Erice 2012, Roy A. Lacey, Stony Brook University
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Quantitative study of the QCD phase diagram is central to our field
Conjectured
Phase Diagram
Interest
 Location of the critical End point
 Location of phase coexistence lines
 Properties of each phase
p
All are fundamental to the phase
diagram of any substance
Spectacular achievement:
Validation of the crossover
transition leading to the QGP
Full characterization of the QGP is a central theme at RHIC and the LHC
Erice 2012, Roy A. Lacey, Stony Brook University
2
QGP Characterization?
Characterization of the QGP produced in RHIC and LHC
collisions requires:
I.
Development of experimental constraints to map the
topological, thermodynamic and transport coefficients
T ( ), cs (T ),  (T ),  (T ),  s (T ), qˆ (T ),  sep (B), etc ?
II. Development of quantitative model descriptions of
these properties
Experimental Access:
 Temp/time-averaged constraints as
a function of √sNN
(II)
(with similar expansion dynamics)
T , cs ,

,

, qˆ ,  s , etc ?
s
s
(I) Expect space-time averages
to evolve with √sNN
Erice 2012, Roy A. Lacey, Stony Brook University
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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%
Essential questions:
 How do the transport coefficients

cs ,
, qˆ ,  s evolve with T?
s
 Any indication for a change in
coupling close to To?
Take home message:
The scaling properties of flow and
Jet quenching measurements give
crucial new insights
Erice 2012, 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

  Bj  
 P  ² 
 




 s/ 

Actual collision profiles are not smooth,
due to fluctuations!
Acoustic viscous modulation of vn
 2 2 t 
 T  t , k   exp 
k
  T  0 
3 s T 
Yield() =2 v2 cos[2(2]
Crucial parameters  , cs ,  /s,  f, T f
Initial Geometry characterized by many
shape harmonics (εn)  drive vn

Yield ( )  a 1  2vn cos n    n  

Staig & Shuryak arXiv:1008.3139
Initial eccentricity (and its attendant fluctuations) εn drive
momentum anisotropy vn with specific scaling properties
Erice 2012, Roy A. Lacey, Stony Brook University
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Flow is partonic @ RHIC
vn PID scaling
KET &  nq  scaling validated for vn
 Partonic flow
n/ 2
Erice 2012, 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?
Erice 2012, 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
Erice 2012, Roy A. Lacey, Stony Brook University
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Hydrodynamic flow is acoustic
εn drive momentum anisotropy
vn with modulation
Modulation Acoustic
 2 2 t
 T  t , k   exp  
k
 3s T

  T  0 

2 R  ng
vn
Associate k with harmonic n
n
k
R
n
   exp    n 2 
Note: the hydrodynamic response to the
initial geometry [alone] is included
Characteristic n2 viscous damping for harmonics
 Crucial constraint for η/s
Erice 2012, Roy A. Lacey, Stony Brook University
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Constraint for η/s & δf
0.30
Hydro - Schenke et al.
20-30%
4
0.25
s = 1.25
(pT)-1/2
4
4
s = 0.0
s = 1.25 f~pT1.5
Deformation
n
k
R
 T  t , k   exp    n 2   T  0 
(pT)
0.20
0.15
0.10
Particle Dist. f  f 0   f ( pT )
pT2
 f ( pT ) ~
Tf
Characteristic pT dependence of β
 reflects the influence of δf and η/s
0.05
0.00
0
1
2
pT (GeV/c)
3
Erice 2012, 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?
Erice 2012, Roy A. Lacey, Stony Brook University
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arXiv:1105.3782
Acoustic Constraint
 2 2 t
k
3
s
T

