Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
1
A central Issue
How to fully characterize of the QGP produced
in RHIC & LHC collisions?
Characterization requires
 Development of experimental constraints
for thermodynamic and transport coefficients
T, cs,
 
s
,
s
,qˆ , etc ?
 Development of quantitative model descriptions of
these properties
Essential question:
Do azimuthal anisotropy (vn) measurements provide constraints
to nail down initial-state geometry & the transport properties of the QGP?
Focus  The role of scaling in
answering this question!
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
2
A scenario for Azimuthal Anisotropy
4< pT <10 GeV/c
Transition
Region
123
Pressure driven
(acoustic )
Path length (∆L)
driven
Both are linked by
Geometry & interactions in the sQGP
This scenario implies very specific scaling properties which must
be validated experimentally
Scaling validation  Flow and Jet Quenching provide
straightforward probes of the QGP
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
3
The Flow Probe
Idealized Geometry
 Bj 
1 1 dET
 R 2  0 dy
GeV
~ 5  15
fm3

y 2  x2
y 2  x2
Control parameters  , cs ,

  Bj  
 P  ² 
 




 s/ 

Acoustic viscous damping

  T  0 

,
s s
,T
Initial Geometry characterized
by many harmonics
Actual collision profiles are not smooth,
due to fluctuations!
 2 2 t
 T  t , k   exp 
k
3
s
T

 
r cos  n part   r sin  n part 
n
n 
2
r
n
n 2
Initial eccentricity (and its attendant fluctuations) εn drive
momentum anisotropy vn with specific scaling properties
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
4
2
Jet quenching
Probe
R AA 
Yield AA
 Nbinary  AA Yield pp
Radiative:
dE
~  L kT2
dx
Control parameters
 s , pT , L, qˆ
Color charge
scattering centers
Range of Color
Force
qˆ ~  kT2
Scattering Power
Of Medium
Obtain
2
~

 and qˆ
via RAA
measurements
Suppression for ∆L
N ( , pT )  [1  2v2 ( pT ) cos(2 )]
RAA (90o , pT ) 1  2v2 ( pT )
Rv2 ( pT , L) 

RAA (00 , pT ) 1  2v2 ( pT )
Density of
Scattering centers
Gyulassy, Wang, Müller, …
Jet quenching drives RAA & azimuthal
anisotropy with specific scaling properties
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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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.
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
6
Scaling properties of Jet Quenching
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
7
RAA Measurements - LHC
Eur. Phys. J. C (2012) 72:1945
arXiv:1202.2554
Centrality
dependence
pT dependence
Specific pT and centrality dependencies – Do they scale?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
8
Scaling of Jet Quenching
arXiv:1202.5537
RAA scales with L, slopes (SL) encodes info on  s and qˆ
Compatible with the dominance of radiative energy loss
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
9
Scaling of Jet Quenching
arXiv:1202.5537
RAA scales as 1/√pT , slopes (SpT) encodes info on  s and qˆ
 L and 1/√pT scaling  single universal curve
Compatible with the dominance of radiative energy loss
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
10
High-pT v2 measurements
arXiv:1204.1850
pT dependence
Centrality
dependence
Specific pT and centrality dependencies – Do they scale?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
11
Scaling of high-pT v2
arXiv:1203.3605
v2 follows the pT dependence observed for jet quenching
Note the expected inversion of the 1/√pT dependence
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
12
Scaling of high-pT v2
arXiv:1203.3605
Combined ∆L and 1/√pT scaling  single universal curve for v2
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
13
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 v2
Rv2 scales as 1/√pT , slopes encodes info on  s and qˆ
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
14
Scaling of Jet Quenching
arXiv:1202.5537
qˆLHC
arXiv:1203.3605
GeV 2
~ 0.56
fm
Phys.Rev.C80:051901,2009
qˆRHIC
GeV 2
~ 0.75
fm
 q̂ LHC obtained from high-pT v2 and RAA [same αs]  similar
 qˆ RHIC  qˆ LHC - medium produced in LHC collisions less opaque!
Conclusion similar to those of Liao, Betz, Horowitz,
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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Scaling patterns of low-pT azimuthal anisotropy
Essential argument:
 Flow is dominantly partonic
Flow is pressure driven (acoustic)
 viscous damping follows dispersion relation
for sound propagation
 These lead to characteristic scaling patterns which must
be experimentally validated
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
16
Is hydrodynamic flow acoustic?
εn drive momentum anisotropy vn with modulation
Not analogous
CBM
Modulation
 Acoustic
 2 2 t
k
3 s T
 T  t , k   exp 
2 R  ng
Deformation
vn
n
n
k
R
   exp    n 2 

