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Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 1
Roy A. LaceyRoy A. Lacey
Prospects for locating the QCD Critical End Point (CEP)
Source Imaging Using RHIC Data
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 2
A Central Question of the Field? A Central Question of the Field?
The location of the critical End point and the phase boundaries are fundamental to the QCD phase diagram !
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 3
Theoretical Guidance ?Theoretical Guidance ?
Any search for the CEPAny search for the CEP requires investigationsrequires investigationsover a broad range of over a broad range of μμ & T. & T.
Freeze out CurveFreeze out Curve
Theoretical PredictionsFor the CEP
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 4
For the first time (at last) we have access to the full range
Of μ and T.(via Energy scans at
RHIC, SPS & FAIR)
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 5
The Crossover is a necessary requirement for locating
the CEP
1) The Crossover Transition to the QGP is made clear at RHIC
• Space-time measurements
• Flow Measurements
• Jet Quenching
Better News !Better News !
2) Viscosity Measurements offer a new dynamical probe for the CEP
• Contrasts Stationary State variables
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 6
Courtesy S. BassCourtesy S. Bassinitial state
pre-equilibrium
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
hadronization
Are source Imaging measurements Are source Imaging measurements consistent with the crossover consistent with the crossover
transition ?transition ?
A Cross Over strongly affects A Cross Over strongly affects the Space-time Dynamicsthe Space-time Dynamics
Theory indicate a crossover transitionTheory indicate a crossover transition
The space-time extent (Source The space-time extent (Source Image) can lend crucial insightsImage) can lend crucial insights
Puzzle ?The Space-Time probeThe Space-Time probeThe Space-Time probeThe Space-Time probe
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 7
04 ( , ) ( )j i j j ij jj
R rK q r S r K S
Discretize IntegralDiscretize IntegralSource Imaging Methodology (1D)Source Imaging Methodology (1D)Source Imaging Methodology (1D)Source Imaging Methodology (1D)
20 ( )( ) ( ) 1 4 (1( , ) )R SKq C q drr q r r
Source functionSource function(Distribution of pair
separations)
Encodes FSIEncodes FSICorrelationCorrelation
functionfunction
Inversion of this integral equationInversion of this integral equation Source FunctionSource Function
1D Koonin Pratt Eqn.1D Koonin Pratt Eqn.
)/)(/(
/)(
2111
212
pp
ppq
ddNddN
dddNC
Brown &
Daniel
ewicz
PRC 57(98)2474
Direct Fit
Direct Fit
Vary S(rj) to minimize
Reliable measurement of the fullReliable measurement of the full1D Source Function ! 1D Source Function !
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 8
Source Imaging Methodology (3D)Source Imaging Methodology (3D)Source Imaging Methodology (3D)Source Imaging Methodology (3D)
20 (( ) ( ) 1 ) 1) (,4 ( )K q S rR q C q dr rr
3D Koonin Pratt Eqn.3D Koonin Pratt Eqn.
1 11
1 11
.... ........
.... ........
( ) ( ) (2)
( ) ( ) (3)
l ll
l ll
l lq
l
l lr
l
R q R q
S r S r
Expand R(q) and S(r) in Expand R(q) and S(r) in Cartesian Harmonic basisCartesian Harmonic basis
(Danielewicz and Pratt nucl-th/0501003)(Danielewicz and Pratt nucl-th/0501003)
1 1
2.... ....
( ) 4 ( , ) ( ) (4)l l
l llR q drr K q r S r
1 1
2.... ....
( ) 4 ( , ) ( ) (4)l l
l llR q drr K q r S r
1 1.... ....
2 1 !!( ) ( ) ( ) (4)
! 4l l
ql lq
dlR q R q
l
1 1.... ....
2 1 !!( ) ( ) ( ) (4)
! 4l l
ql lq
dlR q R q
l
)/)(/(
/)(
2111
212
pp
ppq
ddNddN
dddNC
Reliable measurement of the full Source Function in 3D ! Reliable measurement of the full Source Function in 3D !
Substitute (2) and (3) into (1)Substitute (2) and (3) into (1)
The 3D integral equation is reduced to a set of 1D relations for different l coefficients moments
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 9
Correlation MomentsCorrelation Moments
1 1
1
.... ........
( ) ( ) l l
l
l lr
l
S r S r
Robust Experimental Source Functions obtained from Robust Experimental Source Functions obtained from momentsmoments
PHENIX DataPHENIX DataPHENIX DataPHENIX Data
1 1.... ....
( ) ( ) ( ) 4l l
ql lq
dR q R q
1 1
1
.... ........
