s.a. voloshin star qm’06: energy and system size dependence of elliptic flow and v 2 / scaling...

QM’06: Energy and system size dependence of elliptic flow and v2 / scaling

page 1 S.A. Voloshin

STAR

Sergei A. Voloshin

Wayne State University, Detroit,

Michigan

for the STAR Collaboration

Energy and system size dependence of charged

particle elliptic flow and v2 / scaling

Outline:

1. Introduction: Elliptic flow and the system initial eccentricity. Flow fluctuations and non-flow.

2. Measuring flow with STAR detector (Main TPC, Forward TPCs, ZDC-SMD).

3. Estimates of flow fluctuations with Monte-Carlo Glauber model.4. v / scaling(s).



STAR

Elliptic flow and the system initial geometry

Note: uncertainty in the centrality definition- sqrt(s)=130 GeV data: 0.075 < pt < 2.0 GeV/c- sqrt(s)=200 GeV data: 0.15 < pt < 2.0; - the data scaled down by a factor of 1.06 to account for change in (raw) mean pt.- AGS and SPS – no low pt cut- STAR and SPS 160 – 4th order cumulants - no systematic errors indicated

2

1 dN

Sv

dy 2 2S x y

Motivation for the plot:

2 2

2 2

y x

y x

2 cos 2 i RPv Hydro limits: slightly depend on initial conditionsData: no systematic errors, shaded area –uncertainty incentrality determinations.Curves: “hand made”

S.V. & A. Poskanzer, PLB 474 (2000) 27



STAR

v2{2}, v2{4}, non-flow, and flow fluctuations

* 2 21 2 2

* 1/ 22 1 2

* * 4 2 21 2 3 4 2 2

1/ 4* 2 * *2 1 2 1 2 3 4

;

{2}

2 2 2

{4} 2

iu u v u e

v u u

u u u u v v

v u u u u u u

Several reasons for v to fluctuate in a centrality bin:1) Variation in impact parameter in a centrality bin

(taken out in STAR results)2) Real flow fluctuations (due to fluctuations in the

initial conditions or in the system evolution)

* 22 2 2

2

22 12 2

vv uu v vv v

22

2 2* * * 24 42

22 2

2

4 2 12

vv

v uu uuu u v vv

2 equations, at least 3 unknowns: v, δ, σ

Non-flow Flow fluctuations

Non-flow (not related to the orientationof the reaction plane) correlations:- resonance decays- inter and intra jet correlations, etc.

Different directions to resolve the problem:- Find methods which suppress / eliminates non-flow or flow fluctuations

- Add more equations assuming no new unknowns

- Estimate flow fluctuations by other means

- Measure flow fluctuations

22 2 2 2 2; {2} / {2}/v v v v

Correlations with large = |1-2|Lee-Yang Zeroes (Bessel Transform)

Subject of this talk

Use equations for v2{n}, n>4

Talk by P.Sorensen (STAR)



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Data

This analysis used the data taken during RHIC Run IVand based on (after all quality cuts)Au+Au 200 GeV ~ 10.6 M Minimum Bias eventsAu+Au 62 GeV ~ 7 M Minimum Bias eventsCu+Cu 200 GeV ~ 30 M Minimum Bias eventsCu+Cu 62 GeV ~ 19 M Minimum Bias events

Tracking done by two Forward TPCs (East and West)and STAR Main TPC.

Tracks used: | η |<0.9 (Main TPC) -3.9 < η < -2.9 (FTPC East) 2.9 < η < 3.9 (FTPC West)

0.15 < pT < 2.0 GeV/c

Results presented/discussed in this talk: elliptic flow in the Main TPC region (|η|<0.9)

ZDC

Barrel EM Calorimeter

Magnet

Coils

ZDC

FTPC west

Central Trigger Barrel

Main TPC

Silicon Vertex Tracker

FTPC east



STAR

Shown in black are resultsobtained by correlatingtwo random particles from Main TPC. Non-flow contribution can be largeand positive.

In blue are results forv2 in the Main TPC regionobtained from correlations (Forward*Main) and(East*West). Relative systematic error at maximum flow ~< 3% (AuAu 200 GeV)~< 5% (AuAu 62 GeV)~< 12% (CuCu 200 GeV) ~< 20% (CuCu 62 GeV)

Note: significantly largerrelative difference between black and blue points in Cu+Cu case compared to Au+Au

v2 from ( Forward TPC * Main TPC ) correlations

The difference (blue and red) is due to non-flow assuming that flow fluctuates coherently in the Main and Forward TPC regions



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v2{FTPC}(pt) , 20-60% centrality

There still indications of non-flow contribution in v2{FTPC}, especially at high transverse momenta.

The green points show the results “AA-pp” [G.Wang (STAR), QM2005]

AuAu 200 GeV

CuCu 200 GeV

Non-flow contribution in v2{2}, relatively smallin AuAu @200 GeV, increases with pt



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CuCu 200 GeV, v2{FTPC}(pt)

S

TA

R P

reli

min

ary

Indicates strong non-flow contribution in v2{2} (measured within Main TPC).

Non-flow might be still present at high pt in v2{FTPC}



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Initial eccentricity: “optical”, “standard”, “participant”.

