Essential Question
Do recent measurements at RHIC & the LHC, give new
insights for characterization of the QGP?
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
1
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 ( ), 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
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
2
The LHC energy density lever arm
Lacey et. al, Phys.Rev.Lett.98:092301,2007
M. Malek, CIPANP 2012
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 indications for sizeable
changes close to To?
Take home message:
The scaling properties of flow and
Jet quenching measurements give
crucial new insights
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
3
The Flow Probe
Idealized Geometry
 Bj 
1 1 dET
 R 2  0 dy
~ 5  15
GeV
fm3

v2  cos 2    2 
y 2  x2
y 2  x2

  Bj  
 P  ² 
 




 s/ 

Control parameters  , cs ,
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 
Staig & Shuryak arXiv:1008.3139
 
,
s s
,T
Initial Geometry characterized by many
shape harmonics (εn)  drive vn
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; ICFP 2012, 10-16 June, Crete, Greece
4
2
A few insights from the scaling patterns of flow
Flow
 is dominantly partonic,
 is sensitive to the harder EOS sampled in LHC collisions
 is acoustic
 viscous damping follows dispersion relation
for sound propagation  important constraint for <η/s>
and its Temp. dependence
 These reflect characteristic scaling patterns which are
experimentally validated
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
5
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
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
6
Flow is partonic @ RHIC
0.04
K
p
vn PID scaling
n=3
0-60%
vn/(nq)n/2
0.03
0.02
0.01
STAR
0.00
0.0
0.5
1.0
1.5
KET/nq (Gev)
2.0
2.5
KET &  nq  scaling validated for vn
 Partonic flow
n/ 2
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
7
Flow is partonic @ the LHC
0.15
Pb+Pb @ 2.76 TeV
0.15
10-20%
30-40%
20-30%
40-50%
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
KET (GeV)
Scaling for partonic flow validated after Proton flow blueshifted
[hydrodynamic prediction]
accounting for proton blueshift
 Sensitivity to harder EOS
Role of radial flow
Role of hadronic re-scattering?
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
8
Is hydrodynamic flow acoustic?
εn drive momentum anisotropy vn with modulation
Initial Geometry
characterized by many
shape harmonics (εn)
 drive vn
Modulation
 Acoustic
 2 2 t
k
3 s T
 T  t , k   exp 
2 R  ng
n
k
R
vn
n
   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; ICFP 2012, 10-16 June, Crete, Greece
9
vn(ψn) Measurements - ATLAS
ATLAS-CONF-2011-074
High precision double differential Measurements are pervasive
Do they scale?
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
10
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
Constraint for β  η/s estimates
at RHIC & LHC
LHC
vn
n
   exp    n 2 

1
~
s 4
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
11
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; ICFP 2012, 10-16 June, Crete, Greece
12
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
single universal curve for vn
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
13
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 
0.15
0.10
Particle Dist. f  f 0   f ( pT )
pT2
 f ( pT ) ~
Tf
0.05
Characteristic pT dependence of β
 Additional constraint for δf and η/s
0.00
0
 <η/s> comparable at LHC and RHIC
1
2
pT (GeV/c)
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
3
14
Scaling properties of Jet Quenching
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
15
Jet quenching
Probe
R AA 
Radiative:
dE
~  L kT2
dx
Yield AA
 Nbinary  AA Yield pp
Radiativ E-loss
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 & high-pT azimuthal
anisotropy with specific scaling properties
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
16
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; ICFP 2012, 10-16 June, Crete, Greece
17
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?
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
18
Scaling of Jet Quenching
, 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
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
19
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
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
20
High-pT v2 measurements - CMS
arXiv:1204.1850
pT dependence
Centrality
dependence
Specific pT and centrality dependencies – Do they scale?
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
21
Scaling of high-pT v2
arXiv:1203.3605
RAA vs. pT
v2 follows the pT dependence observed for jet quenching
Note the expected inversion of the 1/√pT dependence
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
22
∆L 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; ICFP 2012, 10-16 June, Crete, Greece
23
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 αs and q̂
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
24
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?
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
25
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?
 Flow is acoustic
 RAA and high-pT azimuthal
Flow is pressure driven
anisotropy stem from the same
 Obeys the dispersion relation
energy loss mechanism
for sound propagation
 Energy loss is dominantly radiative
 RAA and anisotropy measurements Flow is partonic
 exhibits v ( KE ) ~ vn/2 or vn
give consistent estimates for <ˆqLHC >
n,q
T
2, q
2
(nq )n /2
scaling
~ 0.6 GeV /fm
Constraints for:
 The QGP created in RHIC
initial geometry
collisions is less opaque than that
produced at the LHC
 <η/s> comparable at LHC
and RHIC ~ 1/4π
 actual temp dependence
coming soon
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
26
End
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
27
Transport coefficient estimates – 2009
Lacey et. al,
Phys.Rev.Lett.98:092301,2007
1) T  r , 
2) 
3
4
 r , 
3) s  r , 
PHENIX
Lacey
ASW-1
ASW-2
GLV
AMY-1
HT-1 HT-2 HT-3
0
2
4
6
8 10 12 14 16 18 20
qˆ (GeV /fm)
Unsettled Issues
Detailed mechanistic understanding?
Quantitative values (including T/t dependence)?
 Evidence for change in coupling strength close to Tc?
 ε, αs, δf, etc. !!Much work to be done!!
2
Roy A. Lacey, Stony Brook University; ICFP 2012, 10-16 June, Crete, Greece
28
vn(ψn) Measurements - PHENIX
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; ICFP 2012, 10-16 June, Crete, Greece
29
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; ICFP 2012, 10-16 June, Crete, Greece
30
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; ICFP 2012, 10-16 June, Crete, Greece
31