S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20051 System size, energy and ...

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 2005 1

System size, energy and dependence of directed and elliptic flow

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


For directed flow we use subevents that are symmetric about =0

Flow in PHOBOS

Subevent B

Subevent A


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

CentralitypT

PseudorapidityEnergySystem sizeSpecies

Probing collisions with flow


Au-Au – directed flow

Au-Au 19.6 GeV h± Au-Au 62.4 GeV h±

Au-Au 130 GeV h± Au-Au 200 GeV h±

Update of directed flow result first

shown at QM2004

Similar (2-subevent) technique

Added 62.4 GeV data

Confirmed with mixed harmonic

analysis

See poster by A. Mignerey in Poster 1, section 2, number 47

PHOBOS preliminary PHOBOS preliminary

PHOBOS preliminary PHOBOS preliminary

0-40% centrality

0-40% centrality0-40% centrality

0-40% centrality


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

PHOBOS Au-Au, h±

PHOBOS Au-Au, h±

PHOBOS Au-Au, h±

PHOBOS Au-Au, h±

0-40% centrality

0-40% centrality 0-40% centrality

0-40% centrality

Au-Au – elliptic flow



PHOBOS Au-Au, h±

PHOBOS Au-Au, h±

PHOBOS Au-Au, h±

PHOBOS Au-Au, h±

0-40% centrality

0-40% centrality 0-40% centrality

0-40% centrality

Au-Au – elliptic flow

ó

Recent theoretical progress in understanding v2(η). See, for example:

M.Csanád, T.Csörgó, B.Lörstad, Nucl. Phys. A742 (2004) 80 [nucl-th/0310040]

U.Heinz, P.F.Kolb, J.Phys. G30 (2004) S1229 [nucl-th/0403044]

T.Hirano, M.Isse, Y.Nara, AOhnishi, and K Yoshino, nucl-th/0506058


Directed flow exhibits extended longitudinal scaling, i.e., approximate rest frame of nucleus.

Directed flow – extended longitudinal scaling

Systematic errors only

PHOBOS preliminary h±, Au-Au

0-40% centrality

'=||-ybeam

v 1


Au-Au data, h±

0-40% centrality

'=||-ybeam

Elliptic flow exhibits striking extended longitudinal scaling


v 2

Elliptic flow – extended longitudinal scaling

Systematic errors only


’=||-ybeam

Elliptic flow exhibits striking extended longitudinal scaling


If so, it is an unfortunate

coincidence that we saturate v2 right at the highest energy

density we can achieve: no break

in slope

Mid-rapidity, 200 GeV, Au-Au Reached the hydro limit?

'=||-ybeam

v 2

Elliptic flow – extended longitudinal scaling

Au-Au data, h±

0-40% centralitySystematic errors only


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



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



Longitudinal scaling reminiscent of Au-Au


v 2

'=||-ybeam

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


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?


Fluctuations in eccentricity are important for small A.

22

22

xy

xy


Participant eccentricity (part)

x

Standard eccentricity (standard)

x

Two possibilities


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 asymmetry



dy

dN

s

1v2 Expect in “low density limit”.



Approximate “LDL” scaling observed.

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)



Approximate “LDL” scaling observed.

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)


Elliptic flow – system dependence

Eccentricity difference is important for same centrality selection.

V2(pT) for Cu-Cu is similar 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


preliminarypreliminary

PHOBOS 200 GeV h± 0-40-% centrality

Statistical errors onlyStatistical errors only

Cupart

Aupart


This data shows v2 does not scale linearly with A as expected by AMPT (factor of 3)

AMPT multi-phase transport model (Chen and Ko, nucl-th/0505044)

PHOBOS 62.4 GeV h± 0-40% centrality


preliminarypreliminary

PHOBOS 200 GeV h± 0-40-% centrality

Statistical errors onlyStatistical errors only


Conclusions

Au-Au directed flow including the new 62.4 GeV data.

