2nd International Workshop on the Critical Point and Onset of Deconfinement, 2005Bergen, Norway

Fluctuations at RHIC

Claude A PruneauSTAR Collaboration

Physics & Astronomy Department Wayne State UniversityDetroit, Michigan, USA

Talk Outline

• Net Charge Fluctuations• Transverse Momentum Fluctuations• K/ Fluctuations (proof of principle)

• Questions:• Smoking gun for QGP, phase transition ?• Can we learn about the collision dynamics ?

Prediction by Koch, Jeon, et al., Asakawa et al., Heiselberg et al., of reduced net charge fluctuation variance following the production of a QGP.

CHQ NQ2δω ≡

R =N+

N−

QCH

ch N

QRND ϖ

δδ 44

22 ==≡

ωQ D

QGP Thermal + Fast Hadronization

0.25 1

Resonance/Hadron Gas ~0.7 ~2.8

Poisson / uncorrelated 1 4

Net Charge Fluctuations - a signature for the QGP ?

Q = qi nii∑

ΔQ2 = Q2 − Q2

= qi2 ni

i∑ + cik

(2)qiqk ni nki,k∑Predictions

Consider different scenarios:

ΔQ2 = qi2 ni

i∑

= n+ + n− = NCH

DHAD =4ΔQ2

NCH

=4

Dres ≈2.8

Q =0;cik(2) =0

Neutral resonances decay to charged particles Increases Nch

Do not contribute to <ΔQ2>

Jeon/Koch, PRL83(99)5435

ΔQ2 = 19 4 nu + nd + 4 nu + n

d{ }

ΔQ2 =5

18Nq

NCH =23

Ng +1.2 Nu+u +1.2 Nd+d{ }

DQGP ≈0.75

DLAT ≈1

QGP

QGP - Coalescence Scenario (A. Bialas, PLB 532 (2002) 249)

Gluons “attached” to quarks and forming constituent quarks. Small contribution to the entropy.

Nh =12

Nq Nch =23

Nh =13

Nq

Dcons =103=3.333

Brief Historical Review

Choice of Observable Many different approaches proposed/used “D” - S. Jeon and V. Koch, Phys. Rev. Lett. 85,

2076

ν+−=N+

N+

−N−

N−

⎛

⎝⎜⎞

⎠⎟

2

ν+−,stat =1

N+

+1

N−

ν+−,dyn =N+ N+ −1( )

N+

2 +N− N− −1( )

N−

2 − 2N+N−

N+ N−

ν+−,dyn = ν +− −ν +−,stat

Independent Particle (Poisson) Limit

Definition:

Measurement:

Properties and robustness of this observable discussed in:

1. “Methods for the study of particle production fluctuations”, C.P., S.G., S.V. - PRC 66, 44904 (2002).

2. S. Mrowczynski, PRC C66, 024904 (2002).

3. “On the Net-Charge Fluctuations in Relativistic Heavy-Ion Interactions”, J. Nystrand, E. Stenlund, and H. Tydesjo, PRC 68, 034902 (2003).

Dynamical Net Charge Fluctuations

Physical Motivation:

Rαβ =d6N

dpα3dpβ

3 dpα3dpβ

3∫d3Ndpα

3 dpα3∫ d3N

dpβ3 dpβ

3∫−1=

d3Ndpα

3d3Ndpβ

3∫ Cαβ (rpα ,

rpβ )dpα

3dpβ3

d3Ndpα

3 dpα3∫ d3N

dpβ3 dpβ

3∫

Cαβ (rpα ,

rpβ ) =

d6Ndpα

3dpβ3

d3Ndpα

3d3Ndpβ

3

−1

Independent of volumefluctuations

Independent Particle Production

Collision DynamicsIndependent of collision

centrality

Robust Observable(Independent of efficiency)

Charge Conservation

Perfect N+=N- correlation

ν+−,dyn = 0

dNdy AA

υAA,dyn = dNdy pp

υpp,dyn

N(b) υ+−,dyn(b) =constant

Raa =n(n−1)

n 2 =ε 2 N2 +ε(1−ε) N −ε N

ε 2 N 2 =N(N−1)

N 2

ν+−,dyn = R++ + R−− − 2R+−

ν+−,dyn = −2

N+ 4π

≈ −4

N4π

ν+−,dyn = − 4 Nη

Dynamical Fluctuations Properties

Data Sets - STAR Au + Au

sNN1/2 = 20, 62, 130, 200 GeV

Collision Centrality Determination based on all charged particle multiplicity ||<0.5.

