 with no adjustments
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
Red is data from Cu-Cu collisions, blue is data from Au-Au collisions
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 30
Elliptic flow – system dependence
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
PHOBOS preliminary h±
0-50% centralityPHOBOS preliminary h±
0-50% centrality
PHOBOS preliminary h±
0-50% centrality
S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 31
v2 for Cu-Cu is ~20% smaller than v2 for Au-Au plotted 0-40% centrality. Drops another ~20% if scaled by ratio
PHOBOS 62.4 GeV h± 0-40% centrality
Elliptic flow – system dependence
preliminarypreliminary
PHOBOS 200 GeV h± 0-40-% centrality
Statistical errors onlyStatistical errors only
Cupart
Aupart
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.
PHOBOS preliminary Cu-Cu, h±
Hit based 200 GeV
Track based 200 GeV
PHOBOS preliminary Cu-Cu, 200 GeV, h±
0-40% centrality
S. Manly – U. Rochester Gordon Conf. 2006, New London, New Hampshire 33
Conclusions
The Cu-Cu systems exhibits extended longitudinal scaling.
PHOBOS preliminary Cu-Cu, h±
v 2
'=||-ybeam
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.
h±
1 statistical and systematic errors added in quadrature
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
The Cu-Cu systems exhibits extended longitudinal scaling.
Eccentricity definition very important for small systems.
Cu-Cu elliptic flow large. Similar in shape to Au-Au.
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.
Eccentricity calculated in standard way is not robust and potentially misleading for small systems.
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