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?
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Why RHIC and LHC Measurements?
The energy density lever arm
Lacey et. al, Phys.Rev.Lett.98:092301,2007
Energy scan
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%
Relevant questions:
 How do the transport coefficients
cs ,

s
, qˆ ,  s
evolve with T?
 Any indication for a change in
coupling close to To?
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
2
Why Azimuthal Anisotropy Measurements?
3-4 < pT < 8-10 GeV/c
Transition
Region
More
suppression
Less
suppression
Eccentricity driven
& acoustic
Path length (∆L) driven
Flow and Jet suppression are linked to
Geometry & the interactions in the QGP
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

WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
3
Geometric Quantities for scaling
Phys. Rev. C 81, 061901(R) (2010)
B
A
 n  cos n   n* 
LR
L ~  R
arXiv:1203.3605
σx & σy  RMS widths of density distribution
 Geometric fluctuations included
 Geometric quantities constrained by multiplicity density.
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Scaling properties of high-pT anisotropy
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Fixed Geometry
Jet suppression
Probe
Less
suppression
Modified jet
T
Suppression (L)
R AA ( pT , L) 
More
suppression
Yield AA
 Nbinary  AA Yield pp
I
 e  Lc
I0
Yield ( , pT )  [1  2v2 ( pT ) cos(2 )]
Suppression (∆L) – pp yield unnecessary
RAA (90o , pT ) 1  2v2 ( pT )
R2 ( pT , L) 

0
RAA (0 , pT ) 1  2v2 ( pT )
For Radiative Energy loss:
Path length
(related to collision
centrality)
, Phys.Lett.B519:199-206,2001
Jet suppression drives azimuthal anisotropy at high pT with
specific scaling properties on L, ∆𝑳 𝒂𝒏𝒅 𝒑𝑻
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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High-pT v2 measurements - PHENIX
Au+Au @ 0.2 TeV

0.25
10 - 20%
30 - 40%
20 - 30%
0.25
0.20
v2
0.20
0.15
0.15
0.10
0.10
0.05
0.05
0.00
0.00
0
5
10
0
5
10
0
5
10
pT (GeV/c)
Specific pT and centrality dependencies – Do they scale?
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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High-pT v2 measurements - CMS
arXiv:1204.1850
pT dependence
Centrality
dependence
Specific pT and centrality dependencies – Do they scale?
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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High-pT v2 scaling - LHC
RAA (90o , pT ) 1  2v2 ( pT )
R2 ( pT , L) 

0
RAA (0 , pT ) 1  2v2 ( pT )
arXiv:1203.3605
v2 follows the pT dependence observed for jet quenching
Note the expected inversion of the 1/√pT dependence
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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∆L Scaling of high-pT v2 – LHC & RHIC
arXiv:1203.3605
Au+Au @ 0.2 TeV
0.1
0.2
0.0
0.0
v2/ L (fm-1)
0.4
v2
0.2
10 - 20 (%)
20 - 30
30 - 40
0.2 0.3 0.4 0.5
0.2 0.3 0.4 0.5
-1/2
pT (GeV/c)-1/2
Combined ∆L and 1/√pT scaling  single universal curve for v2
 Constraint for εn
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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∆L Scaling of high-pT v2 - RHIC
Au+Au @ 0.2 TeV
0.2
10 - 20 (%)
20 - 30
30 - 40
6 < pT < 9 (GeV/c)
0.1
0.4
v2/ L
v2
pT > 9
0.0
v2/ L
0.2
0.5
0.0
0.0
0
100
200
Npart
300
0.2
0.4
0.6
pT-1/2 (GeV/c)-1/2
Combined ∆L and 1/√pT scaling  single universal curve for v2
 Constraint for εn
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Jet v2 scaling - LHC
Pb+Pb @ 2.76 TeV
ATLAS
10-20 (%)
20-30
30-40
40-50
0.10
10-20%
v2Jet
Jet - ATLAS
Hadrons
CMS
Hadron - -CMS
Hadrons - scaled (z ~ .62)
0.15
0.10
0.05
v2
0.05
0.00
0.00
-0.05
0.1
0.2
0.3
pT-1/2 (GeV/c)-1/2
0.05
0.10
0.15
(pTJet)-1/2 (GeV/c)-1/2
v2 for reconstructed Jets follows the pT dependence for jet quenching
Similar magnitude and trend for Jet and hadron v2 after scaling
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Jet suppression from high-pT v2
N ( , pT )  [1  2v2 ( pT ) cos(2 )]
RAA (90o , pT ) 1  2v2 ( pT )
Rv2 ( pT , L) 