Centrality slices 0-5%, 5-10%, 10-20 %, … Use Glauber model/MC to estimate the corresponding number of participants.

Events analyzed for |zvertex|<MAX. DCA < 3 cm. Track quality Nhit>15; Nfit/Nhit>0.5. Fluctuations studied in finite rapidity ranges, and azimuthal slices, for 0.2

< pt < 5.0 GeV/c.

Net Charge Dynamical Fluctuations

Beam Energy Dependence StudySTAR TPC - ||<0.5; 0.2 < pt < 5.0 GeV/c

• Finite Fluctuations • @ all energies.• Increased dilution with

increasing Npart

• Some energy dependence |ν+-,dyn| larger at 20 than

62, 130 and 200 GeV.

Au +Au

Effects of Kinematic CutSimulation based on 630k HIJING events @ 62 GeV||<0.6, pt>0., 0.1, 0.2, 0.3 GeV/c

r++ =N+

2 − N+

N+2

r++

Φ=ΔX 2

N− Δx2 ≈

N+

3/2N−

3/2

N2 ν +−,dyn

≈N

8ν +−,dyn

ϖQ =ΔQ2

N≈ 1+

N+ + N−

4ν +−,dyn

Comparisons with Models

1000000/620000 Hijing events, 700000 RQMD events

QGP Signature? 1/N Scaling?

PHOBOS - PRC65, 061901RAu + Au sqrt(sNN)=130 and 200 GeV.Poisson Limit

Coalescence

Resonance Gas

Koch/Jeon QGP ~ -3.

Au +Au 62 GeV

Fluctuations vs Beam Energy

H. Sako (CERES) @ QM 04.

Not corrected for finite efficiency

STAR -Preliminary

Dynamical Fluctuations vs Energy

-0.003

-0.002

-0.001

0

0 50 100 150 200SNN

1/2 (GeV)

%νdyn

STAR ||<0.5PHENIX ||<0.35, Δ=/2CERES 2.0< <2.9UrQMDRQMD

NA49 Results

dyn

CH

qN

NN,2

2/32/3

−+−+≈Φ ν

Summary so far… No smoking gun for D ~ 1 ν+-,dyn dependence on beam energy is not clear. dN/dν+-,dyn exhibits finite dependence on beam

energy and collision centrality - mostly accounted for by the change in dN/d.

More detailed comparison between experiments requires more work…

What about reaction dynamic effects?

Transverse Momentum Fluctuations

Pt Dynamic Fluctuations observed to be finite at RHIC. PHENIX STAR

Non-monotonic change in pt correlations with incident energy/centrality might indicate the onset of QGP.

STAR - Au + Au sNN1/2 = 20, 62,

130, 200 GeV. ||<1, 0.15 < pt < 2.0 GeV/c

pt k

= pt,ii=1

Nk

∑⎛

⎝⎜⎞

⎠⎟/ Nk

Measurement of Pt Fluctuations

To quantify dynamical pt fluctuations We define the quantity <Δpt,1Δpt,2>. It is a covariance and an integral of 2-body correlations. It equals zero in the absence of dynamical fluctuations Defined to be positive for correlation and negative for anti-

correlation.