“New” coordinate system –rotated, shifted

2 2

2 2Std

y x

y x

2 2

2 2

' '

' 'part

y x

y x

S. Manly, QM2005

x

'x

y'y

“Optical” Glauber calculations: “Monte-Carlo” Glauber model:

[neglecting shift ]

cos(2 )std part



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Eccentricity fluctuations: ‘Standard’ vs ‘Participant’

Note:- Relative fluctuations in part are much smaller than in std

- “participant” eccentricity values are larger compared to “standard” std ≈ part cos(Ψ).-In Cu+Cu Std{4} fails almost at all centralities- The difference between std and part is bigger for Cu+Cu than Au+Au- Very weak dependence on collision energy (not shown)

- Very small values of part{4} for central collisions difficult to use it to rescale v2{4}

Monte Carlo Glauber nTuples from J. Gonzales (STAR)

22 2 22

24 2 44 2

Black line on the left is optical used earlier in STAR and NA49 publi-cations. Note that it is about 15%

larger than part almost at all centralities.

Main idea: use proper ε{n} torescale corresponding v2{n}:

{ } { }/v n v n


page10 S.A. Voloshin

STAR

One more equation: Flow fluctuations from v2{4}/v2{6}

Assuming:- non-flow does not fluctuate- non-flow exist only on 2-particle level

- Gaussian type of fluctuations

- (For the last approximation)small relative fluctuations

* 2 * * 4 2 2

* * 4 2 2

; 4 2 ;

4 2 ;

uu v uuu u v v

uuu u v v

2 4 22 2 2 2 4

6 4 26 2 4 6

; 6 3

15 15

v v v v v

v v v v

2

2yv

1/ 42

1/ 22

1 24

2 1 /

y yv

v y v

1/ 42 2

1/ 6 2

1 241

6 1 4 6

y yv

v y v

One finds:

where :

Cu+Cu 200 GeV

Au+Au 200 GeV

- Fluctuations in std (green points) are too strong (noticed earlier by R. Snellings.)- Gaussian approximation works rather poorly(no agreement between red and blue points)



STAR

Eccentricity fluctuations in AuAu, MC Glauber vs data

Flow fluctuations from data are somewhat stronger compared to those in eccentricity (shown in blue)though would be within sytematics.

STAR Phys. Rev. C 72 (2005) 014904

22 2 22

24 2 44 2

22 1/ 4

1/ 6 2

4 (1 2 ),

6 (1 4 )v

v y yy

v y v



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Effect of fluctuations in eccentricity

If compare to the “original” v2 / plot (page 2) note the difference in eccentricityoptical, old (using parameterization made for SPS energies) and part (optical, old ~ (1.1– 1.2) * part ) ! )

2{ }/ {2}v FTPC 2{ }/ partv FTPC

Systematic error on dn/dy ~10%, similarly on v2 and S.

Hydro results (Kolb, Sollfrank, Heinz, PRC 62 (2000) 054909 )are rescaled with optical

Scaling with ε should be used ifv2’s in the Main and ForwardTPCs are not correlated.



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v2{ZDC-SMD} and eccentricity scaling

Au +Au 200 GeV

STAR

prelimi

nary

G. Wang (STAR) QM2005

Note that under assumption that the directedflow of spectator neutrons is not correlatedto the elliptic shape of the system at midrapidty,

v2{ZDC-SMD} should follow std .(This assumption requires further study with MC Glauber model).



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v2/ scaling

Scaling holds rather well, thoughAuAu 62 GeV results are somewhat higher.

Hydro curves are obtained from calculationsKolb, Sollfrank, Heinz, PRC 62 (2000) 054909,made at b=7 fm and rescaled by ‘optical’ eccentricity value. The centrality dependence is not fullyreflected by these curves, as it is more ‘flat’ at eachgiven collision energy (very roughly indicatedby strait lines)



STAR

Conclusions

1. The results for elliptic flow at midrapidity in Au+Au and Cu+Cu collisions

have been presented for collision energies √sNN = 200 and 62 GeV using

correlations of particles in the Main TPC and FTPCs regions.

2. Initial eccentricity and its fluctuations have been studied with Monte Carlo

Glauber model.

3. Flow fluctuations have been estimated from v2{4}/v2{6} ratio using Gaussian

approximation.

4. The v2 /2 scaling holds well for all four systems ( Au+Au and Cu+Cu at different

energies ) once the fluctuations in eccentricity have been taken into account.

v2{ZDC-SMD} scales well with std



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Backup slides



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v2{2}/eps{2} and v2{4}/eps{4}



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Eccentricity for the ‘standard’ STAR centrality bins

AuAu200 CuCu200

No multiplicity weight!

Centrality bin 1 2 3 4 5 6 7 8 9 10Fraction of cross section (%) >80 70-80 60-70 50-60 40-50 30-40 20-30 10-20 5-10 0-5



STAR

Observation of non-flow in azimuthal correlations

- In Cu+Cu collisions the azimuthal correlationsin the main TPC are dominated by non-flow.

-The relative contribution of non-flow is at least 2 times smaller in correlations between Forward and Main TPCs.

Main * ForwardMain_a * Main_b

FTPC_east * FTPC_west“a” and “b” are two random particles from Main TPC

In this kind of plots non-flow correlation contributionshould be either flat or slightly increasing

s.a. voloshin star qm’06: energy and system size dependence of elliptic flow and v 2 / scaling...

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