Conjectured Phase Diagram

Acoustic scaling of anisotropic flow in shape-engineered events: implications for extraction (μB,T) of the QGP

Roy A. LaceyStony Brook University

1 Zimanyi Winter School, Roy A. Lacey, Stony Brook University, Dec.. 2 - 6, 2013

p

Conjectured Phase Diagram

2

Quantitative study of the QCD phase diagram

Zimanyi Winter School, Roy A. Lacey, Stony Brook University, Dec.. 2 - 6, 2013

Interest

Location of the critical End point (CEP)

Location of phase coexistence lines

Properties of each phaseAll are fundamental to the phase

diagram of any substanceSpectacular achievement:Validation of the crossover transition leading to the QGP Necessary for the CEP?

A Current Focus of our Field

The extraction of transport coefficients is central to the heavy ion programs at RHIC and the LHC

3

LHC access to high T and small RHIC access to different systems anda broad domain of the (,T)-plane RHICBES to LHC 360 increase

Exploit system size and beam energy lever arm


Energy scan

Current Strategy

LHC + BES access to an even broader domain of the (,T)-plane

(,T) at freezeout

4 DNP Fall Meeting, Roy A. Lacey, Stony Brook University, Oct. 25, 2013

Essential Questions

At the CEP or close to it, anomalies inthe dynamic properties of the medium can drive abrupt changes in transport

coe cientsffi

Lacey et. al, Phys.Rev.Lett.98:092301 (2007)

()-dependence of transport coefficients , , etc? The role of system size and fluctuations? Location of phase boundaries? Indications for a CEP?

Anisotropic flow is an invaluable probe

Lacey et. al, arXiv:0708.3512 (2008)

http://arxiv.org/abs/arXiv:0708.3512

η/s estimates – QM2009 Excellent Convergence on the magnitude of η/s at RHIC

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

4πη/s ~ 1 - 2

5 of 17

Reminder

Status QuoA major uncertainty in theextraction of η/s stems from Incomplete knowledge of the Initial eccentricity

εn – η/s interplay?

T dependence of η/s? μB dependence of η/s? Possible signal for CEP?

Observations

Song et al

6DNP Fall Meeting, Roy A. Lacey, Stony Brook University, Oct. 25, 2013

η/s is a property of the medium and should not depend on initial

geometry!This is NOT an uncertainty; It is a

failure of the method of extraction

Status Quo

Status QuoA major uncertainty in theextraction of η/s stems from Incomplete knowledge of the Initial eccentricity

εn – η/s interplay?

New methodology and constraints required

Luzum et al. arXiv 0804.4015


Discovery of the acoustic nature of flow leads to specific scaling patterns which :

I. Give profound mechanistic insight on viscous damping

II. Provide constraints for

initial state geometry and its fluctuations Extraction of the specific viscosity

(,T) dependence of the viscous coefficients Hints for a possible critical point?

Essential message

This constitutes one of the most important recent developments in the field!

s/

P ² Bj

, , /s, f, Ts fc

20

3

1 1

~ 5 45

TBj

dER dyGeVfm

8

Idealized Geometry

2 2

2 2

y x

y x

Crucial parametersActual collision profiles are not smooth,

due to fluctuations!Initial Geometry characterized by many

shape harmonics (εn) drive vn

Initial eccentricity (and its attendant fluctuations) εn drive momentum anisotropy vn with specific viscous modulation

22, exp 03

tT t k k Ts T

Acoustic viscous modulation of vn

Staig & Shuryak arXiv:1008.3139

Isotropic p

Anisotropic p

Yield(f) =2 v2 cos[2(fY2]

The Flow Probe

1

1 2 cosn nn

dN v nd

ff

Y


9

1

1 2 cosn nn

dN v nd

ff

Y

22, exp 03

tT t k k Ts T

Acoustic viscous modulation of vn

Staig & Shuryak arXiv:1008.3139

(II) Scaling properties of flow

/k n R

Scaling expectations:

2( ) expn T

n

v p n

2

2 2

( ) exp ( 4)( )n T n

T

v p nv p

ln n

n

vR

vn is related to v2 System size dependencen2 dependence

Each of these scaling expectations has been validated

Initial Geometry characterized by many shape harmonics (εn) drive vn

Scaling properties of flow


10

Demonstration of acoustic scaling

What do we learn from these scaling patterns?