  T  0 

vn
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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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
0.20
(pT)
Deformation
n
k
R
 T  t , k   exp   n 2   T  0 
Particle Dist. f  f 0   f ( pT )
pT2
 f ( pT ) ~
Tf
0.15
0.10
0.05
Characteristic pT dependence of β expected,
 reflects the influence of δf
0.00
0
1
2
pT (GeV/c)
3
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
18
Is flow partonic?
AMPT – Simulations with fluctuating initial conditions
Deformation
vn,q ( pT ) ~ v
n /2
2, q
n
k
R
vn
or
(nq )n /2
Characteristic scaling patterns are to be expected
for the ratios of vn
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
19
Is flow partonic?
Deformation
vn,q ( pT ) ~ v
n /2
2, q
AMPT – Simulations with (w) and without (wo)
fluctuating initial conditions
n
k
R
vn
or
(nq )n /2
Characteristic scaling patterns
are to be expected for identified
particle species vn
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
20
vn(ψn) Measurements
Phys.Rev.Lett. 107 (2011) 252301 (arXiv:1105.3928)
v4(ψ4) ~ 2v4(ψ2)
High precision double differential Measurements are pervasive
Do they scale?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
21
vn(ψn) Measurements
ATLAS-CONF-2011-074
High precision double differential Measurements are pervasive
Do they scale?
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
22
Flow is acoustic
 2 2 t
k
3
s
T

 T  t , k   exp 

  T  0 

2 R  ng
Deformation
k
RHIC
n
R
Characteristic viscous damping
of the harmonics validated
 Crucial constraint for η/s
LHC
vn
n
   exp    n 2 
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
23
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
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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Acoustic Scaling
vn
n
   exp    n 2 
Pb+Pb - 2.76 TeV
0.7 GeV/c
1.3 GeV/c
1.9 GeV/c
2.3 GeV/c0.25
Pb+Pb - 2.76 TeV
20-30%
1
1
20-30%
0.15
0.1
vn/
vn/
n
n
0.20
0.1
0.10
  2
   exp  
n 


n
p
T


vn
0.01
0.05
0.01
0.00
2
4
6
2
4
6
2
4
n
6
1
2
4
pT (GeV/c)
2
6
β scales as 1/√pT
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
25
Flow is partonic
Scaling for partonic flow validated for vn
Constraints for εn
Similar scaling observed at the LHC
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
26
Flow is partonic
v3 PID scaling
0.05
Au+Au
0.04
Flow is
partonic
K
p
n=3
0-60%
K
sNN  200 GeV
20-50%
0.04
p
0.03
0.02
0.02
0.01
0.01
STAR
0.00
0.0
KET &  nq  scaling
validated for v3
 Partonic flow
n /2
0.5
1.0
1.5
KET/nq (Gev)
v3/(nq)3/2
vn/(nq)n/2
0.03
Flow is
partonic
PHENIX
2.0
2.5
0.00
0
1
(KET/nq) (GeV)
2
Scaling for partonic flow validated for vn
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
27
Decoupling the Interplay between εn and η/s
http://arxiv.org/abs/1105.3928
v3 breaks the ambiguity between MC-KLN vs. MC-Glauber initial
conditions and η/s, because of the n2 dependence of viscous
corrections
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
28
η/s estimates – QM2009
Good Convergence
Conjectured
Lower bound
4πη/s ~ 1
Temperature dependence
Not fully mapped yet
Much work remains to be done
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
29
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 transport and thermodynamic coefficients!
What do we learn?
 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
 The QGP created in RHIC
collisions is less opaque than
that produced at the LHC
 Flow is acoustic
Flow is pressure driven
 Obeys the dispersion relation
for sound propagation
Flow is partonic
 exhibits v ( p ) ~ vn /2 or vn
n,q
T
2, q
(nq )n /2
scaling
Constraints for:
initial geometry
 η/s
 viscous horizon
 sound horizon
Roy A. Lacey, Stony Brook University; Ridge Workshop, INT, Seattle, May 7-11, 2012
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End
Roy A. Lacey, Stony Brook University; Ridge
Workshop, INT, Seattle, May 7-11, 2012
31