Roy A. Lacey

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


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 !


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


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

Of μ and T.(via Energy scans at

RHIC, SPS & FAIR)


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


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


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 !


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


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


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?


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


initial state

pre-equilibrium

QGP andhydrodynamic

expansion

hadronization


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


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


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


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


The prediction for thermalization is explicit and specificThe prediction for thermalization is explicit and specific


As a predictor of ThermalizationAs a predictor of Thermalization


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


initial state

pre-equilibrium


hadronization



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


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


4 ~ 1 2s

4 ~ 1 2s

Transport CoefficientTransport CoefficientTransport CoefficientTransport Coefficient

Thermalization facilitated by 2Thermalization facilitated by 23 processes3 processes

C. Greiner et al


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


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


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


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


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


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


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


initial state

pre-equilibrium


hadronization



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 !

Roy A. Lacey

Documents

Transcript of Roy A. Lacey