11

A B

Geometric fluctuations included Geometric quantities constrained by multiplicity density.

*cosn nn f

Phys. Rev. C 81, 061901(R) (2010)

arXiv:1203.3605

σx & σy RMS widths of density distribution

Geometric quantities for scalingGeometry


12

Acoustic Scaling – n2

Characteristic n2 viscous damping validated Characteristic 1/(pT)α dependence of extracted β values validated Constraint for η/s and δf

2( ) expn T

n

v p n

ATLAS data - Phys. Rev. C86, 014907 (2012)

arXiv:1301.0165



13

Npart

0 100 200 300 400v 2

0.10

0.15

0.20

0.25pT = 2-3 GeV/c

ATLAS Pb+Pb @ 2.76 TeV

Centrality 5-70%

ln n

n

vR

Characteristic scaling prediction is non-trivial

Eccentricity change alone is not sufficientTo account for the Npart dependence of vn

Transverse size ( ) influences viscous damping

Acoustic Scaling –



14

ln n

n

vR


Characteristic viscous damping validated at RHIC & the LHC A further constraint for η/s



15

Shape-engineered events

Cuts on qn should change the magnitudes , , at a given centrality due to fluctuations


Characteristic anti-correlation predicted for v3(q2) in mid-central events

Shape fluctuations lead toa distribution of the Q vector

at a fixed centrality

16

Shape-engineered events

Cuts on qn should change the magnitudes , , at a given centrality due to fluctuations


ALICE data

q2(Lo)

q2(Hi)

Viable models for initial-state fluctuations should still scale

Shape fluctuations lead toa distribution of the Q vector

at a fixed centrality

17

Acoustic Scaling of shape-engineered events



Characteristic viscous damping validated for different event shapes at the same centrality A further constraint for initial fluctuations model and η/s

Song et al

18Zimanyi Winter School, Roy A. Lacey, Stony Brook University, Dec.. 2 - 6, 2013

Characteristic viscous damping validated in viscous hydrodynamics; calibration 4πη/s ~

Extracted η/s value insensitive to initial conditions

η/s show 100% uncertainty due to “uncertainty” about the initial geometry

η/s is a property of the medium and should not depend on initial geometryThis is NOT an uncertainty; It is an incorrect method of extraction

Extraction of η/s ln n

n

vR

Slope sensitive to 4η/s


n2 scaling validated in experiment and viscous hydrodynamics;

calibration 4πη/s ~ 2

2( )expn T

n

v pn

n20 10 20 30 40

ln(v

n/ n)

-6

-5

-4

-3

-2

-1

0

1

012.5

s0 1 2 3

0.050

0.075

0.100

0.125

0.1504s

n20 10 20 30 40

Data

(a) (b) (c)Pb+Pb @ 2.76 TeV

0.1%

Viscous Hydro

arXiv:1301.0165 & CMS PAS HIN-12-011

Slope sensitive to η/s

Extraction of η/s


20

Anisotropy Measurements

An extensive set of measurements now span a broad range of beam energies ().

STAR - Phys.Rev.C86, 014904 (2012); Phys.Rev.C86, 054908 (2012) CMS - Phys.Rev.C87, 014902 (2013)

arXiv:1305.3341


21

ln n

n

vR

Characteristic viscous damping validated across beam energies

First experimental indication for η/s variation in the -plane

7.7 GeV 19.6 GeV 39 GeV 62.4 GeV 200 GeV

2.76 TeV




Flow is acoustic – “as it should be” Obeys the dispersion relation for sound propagation

(n2 & ) constraints for 4πη/s & viable initial-state models

4πη/s for RHIC plasma ~ 1 ~ my 2006 estimate4πη/s for LHC plasma ~ 2Extraction insensitive to initial geometry model

Characteristic dependence of viscous coefficient β” on beam energy give constraints for:

()-dependence η/s Indication for CEP??

