1July 16th-19th, 2007

McGill University

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July 16th-19th, 2007 McGill University, Montréal, Canada

July 2007 Early Time Dynamics Montreal

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for the STAR Collaboration

2July 16th-19th, 2007

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introductionmotivation for this study

• perfect fluid claims• data and model uncertainties

v2 fluctuations: possible access to initial geometry and reduction of data uncertainties

analysis strategy and correction to QM analysis

new results• non-flow (with comparisons to models and fits to autocorrelations measurements)• v2 and v2

• relatioinship to cumulants v{2}, v{4}, v{6}• v2/v2 (with model comparisons)

relationship to preliminary PHOBOS results

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perfect fluid

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why perfect?

ballistic expansion

zero mean-free-path zero mean-free-path limitlimit

STAR Preliminary

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why perfect?

small viscosity suggested by: 1) pretty good agreement with ideal hydro and

2) independence of v2 shape on system size

in a hydro model viscosity seems to reduce v2

but large v2 is observed in data

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why perfect?

Teaney QM2006

small viscosity suggested by: 1) pretty good agreement with ideal hydro and

2) independence of v2 shape on system size

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model and data uncertaintiestypically the real reaction plane is not detected

inter-particle correlations unrelated to the reaction plane (non-flow) can contribute to the observed v2

different methods will also deviate as a result of event-by-event v2 fluctuations.

ambiguity arises in model calculations ambiguity arises in model calculations from initial conditionsfrom initial conditions

perfect fluid conclusion depends on vperfect fluid conclusion depends on v22 measurement and ambiguous comparison measurement and ambiguous comparison to ideal hydroto ideal hydro

my motivation to measure v2 fluctuations: eliminate source of data uncertaintyfind observable sensitive to initial conditions

8July 16th-19th, 2007

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flow vector distribution

q-vector and v2 related by definition: v2 = cos(2i) = q2,x/√M

sum over particles is a random-walk central-limit-theorem

width depends on• multiplicity: narrows due to failure of CLT at low M• non-flow: broadens n = cos(n(i- j)) (2-particle corr. nonflow)• v2 fluctuations: broadens

J.-Y. Ollitrault nucl-ex/9711003; A.M. Poskanzer and S.A. Voloshin

nucl-ex/9805001

€

q x = Mvsimulated q distribution

j

j is observed angle for event j after summing over tracks i

qx

qy

€

qn,x =1

Mcos(nϕ i)

i=1

M

∑

qn,y =1

Msin(nϕ i)

i=1

M

∑

σ n,x2 =

1

2(1+ v2n − 2vn

2 + Mδn )

σ n,y2 =

1

2(1− v2n + Mδn )

9July 16th-19th, 2007

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flow vector distribution

€

1

q

dN

dqd(ΔΦ)=

1

2πσ Xσ Y

e−

1

2

q cos2ΔΦ− M v2( )2

σ X2

+q 2 sin 2 2ΔΦ

σ Y2

⎡

⎣

⎢ ⎢ ⎢

⎤

⎦

⎥ ⎥ ⎥

σ X2 =

1

2(1+ v4 − 2v2

2 + Mδ2) and σ Y2 =

1

2(1− v4 + Mδ2)

experimentally x, y directions are unknown: integrate over all and study the length of length of the flow vector |qthe flow vector |q22||

from central limit theorem, q2 distribution is a 2-D Gaussian

fold various assumed v2 distributions (ƒ) with the q2 distribution.

function accounts for non-flow non-flow , , vv22, and , and fluctuations fluctuations v2v2

€

1

q2

d ˜ N

d q2

=1

q2

dv2

dN

d q2

f v2 − v2 ,σ v2( )−∞

∞

∫

Ollitrault nucl-ex/9711003;Poskanzer & Voloshin

nucl-ex/9805001

note: QM results found with wrong multiplicity dependence for this term:

• forced this fit parameter to zero• forced v2 to it’s maximum value

that data therefore represents upper limit on v2 fluctuations: derived under the accidental approximation of minimal non-flow