RAA (00 , pT ) 1  2v2 ( pT )
arXiv:1203.3605
Jet suppression obtained directly from pT dependence of v2
 Compatible with the dominance of radiative energy loss
Rv2 scales as 1/√pT , slopes encodes info on αs and q̂
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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pT scaling of Jet Quenching
, Phys.Lett.B519:199-206,2001
arXiv:1202.5537
ˆ
RAA scales as 1/√pT ; slopes (SpT) encode info on αs and q
 L and 1/√pT scaling  single universal curve
Compatible with the dominance of radiative energy loss
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Extracted stopping power
Phys.Rev.C80:051901,2009
arXiv:1202.5537
qˆLHC
arXiv:1203.3605
GeV 2
~ 0.56
fm
qˆRHIC
GeV 2
~ 0.75
fm
ˆ LHC obtained from high-pT v and R [same α ]  similar
q
2
AA
s
ˆ RHIC > qLHC - medium produced in LHC collisions less opaque!
q
(note density increase from RHIC to LHC)
Conclusion similar to those of Liao, Betz, Horowitz,
 Stronger coupling near Tc?
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Heavy quark suppression
Pb+Pb @ 2.76 TeV
0.0
ALICE
D (prompt)
6 - 12 GeV/c
ln(RAA)
-0.5
-1.0
-1.5
0.5
1.0
1.5
L (fm)
Consistent
ˆ LHC
q
2.0
obtained
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Scaling properties of low pT anisotropy
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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The Flow Probe
Anisotropic p
Idealized Geometry
 Bj 
1 1 dET
 R 2  0 dy
~ 5  45
GeV
fm3

Isotropic p
y 2  x2
y 2  x2
Yield() =2 v2 cos[2(Y2]

  Bj  
 P  ² 
 




 s/ 

Crucial parameters  , cs ,  /s,  f, T f
Actual collision profiles are not smooth,
due to fluctuations!
Initial Geometry characterized by many
shape harmonics (εn)  drive vn
Acoustic viscous modulation of vn
 2 2 t 
 T  t , k   exp 
k
  T  0 
3 s T 
Staig & Shuryak arXiv:1008.3139
Initial eccentricity (and its attendant fluctuations) εn drive
momentum anisotropy vn with specific scaling properties
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Acoustic Modulation
εn drive momentum anisotropy
vn with modulation
 2 2 t
k
 3s T
 T  t , k   exp  
2 R  ng

  T  0 

Associate k with harmonic n
k n/R
Particle Distribution
Scaling expectation
vn ( pT )
n
   exp    n 2 
vn ( pT )  n
  exp    (n 2  4) 
v2 ( pT )  2
Note that vn is related to v2
tR
 vn    
ln   
R
 n 
Characteristic n2 viscous
damping for harmonics
 Crucial constraint for η/s
Characteristic centrality (1/R) viscous
damping for a given harmonic 
Crucial constraint for η/s
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Is viscous hydrodynamic flow acoustic?
Hydro - Schenke et al.
20-30%
0.30
4
s = 1.25
(pT)-1/2
4
0.25
s = 1.25 & f~pT1.5
(pT)
0.20
0.15
0.10
vn
n
0.05
   exp    n 2 
Note: the hydrodynamic response to the
initial geometry [alone] is included
0.00
0
1
2
pT (GeV/c)
3
Characteristic n2 viscous damping and 1/(pT)α
dependence  Crucial constraint for η/s and δf
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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vn(ψn) Measurements - ATLAS
ATLAS-CONF-2011-074
High precision double differential Measurements are pervasive
Do they scale?
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Acoustic Scaling
vn ( pT )
n
   exp    n 2 
 Characteristic n2 viscous damping validated
 Characteristic 1/(pT)α dependence of β validated
Constraint for η/s
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Acoustic Scaling
 Characteristic n2 viscous damping validated
 Characteristic 1/(pT)α dependence of β validated
Constraint for η/s
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Acoustic Scaling
vn  pT    v2 
Straightforward constraint for eccentricity models
n /2
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Acoustic Scaling
 v    
ln  n  
R
 n 
0.4
ATLAS Pb+Pb @ 2.76 TeV
pT (GeV/c)
1.7
1.1
0.7
0.4
0.0
ln(v2/ 2)
0.0
ln(v2/ 2)
ATLAS Pb+Pb @ 2.76 TeV
pT (GeV/c)
1.7
1.1
0.7
ATLAS p+Pb @ 5.02 TeV
-0.4
-0.8
-0.4
-0.8
Centrality – 5-50%
-1.2
-1.2
-1.6
-1.6
-2.0
0.0
-2.0
0.0
0.5
1.0
1/R (fm-1)
1.5
0.5
1.0
1/R (fm-1)
1.5
 Characteristic 1/R viscous damping validated

