The Role of higher-order flow harmonics in the search for the critical point Roy A. Lacey

The Role of higher-order flow harmonics in the search for the

critical point

Roy A. LaceyChemistry Dept.

Stony Brook University

1Roy A. Lacey, Stony Brook University; CPOD, Wuhan, Nov., 2011

Essential message!

Much emphasis currently placed on stationary state variablesDynamic variables may offer robust probes of the CEP

2

A fundamental understanding requires

knowledge of: i) The location of the

Critical End Point (CEP)ii) The location of phase

coexistence lines iii) The properties of each

phase

Phase Diagram (H2)

This knowledge is elemental to the phase diagram of any substance !

H2 phase diagram is rich

Roy A. Lacey, Stony Brook University; CPOD, Wuhan, Nov., 2011

3

The Crossover is a necessary requirement for existence

the CEP

What Motivates the Search for the Critical end point (CEP)?

• Lattice results • More sensitive observables• Possible dynamic observables• Shine, HADES,CBM, NICA

Discovery of the crossover transition, as well as new techniques and tools for

studying the properties of QCD matter!

M. A. Stephanov, K. Rajagopal and E. V. Shuryak, Phys. Rev. Lett. 81 (1998) 4816; Phys. Rev. D 60 (1999) 114028


Aoki et al

Hot QCD Collab

Roy A. Lacey, Stony Brook University; CPOD, Wuhan, Nov., 2011 4

How do we search for the CEP?

Theoretical Guidance?

Key search variables? Search Strategy?

5

Theoretical Guidance for CEP ?

Search strategy for the CEP requires experimental investigations over a broad range of μ & T.

ChemicalFreeze-out Curve

Theoretical Predictions

from Lattice QCD


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Which search variable/s?

Dynamic variablesStationary state variables

Operational AnsatzThe physics of the critical point is universal.

Members of a given universality class show “identical” critical properties

The CEP belongs to the same dynamic universality class (Model H) as the liquid gas phase

transitionSon & Stephanov


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Singular behavior of stationary statevariables near the CEP

• Non-monotonic dependence of event-by-event fluctuations as a function of

NNs

2 Stephanov, Rajagopal,Shuryak, Phys. Rev. D 60, 114028 (1999)

Fluctuations Correlation length

Divergence of ξ restricted:

• Finite system size ξ < size

• Finite evolution time ξ < (time)1/z

~ z z=3

Net proton number fluctuation, higher moments, etc.


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Singular behavior of Dynamicvariables near the CEP

• D “vanishes’’ at the CEP• “mild’’ dependence for viscosity

1~D Son & Stephanov,

Diffusion Constant Correlation length

Divergence of ξ restricted:

• Finite system size ξ < size

• Finite evolution time ξ < (time)1/z

~ z z=3

.05 .06~

viscosity


9

Lacey et al.arXiv:0708.3512 [nucl-ex]

B

The CEP belongs to the Model H dynamic universality class -Son & Stephanov


η/s could be a potent signal for the CEPEvolution in the degrees of freedom (dof)

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How to access η/s and dof?

Higher order flow harmonics provide new constraints for: partonic flow initial eccentricity model sound speed cs δf etc


Flow is acoustic!

Crucial for reliable η/s extraction

The Flow Probe

s/

P ² Bj

, , , Tsc s

20

3

1 1

~ 5 15

TBj

dER dyGeVfm

11 Roy A. Lacey, Stony Brook University; CPOD, Wuhan, Nov., 2011

2 2

2

cos sinn npart part

n n

r n r n

r

Idealized Geometry

2 2

2 2

y x

y x

Control parameters

Actual collision profiles are not smooth, due to fluctuations!

Initial Geometry characterized by many harmonics

Initial eccentricity (and its attendant fluctuations) εn

drive momentum anisotropy vn


PHENIX Central Arms (CA) |η’| < 0.35(particle detection)

RXNRXN

BBC/MPC BBC/MPC

Planes (EP)

Event6 7 8 Planes (EP)

Event6 7 8

∆η’ = 5-7 1

1 2 cos ( )n nn

dN v nd

n , 1,2,3..,{ } co sn nv n n

pairs

1

1 2 cos( )a bn n

n

dN v v nd

Two complimentary analysis methods employed:

Correlate hadrons in central Armswith event plane (RXN, etc)

∆φ correlation function for EPN - EPS

Correlations between sub-event planes (EPN - EPS ) also

studied!

