Roy A. Lacey

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


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 !


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.


For the first time (at last) we have access to the full range

Of μ and T.(via Energy scans at

RHIC, SPS & FAIR)


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 !


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) !


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


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


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


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


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


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

= ?


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


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


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


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


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


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


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


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


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


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


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


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


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 ?


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


End

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Roy A. Lacey