Anisotropic Flow

Anisotropic Flow

Raimond Snellings

Raimond Snellings; Trento 2004 2

What have we learned from elliptic flow so far? According to:

– U. Heinz: Resulting in a well-developed quark-gluon plasma with almost ideal fluid-dynamical collective behavior and a lifetime of several fm/c (arXiv:hep-ph/0109006).

– E. Shuryak: Probably the most direct signature of QGP plasma formation, observed at RHIC (arXiv:nucl-th/0112042).

– L. McLerran: one needs very strong interactions amongst the quark and gluons at very early times in the collision (arXiv:hep-ph/0202025).

– M. Gyulassy: The most powerful probe of the QGP equation of state: the mass dependence of v2; One of the three lines of evidence for the QGP at RHIC (arXiv:nucl-th/0403032).


Outline

• Elliptic flow:– v2 at low pt, the dependence on particle mass

and its relation to freeze-out parameters in a hydro motivated picture

– Some uncertainties related to the measurement – What are the changes from SPS to RHIC

energies?


Elliptic flow of the bulk

• Coordinate space configuration anisotropic (almond shape) however, initial momentum distribution isotropic (spherically symmetric)

• Only interactions among constituents generate a pressure gradient, which transforms the initial coordinate space anisotropy into a momentum space anisotropy (no analogy in pp)

• Multiple interactions lead to thermalization -> limiting behavior ideal hydrodynamic flow

y

x

coordinate space

py

px

Momentum space

12 , tan ( )cos 2( ) y

xrv

p

p

3 2

31

11 2 cos

2 n rnt t

d N d NE v nd p p dp dy


Time evolution

• Elliptic Flow reduces spatial anisotropy -> self quenching

SCIENCE Vol: 298 2179 (2002)

Hydro calculation: P. Kolb, J. Sollfrank and U.Heinz


Main contribution to elliptic flow develops early in the collision

Zhang, Gyulassy, Ko, Phys. Lett. B455 (1999) 45


Non-central heavy-ion collisions: coordinate system

1

2 ,

tan ( )

cos 2( )

y

x

rv

p

p

2 2

2 2

` `

` `

y x

y x


Hydrodynamic limit

STAR

PHOBOS

Hydrodynamic limit

STAR

PHOBOS

Compilation and Figure from M. Kaneta

Integrated Elliptic Flow

First time in Heavy-Ion Collisions a system created which at low pt is in quantitative agreement with ideal hydrodynamic model predictions for v2 up to mid-central collisions

2 cos 2( )rv

PHOBOS: Phys. Rev. Lett. 89, 222301 (2002) STAR: Phys. Rev. Lett. 86, 402 (2001)

PHENIX: Phys. Rev. Lett. 89, 212301 (2002)

RQMD


Identified particle v2 • Typical pt dependence

for different masses• Heavy particles more

sensitive to velocity distribution (less effected by thermal smearing) therefore put better constrained on EOS

Fluid cells expand with collective velocity v, different mass particles get different p

Hydro: P. Huovinen, P. Kolb, U. Heinz

STAR


Hadron Cascade

UrQMD: Marcus Bleicher and Horst Stocker,arXiv:hep-ph/0006147

Magnitude off in v2 and different scale in pt


v2(pt,mass)

• All particles reasonably described at low-pt with common set of parameters

• PHENIX (squares) and STAR agree well

STAR, PHENIX preliminary


Everything flows?

pT [GeV/c]

M. Kaneta (PHENIX) QM2004

J. Castillo (STAR) QM2004

What about charm?


Reaction plane determination

• Anisotropic flow ≡ azimuthal correlation with the reaction plane

• Experimentally the reaction plane r is unknown

• Can introduce “non-flow” contributions


Determining the reaction plane

iii

iii

1B,A2 2cosw

2sinwTan

2

1


Event plane resolution• Event plane resolution N

* v22

• Most non flow contributions v2 1/N

• Kovchegov and Tuchin: N = Nwounded

• Non flow contribution will be constant in this variable. Dashed red line estimate of non-flow in first STAR flow paper

iii

iii

1B,A2 2cosw

2sinwTan

2

1

STAR, PRL 86, (2001) 402, Nucl. Phys. A698 (2002) 193


Elliptic flow as a function of centrality

STAR Nucl. Phys. A698 (2002) 193

Non-flow considerable for central and peripheral events


Calculating flow using multi particle correlations

r( ψ )cos ( ) inn rv n e

2 1 2 1 21 ( ) ( ) (( ) 2) ( ) ( {2})r r r rinn

in in in ine e e ee v

Assumption all correlations between particles due to flow

Non-flow correlation contribute order (1/N), problem if vn≈1/√N

1 2 3 4 3 4 3 21 2 1 4( ) ( ) ( )( ) ( ) 4( {4})in in inin in

n ve e e e e

Non-flow correlation contribute order (1/N3), problem if vn≈1/N¾

N. Borghini, P.M. Dinh and J.-Y Ollitrault, Phys. Rev. C63 (2001) 054906


Higher moments

<v2n> ≠ <v2>n

1/ 636 4 2 21

2

1/ 4

2 2 2

22 42 2 2

22

2

2

4

{4}

{2}

{6} 12

2

9

v

v

v v v v v

v

v v

v

2 2

2 2

y x

y x


Integrated v2 from cumulants

A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020

About 20% reduction from v2{2} to v2{4}

v2{4} ≈ v2{6}


The possible fluctuation contribution

“standard” v2{2} overestimates v2 by 10%, higher order cumulant underestimate v2 by 10% at intermediate centralities

M. Miller and RS, arXiv:nucl-ex/0312008


Integrated v2 from cumulants

A. Tang (STAR), AIP Conf. Proc. 698:701, 2004; arXiv:nucl-ex/0308020

About 20% reduction from v2{2} to v2{4}

v2{4} ≈ v2{6}


How does it compare to data?