ψn RXN (||=1.0~2.8)

MPC (||=3.1~3.7) BBC (||=3.1~3.9)

Schematic Detector Layout

Sub-event participant plane = ΦN,S

∆φ correlation function for EP - CA

(I)

(II)

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Quantifying Flow

Roy A. Lacey, Stony Brook University

Results: vn(ψn)

Robust PHENIX measurements performed at 200 GeV(Crosschecked with correlation method)

http://arxiv.org/abs/1105.3928

v4(ψ4) ~ 2v4(ψ2)

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Results: vn(ψn)

Robust ATLAS measurements performed at 2.75 TeV(Crosschecked with several methods)

ATLAS-CONF-2011-074

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Results: vn(∆φ)

v2,3,4 saturates for the range √sNN 39 - 200 GeV Extract η/s and dof as a function of beam energy

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Roy A. Lacey, Stony Brook University; QM11, Annecy, France 2011

Consistent partonic flow picture for vn

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(KET/nq) (GeV)0 1 2

v 3/(n

q)3/

2

0.00

0.01

0.02

0.03

0.04

0.05

Kp

Au+Au 200 GeVNNs

20-50%

PHENIX

KET/nq (Gev)0.0 0.5 1.0 1.5 2.0 2.5

v n/(n

q)n/

2

0.00

0.01

0.02

0.03

0.04Kp n=3

0-60%

STAR

Flow is partonic

Flow is partonic

Flow is pressure driven

/2n

qnKET & scaling validated for v3 Partonic flow

v3 PID scaling

Flow is acoustic

Characteristic viscous damping

For higher harmonics

Deformation nkR

17 Roy A. Lacey, Stony Brook University

22, exp 03

tT t k k Ts T

Viscous horizon2 ~ 1.8vv

Rr fmn

2 gR n

The viscous horizon (rv) is the length-scale which characterizes the highest harmonic that survives

viscous damping

arxiv:1105.3782

2.76 TeV

Flow is acoustic


Acoustic patterns validated in (3+1)D viscous relativistic Hydrodynamics calculations

2, exp 0T t k n T

Flow is acoustic

Low frequency Super-horizon modes are suppressed

Deformation nkR


22, exp 03

tT t k k Ts T

suppressi n

2

o

2fs

Rr

n

0

( )f

s sr d c

constraint for f s

s

RR r

c

Pb+Pb2.76 TeV

Constraint for δf

Constraint for the Relaxation time

Deformation nkR


2

0

2

, exp 0

Particle Dist. ( )

( ) ~

T

TT

f

T t k n T

f f f p

pf pT

1~Tp

2.76 TeV

Constraint for δf

Constraint for the Relaxation time

Deformation nkR


2

0

2

, exp 0

Particle Dist. ( )

( ) ~

T

TT

f

T t k n T

f f f p

pf pT

pT dependent viscous effects cancel !Same scaling observed at the LHC

22Roy A. Lacey, Stony Brook University

Constraint for εn Note that data take account of the acoustic suppression

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CEP Search


Lacey et al. arXiv:0708.3512 [nucl-ex]

Map vn vs. beam energyto obtain η/s vs. T

Konchakovski, arxiv:1109.3039

1cBcT

:Value similar to that for recent lattice comparisons

which claim an onset of deconfinement

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CEP Search


Currently Mapping η/s vs. T for higher order harmonics

much more sensitive-- Work in progress --

Higher-order harmonics (odd & even) currently being

used to evaluate η/s vs. T [and other properties of the

hot and dense matter created in RHIC & LHC collisions] to

search for the CEP.

Summary

Roy A. Lacey, Stony Brook University 25

Acoustic property for higher-order flow harmonics (odd & even) validated!

Provides important additionalconstraints for initial state model and several properties of the QGP

v

2

4 1

~ 0.3 fmr 1.8 fmT ~165 11 MeV

( ) ~f

T T

s

f p p

:

: √s = 200 GeV

End

Roy A. Lacey, Stony Brook University 26

Relaxation time limits η/s to small values

27Roy A. Lacey, Stony Brook University; CPOD, Wuhan, Nov.,

2011

Temperature dependence of η/s

v2

pT

G. Denicol et al

Roy A. Lacey, Stony Brook University; CPOD, Wuhan, Nov., 2011 28

Viscosity estimates at AGS - SPSIvanov et al

4 ~ 12 25s

From fits

Significant deviations From hydrodynamic

calculations

The Role of higher-order flow harmonics in the search for the critical point Roy A. Lacey

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