What do we learn from Azimuthal Anisotropy Measurements @ RHIC and the LHC Roy A. Lacey

What do we learn from Azimuthal Anisotropy Measurements @ RHIC and

the LHCRoy A. Lacey

Chemistry Dept., Stony Brook University

1 WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

Take home message The scaling (pT, ε, R, ∆L, etc) properties of azimuthal anisotropy

measurements at RHIC & the LHC, inform crucial mechanistic insights and constraints for characterization of the QGP?

2

RHIC (0.2 TeV) LHC (2.76 TeV)Power law dependence (n ~ 0.2) increase ~ 3.3 Multiplicity density increase ~ 2.3 <Temp> increase ~ 30%

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

Relevant questions: How do the transport coefficients evolve with T?

Any indication for a change in coupling close to To?

ˆ, , ,s sc qs

WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

Energy scan

Why RHIC and LHC Measurements?

The energy density lever arm

Why Azimuthal Anisotropy Measurements?

This implies very specific scaling properties for flow and jet suppression (respectively), which can be tested experimentally

Scaling validation provide important insights, as well as straightforward probes of transport coefficients


pT <

3 -

4 G

eV/c

Flow

pT > 8 -10 GeV/c

Jet suppression

3

Eccentricity driven& acoustic

3-4 < pT < 8-10 GeV/c

Path length (∆L) driven

More

suppression

Lesssuppression

TransitionRegion

Flow and Jet suppression are linked to Geometry & the interactions in the QGP

4

Geometric Quantities for scaling

A B

Geometric fluctuations included Geometric quantities constrained by multiplicity density.

~L R

L R

*cosn nn

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

arXiv:1203.3605

σx & σy RMS widths of density distribution


Scaling properties of high-pT anisotropy

WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University 5


Jet suppression Probe

AAAA

binary AA pp

YieldR ( , )N YieldTp L

2( , ) [1 2 ( )cos(2 )]T TYield p v p

2

AA 20

AA 2

(90 , ) 1 2 ( )( , )(0 , ) 1 2 ( )

oT T

TT T

R p v pR p LR p v p

Suppression (∆L) – pp yield unnecessary

Jet suppression drives azimuthal anisotropy at high pT with specific scaling properties on L,

Suppression (L)

, Phys.Lett.B519:199-206,2001

For Radiative Energy loss:

0

LcIT eI

Modified jet

Moresuppression

Lesssuppression

Fixed Geometry

Path length(related to collision

centrality)

Specific pT and centrality dependencies – Do they scale?


0 5 10

v 2

0.00

0.05

0.10

0.15

0.20

0.25

10 - 20%

Au+Au @ 0.2 TeV

pT (GeV/c)0 5 10

20 - 30%

0 5 100.00

0.05

0.10

0.15

0.20

0.2530 - 40%

High-pT v2 measurements - PHENIX

pT dependence

Centrality dependence

High-pT v2 measurements - CMS

Specific pT and centrality dependencies – Do they scale?

8

arXiv:1204.1850

pT dependence

Centralitydependence


9

High-pT v2 scaling - LHC

v2 follows the pT dependence observed for jet quenchingNote the expected inversion of the 1/√pT dependence

arXiv:1203.3605


2

AA 20

AA 2

(90 , ) 1 2 ( )( , )(0 , ) 1 2 ( )

oT T

TT T

R p v pR p LR p v p

pT-1/2 (GeV/c)-1/2

0.2 0.3 0.4 0.5

v 2

0.0

0.1

0.2

10 - 20 (%)20 - 3030 - 40

0.2 0.3 0.4 0.5

v 2/L

(fm-1

)