Nevent = number of events

pt i = average pt for ith event

Nk = number of tracks for k th event

pt ,i = pt for ith track in event

and pt = pt kk=1

Nevent

∑⎛

⎝⎜⎞

⎠⎟/ Neventand pt k

= pt,ii=1

Nk

∑⎛

⎝⎜⎞

⎠⎟/ Nk

Δpt ,1Δpt ,2 =1

Nevent

Ck

Nk Nk −1( )k=1

Nevent

∑

where

Ck = pt,i − pt( ) pt, j − pt( )j=1,i≠j

Nk

∑i=1

Nk

∑

G. Westfall et al., STAR to be submitted to PRC.Pt Correlation Integral

Calculate <<pt>> and <Δpt,1Δpt,2> Vs acceptance Vs centrality - 9 standard STAR centrality bins in Nch, || < 0.5

Results reported here for all centralities for || < 1.0 (full STAR acceptance) for 0.15 < pt < 2.0 GeV/c

• Correlations are positive• Decrease with centrality

• ~ 1/N dependence

• Somee incident energy dependence

• HIJING underpredicts the measured correlations

Scale <Δpt,1Δpt,2> by dN/d to remove 1/N correlation dilutionand allow comparison with Φpt and Δpt

Scaling Properties (1)

HIJING does not agree with the data. - Magnitude - Centrality Dependence

Clear Scaling Violation

Scaling Properties (2)

Take square root of <Δpt,1Δpt,2>, divide by <<pt>> to obtain

dimensionless quantity + remove effects of <<pt>> variation incident energy and centrality

HIJING still does not agree with the data.

CERES - SPS - Adamova et al., Nucl. Phys. A727, 97 (2003)

(<Δpt,iΔpt,j>)1/2/<<pt>>

1.1%

Dynamical Effects

Resonance Decays Radial and Elliptical Flow Diffusion/Thermalization Jet Production/Quenching …

-2.2-2

-1.8-1.6-1.4-1.2

-1-0.8-0.6-0.4

-0.20

0 0.2 0.4 0.6 0.8 1

f3

n

Resonance Contributions - An Example

P(n1,n2 ,n3) =N!

n1!n2 !n3!f1

n1 f2n2 f3

n3

G(t+,t−;N) =( f1et+ + f2e

t− + f3et+ +t− )N

ν +

-,dy

n

Probability - f3

Nv+−,dyn(+ , −, ρo) =

−2 f3f1 + f3( ) f2 + f3( )

Assume multinomial production of +, -, and ρ with probabilities f1, f2, and f3.

Generating functions: ρ ~ 0.17ko

s ~ 0.12~ 0.08 effective with DCA < 3cm.

Resonances 0.3

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

STAR, PRL92 (2004) 092301

CollectivityS. Voloshin, nucl-th/0312065

rv

rv

Uses “blast wave” Model

v ∝ rn

Sensitivity to Velocity Profile

S. Voloshin, nucl-th/0312065

Single Particle Spectrum Two Particle Correlation

Comparison with Data

Scale <Δpt,1Δpt,2>, divide by <<pt>>2 and number of participants.

Compare to Blastwave calculation by S. Voloshin

Effect of radial flow on Net Charge Correlations

Toy model

Multinomial production of +, -, and ρ0.

Isotropic sourceMaxwell Boltzman Dist.T = 0.18 GeVRadial Flowvr as shown.

Toy Model (Continued)

Binomial production of +, -, and X0.

Isotropic sourceMaxwell Boltzman Dist.T = 0.18 GeVNo Radial Flowmx as shown.

Hijing/Rqmd Prediction of Angular Dependence

Au + Au @ sNN1/2 = 62 GeV

RQMDHIJING Version 1.38

ν+-,dyn vs || range

RQMDSTAR @ 200 GeV

Azimuthal DependenceAu+Au @ sNN

1/2 = 62 GeV

0-5%

10-20%

30-40%

70-80%

Indications of resonance + flow effectsInterpretation requires detailed model comparisons

Resonance Gas - Toy Model

T=0.18 GeV; +, -, ρ, K0s, vr as shown

K/ Fluctuation Measurement

Consider two approaches:1. Fluctuations of the Kaon to Pion yields ratios2. Measure integral correlations

Particle identification from dE/dx in TPC

M. A

nderson et al. NIM

A499 (2003)

K/ Fluctuations

Experiment Ratio type data mixed dyn

NA49 K/ 23.27% 23.1% 2.8%±0.5

STAR K/ 17.78% 17.23% 4.6%±0.025

STAR K+/+ 24.29% 24.10% 3.06%±0.066

STAR K-/- 24.81% 24.55% 3.61%±0.055

Suprya Das, STAR Preliminary

K/ Dynamical Fluctuations

ν k,

dyn

ν k,

dyn

(||

<0.