A further constraint for η/s
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Acoustic Scaling
 v    
ln  n  
R
 n 
0.4
PHENIX Au+Au @ 0.2 TeV
pT (GeV/c)
1.79
1.19
0.79
0.4
0.0
ln(v2/ 2)
ln(v2/ 2)
0.0
PHENIX Au+Au @ 0.2 TeV
pT (GeV/c)
1.79
1.19
0.79
ATLAS p+Pb @ 5.02 TeV
-0.4
-0.8
-0.4
-0.8
-1.2
-1.2
-1.6
-1.6
-2.0
0.0
-2.0
0.0
0.5
1.0
-1
1/R (fm )
1.5
0.5
1.0
-1
1/R (fm )
1.5
 Characteristic 1/R viscous damping validated

A further constraint for η/s
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Flow increases from RHIC to LHC
Flow increases from RHIC
to LHC
 Sensitivity to EOS
 increase in <cs>
 Proton flow blueshifted
[hydro prediction]
 Role of radial flow
Role of hadronic rescattering?
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Constraint for η/s & δf
arXiv:1301.0165

T3
~ 1.2
s
qˆ RHIC
Phys.Rev. C80 (2009) 051901

T3
 1.2
s
qˆ LHC
β  Important constraint for η/s and δf
<η/s> ~ 1/4π at RHIC; 25-30% increase for LHC
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Summary
Remarkable scaling have been observed for both Flow and
Jet Quenching
They lend profound mechanistic insights, as well as New constraints for
estimates of the transport and thermodynamic coefficients!
What we learn?
 RAA and high-pT azimuthal
 Flow is acoustic
anisotropy stem from the same
Flow is pressure driven
energy loss mechanism
 Obeys the dispersion relation
 Energy loss is dominantly radiative
for sound propagation
 RAA and anisotropy measurements Flow is partonic
give consistent estimates for <ˆq >
 exhibits vn,q ( KET ) ~ v2,n/2q or vnn/2
(nq )
 RAA for D’s give consistent
scaling
estimates for <ˆq >
Constraints for:
initial geometry
 The QGP created in LHC collisions
is less opaque than that produced at
 small increase in η/s from
RHIC
RHIC (~ 1/4π) to LHC
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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End
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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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
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Flow is partonic @ the LHC
0.15 Pb+Pb @ 2.76 TeV
05-10%
10-20%
20-30%
40-50%
30-40%
0.15
K
p
0.10
v2/nq
0.10
0.05
0.05
0.00
0.00
0.5 1.0 1.5
0.5 1.0 1.5
0.5 1.0 1.5
0.5 1.0 1.5
0.5 1.0 1.5
KET (GeV)
Scaling for partonic flow validated after
accounting for proton blueshift
 Larger partonic flow at the LHC
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Is flow partonic?
Expectation: vn ( KET ) ~ v n2 /2 or
vn
(nq )n /2
Note species dependence for all vn
For partonic flow, quark number scaling expected
 single curve for identified particle species vn
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Acoustic Scaling
 v    
ln  n  
R
 n 
 Increase of s2 for most central collisions is to be expected
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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Flow @ RHIC and the LHC
 Charge hadron flow similar
@ RHIC & LHC
 Multiplicity-weighted PIDed flow results
reproduce inclusive charged hadron flow
results at RHIC and LHC respectively
WWND13 @ Squaw Valley, Feb. 2013, Roy A. Lacey, Stony Brook University
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