Non-flow or fluctuations?


NA49: Phys.Rev. C68 (2003) 034903

N

gvv 22

222 42

N. Borghini, P.M. Dinh, J-Y Ollitrault: Phys. Rev. C 63 (2001) 054906


Uncertainties

• Non-flow and fluctuations expected in general to both contribute

• At mid-central collisions (20-60%) the estimated effect is about 10%. IMO best estimate of the true flow are in between (v2{2}+v2{4})/2 and v2{4}


Elliptic flow at lower energies

P. Kolb, J. Sollfrank, and U. Heinz, Phys. Rev. C. C62 054909 (2000).

• Increase of about 50% in v2 from top SPS to top RHIC energy


Hydrodynamics + RQMD

D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).


Energy dependence

NA49Phys.Rev. C68

(2003) 034903

At low energies pions, at RHIC charged hadrons. This makes a difference, this figure approximates the excitation plot of h-


v2(pt) SPS-RHIC

• Integrated v2 depends on slope and <pt>

• <pt> pions 17 GeV ≈ 400 MeV/c, 130 GeV charged particles <pt> ≈ 500 MeV/c

NA49: Phys. Rev. C68 (2003) 034903;

CERES: Phys. Rev. Lett. 92 (2004) 032301


Similar or very different?

arXiv:nucl-ex/0305001


Similar or very different??

• Note: only statistical errors plotted


Similar or very different?


Summary• Consistent measurements of elliptic flow at RHIC from PHENIX, PHOBOS

and STAR• Elliptic flow for all measured particles at low-pt well described by boosted

thermal particle distributions• Smooth increase in elliptic flow from SPS to RHIC. Detailed measurements

of identified particle v2(pt) by the RHIC experiments (or perhaps SPS data not presented yet) will provide a clearer picture

• At intermediate centralities (20-60%) I estimate not more than 10% uncertainty in the integrated elliptic flow values

• At RHIC the large elliptic flow is not described by hadronic models; strong (partonic) interactions at early stage of the collision are needed

• From comparisons with ideal hydro calculations early thermalization deduced (is this the only possibility? what is the freedom in EOS? What about HBT?)

D. Teaney, J. Lauret, E.V. Shuryak, arXiv:nucl-th/0011058; Phys. Rev. Lett 86, 4783 (2001).


Backup


Elliptic flow; excitation function

NA49Phys.Rev. C68

(2003) 034903 NA49

STAR


Hydro + Jet Quenching?

X.-N. Wang: nucl-th/0305010

T. Hirano and Y. Nara: nucl-th/0307015

Coupling of hydro and parton energy loss gives a reasonable description of the data and also has a mass dependence at higher-pt


Flow (radial, directed and elliptic)

x

y

x

y

z

x

• Only type of transverse flow in central collision (b=0) is transverse flow.

• Integrates pressure history over complete expansion phase

• Elliptic flow, caused by anisotropic initial overlap region (b > 0).

• More weight towards early stage of expansion.

• Directed flow, sensitive to earliest collision stage (pre-equilibrium, b > 0)


v1 predictions (QGP invoked)

J. Brachmann et al., Phys. Rev. C. 61 024909 (2000)

L.P. Csernai, D. Rohrich: Phys. Lett. B 458 (1999) 454


v1 predictions (more general, QGP interpretation not necessary)

R.S., H. Sorge, S.A. Voloshin, F.Q. Wang, N. Xu: Phys. Rev. Lett 84 2803 (2000)

M. Bleicher, H. Stocker: Phys. Lett. B 526 (2002) 309 (UrQMD)


Directed flow at the SPS (NA49)

NA49: Phys.Rev. C68 (2003) 034903


First measurement of v1 at RHIC

A. Tang, M. Oldenburg, A. Poskanzer, J. Putschke, RS, S. Voloshin

• Confirms v2 is in-plane at RHIC

• Suggestive of limiting fragmentation picture

• Consistent with theory predictions

• The data with current statistics shows no sign of a wiggle (also does not exclude the magnitude of the wiggle as predicted


Is there boost invariance?PHOBOS v2()

Preliminary v2200

Final v2130

200

130

average over

all centrality

(Npart ~200)

PHOBOS: Phys. Rev. Lett. 89, 222301 (2002)


Elliptic flow at higher pt, extracted using multi-particle correlations

Significant v2 up to ~7 GeV/c in pt as expected from jet quenching. However at intermediate pt the magnitude is unexpectedly large

STAR Preliminary

v2{2}

v2{RP}

v2{4}

A. Tang (STAR) QM 2004


Early freeze-out in a blast wave approach

• Low-pt measurements and comparison to full dynamical calculations important for drawing a conclusion !!!!

STAR, PHENIX preliminary

Anisotropic Flow

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