5)

HIJING 1.38 - Au + Au 200

GeV

M

Preliminary

Summary

Net Charge fluctuations No smoking gun for reduced fluctuations as predicted by

Koch et al. Bulk of observed correlations due to resonance decays. A new tool to evaluate the role of resonances and radial

flow. Observed centrality dependence of ν+-,dyn vs .

Pt fluctuations No smoking gun for large fluctuations. No beam energy dependence. A tool to study the velocity profile (see Sergei Voloshin’s

talk). K/ Yield fluctuations

Results by STAR on their way...

Energy Dependence

sNN1/2 ν+-,dyn ν+-,q-lim ν+-,q-lim/ ν+-,dyn

20 GeV -0.00351 ± 0.00026 -0.0016 ~46%

62 GeV -0.00290 ± 0.00018

130 GeV -0.00217 ± 0.00014 -0.00095 ~40%

200 GeV -0.00242 ± 0.00007 -0.00086 ~35%

Charge Conservation Limit: ν+-,q-lim = -4/NCH,4

Au + Au 0-5 % most central collisions

Comparison with HIJING/RQMD

Thermalization

Solves Boltzmann equation with Langevin noise phase-space correlations dynamic fluctuations

S. Gavin, Nucl. Dyn. Conf. Jamaica

Summary of Charge Fluctuation Measuresbased on a slide from J. Mitchell’s QM04 talk.

CHNQQv 2)( δ≡

−

+=N

NR

CHch N

QRND

2

2 4δ

δ =≡

2

2

zN

Z

CHq −=Φ

2

⎟⎟⎠

⎞⎜⎜⎝

⎛−=

−

−

+

+−+ N

NNNν

−+−+ +=

NNstat11

,ν

dyn

NNQv ,4

1)( −+−+ ++≈ ν

dynNND ,4 −+−+ ++≈ ν

222: XXXVariance −=δ −+ += NNNCH

−+ −= NNQ

dyn

CH

qN

NN,2

2/32/3

−+−+≈Φ ν2

2 4CHN

NNz −+=

CHCH

NN

QQZ −=

2

1⎟⎟⎠

⎞⎜⎜⎝

⎛−≡Γ CH

CHCH

NNQ

QN

)(4 QD ν=

)(Qv=Γ

Basic Observable - Mixed Events

Au+Au at 200 GeV

<Δpt,iΔpt,j> is zero for mixed events

Estimate Contribution from Short Range Correlations

To get an estimate for the contribution from short range correlations, we calculate <Δpt,iΔpt,j> excluding pairs with qinv < 100 MeV

To do this calculation, we assume all particles are pions model dependent

CERES carried out somewhat different calculation to estimate the contribution from SRC

When pairs with qinv < 100 MeV are removed, a strong, artificial anti-correlation is introduced CERES compensated for this effect by introducing randomly chosen

particles We compensate by subtracting mixed events with the same cut on pairs

with qinv < 100 MeV

Results for SRC Estimation

Correlation Function <Δpt,iΔpt,j>, qinv > 100 MeV

Au+Au 62 GeV

Ratios<Δpt,iΔpt,j> for pairs with qinv > 100 MeVto <Δpt,iΔpt,j> for all pairs

Au+Au 62 GeV

<Ratio> = 0.80 0.06

<Ratio> = 0.90 0.01

<Ratio> = 0.90 0.01

<Ratio> = 0.90 0.04

Estimate of Contributionfrom SRC to <Δpt,iΔpt,j>