0.0

0.2

0.4

Au+Au @ 0.2 TeV

10

∆L Scaling of high-pT v2 – LHC & RHIC

Combined ∆L and 1/√pT scaling single universal curve for v2 Constraint for εn

arXiv:1203.3605


Npart

0 100 200 300

v 2/L

0.0

0.5

v 2

0.0

0.1

0.2 6 < pT < 9 (GeV/c)pT > 9

pT-1/2 (GeV/c)-1/2

0.2 0.4 0.6

v 2/L

0.0

0.2

0.4

10 - 20 (%)20 - 3030 - 40

Au+Au @ 0.2 TeV


∆L Scaling of high-pT v2 - RHIC

Combined ∆L and 1/√pT scaling single universal curve for v2

Constraint for εn

(pTJet)-1/2 (GeV/c)-1/2

0.05 0.10 0.15

v 2Jet

0.00

0.05

0.10

10-20 (%)20-30 30-40 40-50

Pb+Pb @ 2.76 TeV

12

Jet v2 scaling - LHC

v2 for reconstructed Jets follows the pT dependence for jet quenchingSimilar magnitude and trend for Jet and hadron v2 after scaling


pT-1/2 (GeV/c)-1/2

0.1 0.2 0.3

v 2

-0.05

0.00

0.05

0.10

0.15Jet - ATLASHadron - CMS

pT-1/2 (GeV/c)-1/2

0.1 0.2 0.3

v 2

-0.05

0.00

0.05

0.10

0.15Jet - ATLASHadrons - CMSHadrons - scaled (z ~ .62)

ATLAS

10-20%

13

Jet suppression from high-pT v2

Jet suppression obtained directly from pT dependence of v2 Compatible with the dominance of radiative energy loss

arXiv:1203.3605

2( , ) [1 2 ( )cos(2 )]T TN p v p

2

AA 20

AA 2

(90 , ) 1 2 ( )( , )(0 , ) 1 2 ( )

oT T

v TT T

R p v pR p LR p v p

Rv2 scales as 1/√pT , slopes encodes info on αs and q̂


RAA scales as 1/√pT ; slopes (SpT) encode info on αs and q L and 1/√pT scaling single universal curveCompatible with the dominance of radiative energy loss

14

arXiv:1202.5537

pT scaling of Jet Quenching

ˆ

, Phys.Lett.B519:199-206,2001


15

Extracted stopping power

2

ˆ ~ 0.75 RHICGeVq

fm

Phys.Rev.C80:051901,2009

2

ˆ ~ 0.56 LHCGeVq

fm

obtained from high-pT v2 and RAA [same αs] similar - medium produced in LHC collisions less opaque! (note density increase from RHIC to LHC)

arXiv:1202.5537 arXiv:1203.3605

Conclusion similar to those of Liao, Betz, Horowitz, Stronger coupling near Tc?

qRHIC > qLHCˆqLHC ˆ


L (fm)0.5 1.0 1.5 2.0

ln(R

AA)

-1.5

-1.0

-0.5

0.0D (prompt)6 - 12 GeV/c

Pb+Pb @ 2.76 TeV

ALICE

Consistent obtained


qLHC ˆ

Heavy quark suppression

Scaling properties of low pT anisotropy

WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University 17

The Flow Probe

s/

P ² Bj

, , /s, f, Ts fc

20

3

1 1

~ 5 45

TBj

dER dy

GeVfm

18

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 scaling properties

22, exp 03

tT t k k Ts T

Acoustic viscous modulation of vn

Staig & Shuryak arXiv:1008.3139

Isotropic p

Anisotropic p


Yield() =2 v2 cos[2(Y2]

Characteristic n2 viscous damping for harmonics

Crucial constraint for η/s

Associate k with harmonic n /k n R


2 gR n

εn drive momentum anisotropy vn with modulation

22, exp 03

tT t k k Ts T

Scaling expectation

2( )expn T

n

v pn

Acoustic Modulation

2

2 2

( ) exp ( 4)( )

n T n

T

v p nv p

t R ln n

n

vR

Characteristic centrality (1/R) viscous damping for a given harmonic

Crucial constraint for η/s

Particle Distribution

Note that vn is related to v2

Characteristic n2 viscous damping and 1/(pT)α dependence Crucial constraint for η/s and δf


2expn

n

vn

Is viscous hydrodynamic flow acoustic?

pT (GeV/c)0 1 2 3

(p T)

0.00

0.05

0.10

0.15

0.20

0.25

0.304s = 1.25(pT)-1/2

4s = 1.25 & f~pT1.5

20-30%Hydro - Schenke et al.