Scaling properties of anisotropic flow lend profound mechanistic insights, as well as new constraints for

transport coefficients

22

What do we learn?

Summary


End


24

Geometric quantities for scaling


R_side scales with R_bar for a broad

range of system sizes and beam energies

Femtoscopic measurements

25


High precision double differential measurements obtained for identified particle species at RHIC and the LHC.


26

vn PID scaling

/2 n2 /2

vExpectation validated: v ( ) ~ v or ( )

nn T n

q

KEn

Acoustic Scaling – Ratios



27

LHC access to high T and small RHIC access to different systems anda broad domain of the (,T)-plane RHICBES to LHC 360 increase


Essential Questions

Luzum et al. arXiv 0804.4015

28

Does the value of depend on the initial geometry model or the method of extraction?


An Essential Question

Song et al


30

n20 10 20 30 40

ln(v

n/ n)

-6

-5

-4

-3

-2

-1

0

1

012.5

s0 1 2 3

0.050

0.075

0.100

0.125

0.1504s

n20 10 20 30 40

Data

(a) (b) (c)Pb+Pb @ 2.76 TeV

0.1%


Data and calculated points from CMS PAS HIN-12-011

2( )expn T

n

v pn

n2 scaling validated in viscous hydrodynamics; calibration 4πη/s ~ 2

Viscous Hydro

31

4/s0 1 2 3

0.0

0.5

1.0

1.5

2.0

1/R (fm-1)0.5 1.0 1.5

ln(v

2/ 2)

-4

-3

-2

-1

0123

s)QGP

MC-Glauber

1/R (fm-1)0.5 1.0 1.5 2.0

MC-KLN

(a) (b) (c)Data


Characteristic viscous damping validated in viscous hydrodynamics; calibration 4πη/s ~ 1.3

ln n

n

vR

Viscous Hydro Viscous Hydro

Song et al

32DNP Fall Meeting, Roy A. Lacey, Stony Brook University, Oct. 25, 2013

Characteristic viscous damping validated in viscous hydrodynamics; calibration 4πη/s ~

Extracted η/s value insensitive to initial conditions

η/s is a property of the medium and can not depend on initial geometryThis is NOT an uncertainty; It is an incorrect method of extraction

Validation of 1/R scaling

ln n

n

vR

Slope sensitive to 4η/s

0.0 0.5 1.0 1.5

ln(v

2/ 2)

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

Au+Au 0.2 TeV (PHENIX)

Cu+Cu 0.2 TeV (STAR)

pT = 0.79 GeV/c

0.5 1.0 1.5

ln(v

2/ 2)

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

1/R (fm-1)0.5 1.0 1.5

pT = 1.19 GeV/c pT = 1.79 GeV/c

33

ln n

n

vR

Acoustic Scaling – 1/R

Slope difference encodes viscous

coefficient difference

Compare system size @ RHIC

Viscous coefficient larger for more dilute system


p

Quantitative study of the phases of QCD is a central goal of our field


The extraction of transport coefficients is central to the heavy ion programs at RHIC and the LHC

34 of 17

Interest

Location of the critical End point (CEP)

Location of phase coexistence lines

Properties of each phaseAll are fundamental to the phase

diagram of any substanceSpectacular achievement:Validation of the crossover transition leading to the QGP Necessary for the CEP?


Acoustic Scaling – Ratios

The expected relation between vn and v2 is

validated

/2

2

n

n T Tv p v p

arXiv:1105.3782



36

For partonic flow, quark number scaling expected single curve for identified particle species vn

Flow is partonic & Acoustic?

/2 n2 /2

vExpectation: v ( ) ~ v or ( )

nn T n

q

KEn Note species dependence for all vn

arXiv:1211.4009



37

High precision double differential measurements obtained for higher harmonics at RHIC and the LHC.

ATLAS data - Phys. Rev. C86, 014907 (2012) & ATLAS-CONF-2011-074





Event-by-Event v2 measurements obtained via 2PC followed by unfolding.

v2 described by Bessel-Gaussian distribution: Contribution from mean geometry+fluctuations.

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Conjectured Phase Diagram