PHOBOS preliminary

Au-Au 19.6 GeV Au-Au 62.4 GeV

Au-Au 130 GeV Au-Au 200 GeV


Conclusions

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

PHOBOS preliminary Cu-Cu, 62.4 GeV, h±

0-40% centrality

PHOBOS preliminary Cu-Cu, 200 GeV, h±

0-40% centrality


Conclusions

Au-Au and Cu-Cu systems exhibit extended longitudinal scaling. No break in evolution as function of η due to

reaching hydro limit.

PHOBOS Au-Au, h± PHOBOS preliminary Cu-Cu, h±

v 2

'=||-ybeam'=||-ybeam

v 2

statistical errors only


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

Au-Au directed flow results updated.

Au-Au and Cu-Cu systems exhibit extended longitudinal scaling. No break in evolution as function of η due to reaching hydro limit.

Eccentricity definition very important for small systems.

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

v2(pT) is similar in Au-Au and Cu-Cu systems when part is used.

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.


Backup Slides


Elliptic flow subevent regions

Cu-Cu, 200 and 62.4 GeV and Au-Au, 19.6, 62.4, 130 and 200 GeV: 0.1<|η|<3.0

(use 0.5<|η|<3.0 and 1.0<|η|<3.0 for systematic studies)

Regions used to determine reaction plane and resolution.


Directed flow subevent regionsRegions used to determine reaction plane and resolution.

v1 baseline Au-Au, 19.6, 62.4, 130 and 200 GeV: 1.5<|η|<3.0 and 3.0<|η|<5.0

(use 1.5<|η|<2.5 and 3.5<|η|<5.0 for systematic studies)

v1 mixed harmonic Au-Au, 19.6, 62.4, 130 and 200 GeV: 1.5<|η|<3.0

and 3.0<|η|<5.0 for the first harmonic part and 0.1<|η|<3.0 for

the second harmonic part


Baseline analysis overlaid with new PHOBOS mixed

harmonic analysis

Shows non-flow correlations small

Mixed harmonic method: STAR collaboration, Phys. Rev. C 72 (2005) 014904

PHOBOS preliminary h± Au-Au

Au-Au update – directed flow






62.4 GeV results are particularly good due to:

large directed flow

large number of tracks/event

large elliptic flow (for mixed harmonic)

STAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/0409029

Preliminary PHOBOS and STAR results agree

well at 62.4 GeV except at highest ||

62.4 GeV Au-Au, h±



62.4 GeV directed flow comparisonSTAR 62.4 GeV results from A.H. Tang (STAR Collaboration), nucl-ex/0409029



Comparison of directed flow results at 62.4 GeV

Estimated by PHOBOS from weighted average of STAR data in multiple centrality bins

We used the centrality dependence of STAR’s results to estimate the STAR results in the 10-50% centrality bin

62.4 GeV Au-Au, h±

Discrepancy at high η possibly due to differences in low momentum cutoff?


Comparison of preliminary PHOBOS 200 GeV v1 with published STAR results. Plots identical

except for STAR centrality selection.


STAR 200 GeV results from Phys. Rev. C 72 (2005) 014904


Only statistical errors shown

Au+Au data(0-40% central)

Au-Au update – elliptic flow




Models from Hirano et al., nucl-th/0506058, probably see more later this session

Cu-Cu more like Hydro than JAM hadron string cascade model

Here JAM uses a 1 fm/c formation time. Hydro (160) has kinetic freezeout temperature at 160 MeV

preliminary 200 GeV Cu-Cu

preliminary 200 GeV 15-25% Cu-CuStatistical errors only

Statistical errors only



Au-Au

Au-Au

Cu-Cu

Cu-Cu

PHOBOS-Glauber MC preliminary




Mean eccentricity shown in black

S. Manly – U. Rochester Quark Matter, Budapest, Hungary - August 20051 System size, energy and ...

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