Note: the hydrodynamic response to the initial geometry [alone] is included

ATLAS-CONF-2011-074

21

High precision double differential Measurements are pervasiveDo they scale?


vn(ψn) Measurements - ATLAS


Acoustic Scaling

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

2( ) expn T

n

v p n


Acoustic Scaling

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


Acoustic Scaling

Straightforward constraint for eccentricity models /2

2n

n Tv p v


1/R (fm-1)0.0 0.5 1.0 1.5

ln(v

2/2)

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4 1.7 1.1 0.7

pT (GeV/c)ATLAS Pb+Pb @ 2.76 TeV

1/R (fm-1)0.0 0.5 1.0 1.5

ln(v

2/ 2)

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4 1.7 1.1 0.7

ATLAS p+Pb @ 5.02 TeV

pT (GeV/c)ATLAS Pb+Pb @ 2.76 TeV

Acoustic Scaling

ln n

n

vR

Characteristic 1/R viscous damping validated A further constraint for η/s

Centrality – 5-50%


1/R (fm-1)0.0 0.5 1.0 1.5

ln(v

2/ 2)

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4 1.79 1.19 0.79

pT (GeV/c)PHENIX Au+Au @ 0.2 TeV

1/R (fm-1)0.0 0.5 1.0 1.5

ln(v

2/ 2)

-2.0

-1.6

-1.2

-0.8

-0.4

0.0

0.4 1.79 1.19 0.79

ATLAS p+Pb @ 5.02 TeV

pT (GeV/c)PHENIX Au+Au @ 0.2 TeV

Acoustic Scaling

ln n

n

vR

Characteristic 1/R viscous damping validated A further constraint for η/s


Flow increases from RHIC to LHC Sensitivity to EOS increase in <cs>

Proton flow blueshifted [hydro prediction] Role of radial flowRole of hadronic re-

scattering?

Flow increases from RHIC to LHC

28

β Important constraint for η/s and δf


Constraint for η/s & δf

<η/s> ~ 1/4π at RHIC; 25-30% increase for LHC

3

1.2ˆLHC

Ts q

arXiv:1301.0165 3

~ 1.2ˆRHIC

Ts q

Phys.Rev. C80 (2009) 051901

Remarkable scaling have been observed for both Flow and Jet Quenching

They lend profound mechanistic insights, as well as New constraints forestimates of the transport and thermodynamic coefficients!

29

RAA and high-pT azimuthal anisotropy stem from the same energy loss mechanism

Energy loss is dominantly radiative

RAA and anisotropy measurements give consistent estimates for <ˆq >

RAA for D’s give consistent estimates for <ˆq >

The QGP created in LHC collisions is less opaque than that produced at RHIC

Flow is acousticFlow is pressure driven Obeys the dispersion relation

for sound propagation Flow is partonic

exhibits scalingConstraints for:

initial geometry small increase in η/s from

RHIC (~ 1/4π) to LHC

What we learn?

/2 n, 2, /2

vv ( ) ~ v or ( )

nn q T q n

q

KEn

Summary


End

30WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University

31

Flow Saturates for 39 - 200 GeV


No sizeable beam energy dependence observed for v2 and v3 for each particle

species

flow saturates for 39-200 GeV Soft EOS

32

Flow is partonic @ the LHC

Scaling for partonic flow validated after accounting for proton blueshift

Larger partonic flow at the LHC

KET (GeV)

0.5 1.0 1.5 0.5 1.0 1.5 0.5 1.0 1.5

10-20%

0.5 1.0 1.50.00

0.05

0.10

0.1520-30% 30-40% 40-50%

0.5 1.0 1.5

v 2/nq

0.00

0.05

0.10

0.15

Kp

Pb+Pb @ 2.76 TeV 05-10%



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

Is flow partonic?

/2 n2 /2

vExpectation: v ( ) ~ v or ( )

nn T n

q

KEn Note species dependence for all vn


Acoustic Scaling

Increase of s2 for most central collisions is to be expected

ln n

n

vR

35

Flow @ RHIC and the LHC


Multiplicity-weighted PIDed flow results reproduce inclusive charged hadron flow

results at RHIC and LHC respectively

Charge hadron flow similar @ RHIC & LHC

What do we learn from Azimuthal Anisotropy Measurements @ RHIC and the LHC Roy A. Lacey

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