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

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


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


Flow in PHOBOS

Ring counter

Octagon

Spectrometer arm

Paddle trigger

Vertex detector


Correlate reaction plane determined from azimuthal pattern of hits in one part of detector

Flow in PHOBOS

Subevent A


with azimuthal pattern of hits in another part of the detector

Flow in PHOBOS

Subevent B


Or with tracks identified in the spectrometer arms

Flow in PHOBOS

Tracks


Separation of correlated subevents typically large in

Flow in PHOBOS


Differential flow has proven to be a useful probe of heavy ion collisions:

CentralitypT

PseudorapidityEnergySystem sizeSpecies

Probing collisions with flow


Differential flow has proven to be a useful probe of heavy ion collisions:

CentralitypT

PseudorapidityEnergySystem sizeSpecies

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±


Hit based 62.4 GeV

Hit based 200 GeV

Track based 200 GeV

S. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031



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


Au-Au



Longitudinal scaling reminiscent of Au-Au


v 2

'=||-ybeam

Cu-Cu collisions also exhibit extended longitudinal scaling statistical errors only

Au-Au


PHOBOS Collaboration, Phys. Rev. Lett. 94 (2005) 122303


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


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


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


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


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.


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


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


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


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


Fluctuations in eccentricity are important for small A.

22

22

xy

xy


Participant eccentricity (part)

x

Standard eccentricity (standard)

x

Two possibilities



Au-Au

Au-Au

Cu-Cu

Cu-Cu

PHOBOS-Glauber MC preliminary




Mean eccentricity shown in blackS. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031


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.



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±




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 asymmetryS. Manly et al., PHOBOS Collaboration, Proc. QM05, nucl-ex/0510031



dy

dN

s

1v2 Expect in “low density limit”.


Red is data from Cu-Cu collisions, blue is data from Au-Au collisions



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)





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.




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



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



Conclusions

Cu-Cu elliptic flow large. Similar in shape to Au-Au.


Hit based 200 GeV

Track based 200 GeV

PHOBOS preliminary Cu-Cu, 200 GeV, h±

0-40% centrality


Conclusions

The Cu-Cu systems exhibits extended longitudinal scaling.


v 2

'=||-ybeam

statistical errors only


Conclusions

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


Conclusions

Eccentricity definition very important for small systems.

h±


h±


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.


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.

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

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