( ) ( ) l l
l
l lq
l
R q R q
Contributions froml > 6 is negligible
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 10
Source Function Comparison to Models Give robust life time Source Function Comparison to Models Give robust life time estimates estimates Consistent with Crossover transition Consistent with Crossover transition
Therminator:A.Kisiel et al. Comput.Phys.Commun.174, 669 (2006)
Thermal model with Bjorken longitudinal expansion and transverse Flow
• Spectra & yields constrain thermal properties • Transverse radius ρmax : controls transverse extent• Breakup time in fluid element rest frame, : controls longitudinal extent• Emission duration : controls tails in long and out directions • a controls x-t correlations
LCM
~ 9
~ 2
~ 12
Outside-in burning
fm
fm
t fm
LCM
~ 9
~ 2
~ 12
Outside-in burning
fm
fm
t fm
The transition is Not a Strong The transition is Not a Strong First order Phase Transition?First order Phase Transition?
The transition is Not a Strong The transition is Not a Strong First order Phase Transition?First order Phase Transition?
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 11
y
x
s/
P ²
20
3
1 1
~ 5 15
TBj
dE
R dy
GeV
fm
From EFrom ETT Distributions Distributions2 2
2 2
y x
y x
Expect Large Pressure Gradients Hydro FlowExpect Large Pressure Gradients Hydro Flow
...])φ[2(2φcos211
2122
3
3
RRT
vvdydp
Nd
pd
NdE
])φ[2cos(2 Rv
The Flow ProbeThe Flow ProbeThe Flow ProbeThe Flow Probe
Control Params.Control Params. 0 , , , sc 0 , , , sc
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 12
initial state
pre-equilibrium
QGP andhydrodynamic
expansion
hadronization
hadronic phaseand freeze-out
Courtesy S. BassCourtesy S. Bass
We hold these truths to be self evident !We hold these truths to be self evident !
Scaling for identified hadrons
Scaling for Heavy Quark
Scaling for Phi Mesons
Universal Scaling
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 13
F. Karsch, hep-lat/0601013
Saturation of Elliptic flow consistent Saturation of Elliptic flow consistent with a soft EOS associated with with a soft EOS associated with
CrossoverCrossover
The expected saturation of vThe expected saturation of v22
Is observed Is observed
The expected saturation of vThe expected saturation of v22
Is observed Is observed
Phys.Rev.Lett.94:232302,2005 2 Pc
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 14
The prediction for thermalization is explicit and specificThe prediction for thermalization is explicit and specific
Hexadecapole Flow (vHexadecapole Flow (v44))
As a predictor of ThermalizationAs a predictor of Thermalization
Hexadecapole Flow (vHexadecapole Flow (v44))
As a predictor of ThermalizationAs a predictor of Thermalization 1
1 12 2 0
v vhydron nn n
K
K K
v 4/(
v 2)2
0.5-0.6
1.0
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 15
The prediction for thermalization is explicit and specificThe prediction for thermalization is explicit and specific
Hexadecapole Flow (vHexadecapole Flow (v44))
As a predictor of ThermalizationAs a predictor of Thermalization
Hexadecapole Flow (vHexadecapole Flow (v44))
As a predictor of ThermalizationAs a predictor of Thermalization 1
1 12 2 0
v vhydron nn n
K
K K
v4
pT (GeV/c)0 1 2 3
v 4/(
v 2)2
0.0
0.5
1.0
1.5
2.0
20-3030-4020-60Fit
PHENIX Preliminary
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 16
initial state
pre-equilibrium
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
Courtesy S. BassCourtesy S. Bass
The ratio of the harmonics for quarks is compatible with hydrodynamic predictionThe ratio of the harmonics for quarks is compatible with hydrodynamic prediction
4,q T4,M
2 22,M T 2,q T
4,q T4,B
2 22,B T 2,q T
v (p )v (2p ) 1 1
v (2p ) 4 2 v (p )
v (p )v (3p ) 1 1
v (3p ) 3 3 v (p )
T
T
a
a
2
1
) (pv
) (pv
T2
q2,
Tq4,
1.8a
Scaling for Higher Harmonics 4,q T4,M
2 22,M T 2,q T
4,q T4,B
2 22,B T 2,q T
v (p )v (2p ) 1 1
v (2p ) 4 2 v (p )
v (p )v (3p ) 1 1
v (3p ) 3 3 v (p )
T
T
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 17
Au+Au
KET (GeV)
0 1 2 3 4
v 20.00
0.05
0.10
0.15
0.20
0.25
Moore
K K p pD
200 NNs GeV
PHENIX PRELIMINARYDATA
0222 kiDv ls
TsD
TsD lt
3/4
1~ 1.3
4
1~ 1.3
4
4~ 0.16
3s fmsT
3~ ~ 0.5
2D fm
T
Re
1~ 4lax
D
MD fm
T
1~ 1.9
4s
1~ 1.9
4s
Model Model ComparisonComparison
Transport Coefficient Transport Coefficient Estimates - IEstimates - I
Transport Coefficient Transport Coefficient Estimates - IEstimates - I
1-2 X the conjectured lower bound1-2 X the conjectured lower bound~s
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 18
4 ~ 1 2s
4 ~ 1 2s
Transport CoefficientTransport CoefficientTransport CoefficientTransport Coefficient
Thermalization facilitated by 2Thermalization facilitated by 23 processes3 processes
C. Greiner et al
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 19
x10
x20
4 1~ 0.1, 0.2, 0.5
3s sT T
QCD Sonic BoomQCD Sonic Boom
Same-Side Jet
High pT trigger
**
Gives sound speed directly; Sets upper limit on viscosity.Gives sound speed directly; Sets upper limit on viscosity.