€

2 = cos2 ϕ1 −ϕ 2( )nonflow

€

2 ≈1

21+ v4 − 2v2

2 + M δ2 + 2σ v2

2( )( )

10July 16th-19th, 2007

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flow vector distribution

=-1 =0 =1

{/2} {full}

- --

+++- - -

{like-sign}

The width depends on how the track sample is selected. Differences are due to more or less non-flow in various samples:

• less for like-sign (charge ordering)• more for small (strong short range correlations)

€

2 ≈1

21+ v4 − 2v2

2 + M δ2 + 2σ v2

2( )( )

€

2 = cos2 ϕ1 −ϕ 2( )

STAR Preliminary

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non-flow term 2

=-1 =0 =1

{/2} {full}

- --

+++- - -

{like-sign}

differences in the width provide a lower limit on the amount of non-flow in the full eventthe total width provides an upper limit

€

2 = cos2 ϕ1 −ϕ 2( )

STAR Preliminary

€

2 ≈1

21+ v4 − 2v2

2 + M δ2 + 2σ v2

2( )( )

12July 16th-19th, 2007

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non-flow term 2

€

2 ≈1

21+ v4 − 2v2

2 + M δ2 + 2σ v2

2( )( )

differences in the width provide a lower limit on the amount of non-flow in the full eventthe total width provides an upper limit

€

2 = cos2 ϕ1 −ϕ 2( )

STAR Preliminary

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v2 and v2

STAR Preliminary

range of allowed v2 values specifiedupper limit on v2 fluctuations given

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comparison to cumulant analysisInformation determined from analysis of cumulants

€

v 2{ }2

= v2

+ σ v2 + δ

v 4{ }2

≈ v2

−σ v2

width ≈ δ + 2σ v2 = v 2{ }

2− v 4{ }

2

centroid ≈ v2

−σ v2 ≈ v 4{ }

from fit to the q-distribution

only values on curves are allowed: all parameters are correlatedonce one is determined, the others are specified

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v2 and v2

STAR Preliminary

new level of precision being approachedstill significant fluctuations after including minijets from the autocorrelations

with fit to autocorrelations

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comparison to geometric

fluctuations from finite bin widths have not been removed yetlikely to reduce ratio below the model!

STAR Preliminary

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comparison to geometric

fluctuations from finite bin widths have not been removed yetlikely to reduce ratio below the model!

STAR Preliminary

systematic uncertainties are still large and under investigation

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relationship to PHOBOS results

this is essentially an acceptance corrected q-distribution

the underlying analysis turns out to be quite similar and susceptible to the same uncertainties i.e. the width of this distribution can be explained either by non-flow or fluctuations

PHOBOS STAR Preliminary

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conclusionsnew analysis finds that case of zero v2 fluctuations cannot be excluded using the q-vector distributions the non-flow term needs to be accurately determined (see T. Trainor)

analysis places stringent constraints on , v2, and v2: when one parameter is specified, the others are fixed presents a new challenge to models

measurement challenges standard Glauber models: upper limit coincides with participant eccentricity fluctuations accounting for correlations and finite bin widths will likely exclude most glauber models glauber leaves little room for other sources of fluctuations and correlations

CGC based Monte Carlo may leave room for other fluctuations and correlations

non-flow term and fluctuations may follow expected dependence of CGC: still well below hydro prediction (larger initial eccentricity)? can CGC+QGP+hadronic explain , v2, and v2?

20July 16th-19th, 2007

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correction to previous analysis

but this should be (M-1)2

the difference: how does the fraction of tracks with a partner depend on subevent multiplicity

the consequences: since the multiplicity dependence of the non-flow term is the same as for fluctuations it becomes difficult to distinguish between the two

fraction of tracks with a partner = (n tracks from pair)/Mis a constant*(M-1)= 2 *(M-1)

2 = 0.00047

g2 = 0.109

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correlations and fluctuations