2nd international workshop on the critical point and onset of deconfinement, 2005 bergen, norway...
TRANSCRIPT
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
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
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)
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
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.
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
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
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
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
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