M
cos M sc
Setting an upper limit on Setting an upper limit on The viscosityThe viscosity
Setting an upper limit on Setting an upper limit on The viscosityThe viscosity
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 20
Data
The data is compatible with the presence of a Mach Cone away-side jet The data is compatible with the presence of a Mach Cone away-side jet
Total 3PC jet correlations
True 3PC jet correlations
QCD Sonic Boom?QCD Sonic Boom?QCD Sonic Boom?QCD Sonic Boom?
1~ 0.35, 2
4sc s
1~ 0.35, 2
4sc s
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 21
is a potent signal for the CEP is a potent signal for the CEP s
CEP SearchCEP SearchCEP SearchCEP SearchLacey et al.
arXiv:0708.3512 [nucl-ex]
B
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 22
Nonaka et al.
is a potent signal for the CEP is a potent signal for the CEP s
CEP SearchCEP SearchCEP SearchCEP Search
MeyerKharzeev-Tuchin
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 23
are a potent signals for the CEP are a potent signals for the CEP &s s
How to find the CEP?How to find the CEP?How to find the CEP?How to find the CEP?
First estimate T ~ 165-170 μ ~ 120-150 MeVNeed two energies immediately
MeyerKharzeev-Tuchin
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 24
EpilogueEpilogue
Strong evidence for crossover to the QGP at RHIC.Strong evidence for crossover to the QGP at RHIC.
– Short emission lifetimesShort emission lifetimes
– Matter quenches Jets and Matter quenches Jets and flows flows as a (nearly) perfect fluid with as a (nearly) perfect fluid with
systematic patterns consistent with systematic patterns consistent with quark degrees of freedom.quark degrees of freedom.
– Matter has a soft EOS and a shear viscosity to entropy density Matter has a soft EOS and a shear viscosity to entropy density ratio ratio lower lower than any other known fluid -- a value close to than any other known fluid -- a value close to the the conjectured quantum boundconjectured quantum bound
– Corresponding bulk viscosity to entropy density is large Corresponding bulk viscosity to entropy density is large •
Extracted Transport Coefficients Suggest Decay Trajectories Extracted Transport Coefficients Suggest Decay Trajectories close to the Critical End Point (CEP)close to the Critical End Point (CEP)
Energy scans now required to do the trick !!Energy scans now required to do the trick !!
First estimate T ~ 165 μ ~ 120 -150 MeVNeed two energies immediately
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 25
F. Karsch, hep-lat/0601013
v2/ε for <pT> ~ 0.45 GeV/c
cs ~ 0.35 ± 0.05(cs
2 ~ 0.12), soft EOSSee nucl-ex/0604011 for details
3500 MeV/fmp
The EOS is harder than that for the hadron gas but softer than for the hard QGP no strong first order phase transition
Hydro Calculations(Bhalerao et al.)
The EOS of the The EOS of the Partonic Fluid is Soft Partonic Fluid is Soft
The EOS of the The EOS of the Partonic Fluid is Soft Partonic Fluid is Soft
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 26
Roy A. Lacey, Stony Brook; 24th Winter Workshop on Nuclear Dynamics, April 5-12, 2008 27
initial state
pre-equilibrium
QGP andhydrodynamic expansion
hadronization
hadronic phaseand freeze-out
Courtesy S. BassCourtesy S. Bass
A Crossover transition to the A Crossover transition to the strongly coupled thermalized strongly coupled thermalized
QGP occurs at RHICQGP occurs at RHIC
2
1
) (pv
) (pv
T2
q2,
Tq4,
We hold these truths to be self evident !We hold these truths to be self evident !