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Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 1
Roy A. LaceyRoy A. Lacey
New Prospects for locating the Critical End Point (CEP) in the QCD phase Diagram
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 2
The Central Question of the FieldThe Central Question of the Field
The location of the critical point and the phase boundaries represent two of the most fundamental characteristics of any substance !
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 3
Theoretical guidance Theoretical guidance for the CEPfor the CEP
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.
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 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; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 5
This 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
Better News !Better News !
2) The viscosity to entropy ratio offers a new dynamical probe for the CEP
• Contrasts Stationary State variables
There are NO Puzzles at RHIC -- just a few jig-saws !There are NO Puzzles at RHIC -- just a few jig-saws !
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 6
Life Time measurementsLife Time measurementsAs a probe for the transitionAs a probe for the transition
Life Time measurementsLife Time measurementsAs a probe for the transitionAs a probe for the transition
Strong first order phase transition Strong first order phase transition large large
20 (( ) ( ) 1 ) 1) (,4 ( )K q S rR q C q dr rr
Source functionSource function(Distribution of pair
separations)
Encodes FSIEncodes FSICorrelationCorrelation
functionfunction
Inversion of this integral equationInversion of this integral equation Source FunctionSource Function
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
New !New !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
1 1
.... ....
.... ....
2 1 !!( ) ( ) ( ) (4)
! 42 1 !!
( ) ( ) ( ) (5)! 4
l l
l l
ql lq
l lrr
dlR q R q
ll d
S r S rl
1 1
1 1
.... ....
.... ....
2 1 !!( ) ( ) ( ) (4)
! 42 1 !!
( ) ( ) ( ) (5)! 4
l l
l l
ql lq
l lrr
dlR q R q
ll d
S r S rl
Substitute (2) and (3) into (1)Substitute (2) and (3) into (1)
)/)(/(
/)(
2111
212
pp
ppq
ddNddN
dddNC
Reliable measurement of the fullReliable measurement of the fullSource Function (finally) ! Source Function (finally) !
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 7
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?
Source Function Comparison to Models Give robust life time Source Function Comparison to Models Give robust life time estimates estimates Crossover transition Crossover transition
~ 9
~ 12
ansatz
fm
t fm
Blast wave
~ 9
~ 12
ansatz
fm
t fm
Blast wave
Correlation MomentsCorrelation Moments
1 11
1 11
.... ........
.... ........
( ) ( )
( ) ( )
l ll
l ll
l lq
l
l lr
l
R q R q
S r S r
1 1.... ....
2 1 !!( ) ( ) ( )
! 4l l
ql lq
dlR q R q
l
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 8
y
x
Substantial elliptic flow signals should be present for a variety of particle Substantial elliptic flow signals should be present for a variety of particle species species Constraints for sound speed and viscosity Constraints for sound speed and viscosity
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
Detailed integral and differential Measurements now available forDetailed integral and differential Measurements now available for , , , , , , , , ,h p K d D
...])φ[2(2φcos211
2122
3
3
RRT
vvdydp
Nd
pd
NdE
])φ[2cos(2 Rv
The Matter Flow ProbeThe Matter Flow ProbeThe Matter Flow ProbeThe Matter Flow Probe
Control Params.Control Params.
0 , , , sc 0 , , , sc
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 9
nucl-ex/0610029
A Remarkable Scaling of the fine structure of Elliptic Flow is observed at RHIC
At midrapidity v2 (pt,M,b,A)/n = F(KET/n)*ε(b,A)
This scaling validates the expectations for “near perfect” This scaling validates the expectations for “near perfect” partonic flow and serve as an important constraint partonic flow and serve as an important constraint
for several transport coefficientsfor several transport coefficients
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 10
How to tell if Flow is HydrodynamicHow to tell if Flow is Hydrodynamic
• Fluid hydrodynamics is scale invariant.
• Important parameters
There are several generic scaling predictions that can be There are several generic scaling predictions that can be readily testedreadily tested;;
2
2 ( )
v k
v M k
2
2 ( )
v k
v M k
System size independence
24 2 2,4 6, v kv v v 24 2 2,4 6, v kv v v
12
0
( )
( )
I wv
I wBuda Lund
Hydro Modelnucl-th/0310040
v2 should scale with KET
0 , , , sc 0 , , , sc
( WHY ? ) ( WHY ? ) 21
2Therm colKE KE KE m u
PP
All scaling tests can be validatedAll scaling tests can be validated
Relationship between harmonics is specificRelationship between harmonics is specific
2 2
2 2
y x
y x
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 11
ε scaling validated
εε Scaling Scaling εε Scaling Scaling
pT (GeV/c)0 1 2 3 4 5
v 2(C
en
t, p
T)/
v 2(C
en
t)
0
1
2
3
4
5
00-05 05-10 10-20 20-30 30-4030-40 (PHENIX)
STAR DATA
J. Adams et al, Phys. Rev. C72, 014904 (2005)
x k
We understand this
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 12
Which ε scaling ?