 T  t , k   exp  

  T  0 

2 R  ng
Wave number
k
RHIC
n
R
Characteristic viscous damping
of the harmonics validated
Important constraint
LHC
vn
n

s
~
   exp    n 2 
1
at RHIC; small increase for LHC
4
Erice 2012, Roy A. Lacey, Stony Brook University
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Acoustic Scaling
vn
n
   exp    n 2 
Pb+Pb - 2.76 TeV
1
10-20%
0.25
pT = 1.1 GeV/c
20-30%
30-40%
40-50%
1
Pb+Pb - 2.76 TeV
n
n
pT = 1.1 GeV/c
vn/
vn/
0.20
0.1
0.1
0.15
0.10
0.01
0.01
0.05
2
4
6
2
4
6
2
4
6
2
4
6
n
0.00
15
30
45
Centrality (%)
β is essentially independent of centrality for a broad centrality range
Erice 2012, Roy A. Lacey, Stony Brook University
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vn
Constraint for η/s & δf
n
   exp    n 2 
Pb+Pb - 2.76 TeV
0.7 GeV/c
1.3 GeV/c
1.9 GeV/c
2.3 GeV/c
20-30%
1
vn/
vn/
n
n
1
0.1
0.1
0.01
0.01
2
4
6
2
4
6
2
4
6
2
4
6
n
β scales as 1/√pT  Important constraint
 <η/s> ~ 1/4π at RHIC; small increase for LHC
Erice 2012, Roy A. Lacey, Stony Brook University
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Scaling properties of Jet Quenching
Erice 2012, 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 RAA & azimuthal anisotropy with
specific scaling properties
Erice 2012, Roy A. Lacey, Stony Brook University
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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.
Erice 2012, Roy A. Lacey, Stony Brook University
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RAA Measurements - CMS
Eur. Phys. J. C (2012) 72:1945
arXiv:1202.2554
Centrality
dependence
pT dependence
Specific pT and centrality dependencies – Do they scale?
Erice 2012, Roy A. Lacey, Stony Brook University
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L scaling of Jet Quenching - LHC
, Phys.Lett.B519:199-206,2001
arXiv:1202.5537
ˆ
RAA scales with L, slopes (SL) encodes info on αs and q
Compatible with the dominance of radiative energy loss
Erice 2012, Roy A. Lacey, Stony Brook University
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L scaling of Jet Quenching - RHIC
Phys.Rev.C80:051901,2009
RAA scales with L, slopes (SL) encodes info on αs and q
ˆ
Compatible with the dominance of radiative energy loss
Erice 2012, 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
Erice 2012, 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?
Erice 2012, 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?
Erice 2012, Roy A. Lacey, Stony Brook University
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High-pT v2 scaling - LHC
arXiv:1203.3605
v2 follows the pT dependence observed for jet quenching
Note the expected inversion of the 1/√pT dependence
Erice 2012, 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
Erice 2012, 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
Erice 2012, 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
0.15
v2Jet
Jet - ATLAS
Hadrons
CMS
Hadron - -CMS
Hadrons - scaled (z ~ .62)
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
Erice 2012, 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
Rv2 scales as 1/√pT , slopes encodes info on αs and q̂
Erice 2012, Roy A. Lacey, Stony Brook University
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RAA (90o , pT ) 1  2v2 ( pT )
Rv2 ( pT , L) 

RAA (00 , pT ) 1  2v2 ( pT )
Au+Au @ 0.2 TeV
10 - 20%
ln(R2)
0.2
30 - 40%
20 - 30%
10 - 20 (%)
20 - 30
30 - 40
0.5
0.0
0.0
-0.2
-0.5
-0.4
-1.0
-0.6
-1.5
-0.8
ln(R2)/ L [fm-1]
Jet suppression from high-pT v2 - RHIC
-2.0
-1.0
0.2
0.4
0.2
0.4
-1/2
-1/2
pT (GeV/c)
0.2
0.4
0.2
0.4
-1/2
pT (GeV/c)-1/2
Jet suppression obtained directly from pT dependence of v2
R2 scales as 1/√pT , slopes encodes info on αs and ˆq
Erice 2012, 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
Erice 2012, Roy A. Lacey, Stony Brook University
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Extracted stopping power
arXiv:1202.5537
qˆLHC
arXiv:1203.3605
GeV 2
~ 0.56
fm
Phys.Rev.C80:051901,2009
qˆRHIC
GeV 2
~ 0.75
fm
ˆ LHC obtained from high-pT v and R [same α ]  similar
q
2
AA
s
ˆ
q
>
q
 RHIC
LHC - medium produced in LHC collisions less opaque!
Conclusion similar to those of Liao, Betz, Horowitz,
 Stronger coupling near Tc?
Erice 2012, 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 do 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
 η/s similar at LHC and RHIC
RHIC
~ 1/4π
Erice 2012, Roy A. Lacey, Stony Brook University
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End
Erice 2012, 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
Erice 2012, 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
Erice 2012, Roy A. Lacey, Stony Brook University
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