Further Comments on Further Comments on εε Scaling Scaling
Further Comments on Further Comments on εε Scaling Scaling
http://xxx.lanl.gov/abs/nucl-ex/0610037
v2
= ?
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 13
KET scaling validated
PHENIX preliminary
21
2Therm colKE KE KE m u
PP
KEKETT Scaling Scaling KEKETT Scaling Scaling
Mesons
Baryons
Quark Degrees of Freedom EvidentQuark Degrees of Freedom Evident
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 14
A Phase with Quarks as dynamical degrees of freedom A Phase with Quarks as dynamical degrees of freedom Dominates the flow Dominates the flow
Flow is Partonic Flow is Partonic and Universaland Universal
Flow is Partonic Flow is Partonic and Universaland Universal
v2 for the v2 for the φφ follows that follows that of other mesonsof other mesons
v2 for the D follows that v2 for the D follows that of other mesonsof other mesonsquark
ThadronT
quarkT
quarkhadronT
hadron
nKEKE
KEnvKEv
)()( 22
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 15
0.0 0.5 1.0 1.5 2.0 2.5 3.0
v n (%
)
0
1
2
3
4
5
6
s 200 GeVNNAu Au
( )TKE GeV
22v4v
23
v
nucl-ex/0610029
Non-trivial higher harmonic Non-trivial higher harmonic hydrodynamic scaling validated at hydrodynamic scaling validated at
partonic levelpartonic level
24 2~ 0.5 0.6v v 24 2~ 0.5 0.6v v
The partonic fluid is Strongly The partonic fluid is Strongly Interacting Interacting
The partonic fluid is Strongly The partonic fluid is Strongly Interacting Interacting
STAR 62 GeV data give similar result~Linear
Quadratic
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 16
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; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 17
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; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 18
0222 kiDv ls
TsD
TsD lt
3/4
1~ 1.3
4
1~ 1.3
4
4~ 0.16
3s fmsT
Au+Au
KET (GeV)
0 1 2 3 4
v 2
0.00
0.05
0.10
0.15
0.20
0.25
Moore
K K p pD
200 NNs GeV
PHENIX PRELIMINARYDATA
3~ ~ 0.5
2D fm
T
Re
1~ 4lax
D
MD fm
T
1~ 1.9
4s
1~ 1.9
4s
Model Model ComparisonComparison
Partonic Fluid Flow Partonic Fluid Flow Is near PerfectIs near Perfect
Partonic Fluid Flow Partonic Fluid Flow Is near PerfectIs near Perfect
1-2 X the conjectured lower bound1-2 X the conjectured lower bound~s
Lacey et al. PRL 98:092301
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 19
Small viscosity results inSmall viscosity results inlarge suppressionlarge suppression
Small viscosity results inSmall viscosity results inlarge suppressionlarge suppression
An estimate of the scattering powerAn estimate of the scattering power
10%)ty (Probabili
/fmGeV 24ˆ6 2
q
There are no puzzles at RHICThere are no puzzles at RHIC
3
3.75T
Cs q
3
3.75T
Cs q
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 20
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; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 21
Same-Side Jet
Away-Side Jet
*
High pT trigger
Assoc. pTs
*
(2+1) processes efficiently removed via two-event mixing (2+1) processes efficiently removed via two-event mixing to obtain true three particle correlationsto obtain true three particle correlations
Deflected jet Mach Cone
* *
* * Re* *
,3 ,
,al
Mix
NC
N
Validation test of the use of two event mixing to remove 2+1 processes
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 22
Data
Simulated Deflected jet
Simulated Mach Cone
The data validates the presence of a Mach Cone away-side jet The data validates 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; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 23
Lacey et al. Phys.Rev.Lett.98:092301
Nonaka et al. Curves to guide the eye
LowLow Suggest trajectories close to the critical point ? Suggest trajectories close to the critical point ? s
hep-ph/0604138hep-lat/0406009
~ 0.2s
~ 0.2s
Hints of the CEP?Hints of the CEP?Hints of the CEP?Hints of the CEP?
B
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 24
Nonaka et al.
is a potent signal for the CEP is a potent signal for the CEP s
How to get there?How to get there?How to get there?How to get there?
First estimate T ~ 175 μ ~ 200-250 MeVNeed two energies immediately
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 25
Elliptic Flow at SPS (Pb+Pb at 158 GeV, NA49)
V2 of K0 (preliminary) - G. Stefanek for NA49 collaboration (nucl-ex/0611003)
v2 of p, π, Λ - C. Alt et al (NA49 collaboration) nucl-ex/0606026 submitted to PRL
Scaling ?Scaling ?
Roy A. Lacey, Stony Brook; EDT-HIC, McGill, Montreal, Canada, July 16-19, 2007 26
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 viscosity to entropy density ratio Matter has a soft EOS and a viscosity to entropy density 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
• 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 ~ 175 μ ~ 200-250 MeVNeed two energies immediately