qˆ,
η ζ
,
s s
, cs , Tf ,
Quantitative study of the QGP is a central goal of our field
“The major discoveries in
the first five years at RHIC
must be followed by a
broad, quantitative study of
the fundamental properties
of the quark gluon plasma …”
The Frontiers of Nuclear Science
A Long Range Plan - 2007
Characterization requires
T, cs, qˆ ,η , ζ
etc ?
Roy A. Lacey, Stony Brook University, 2010
2
Probes for estimating transport coefficients
Jet Quenching
Flow
ε Bj =
1 1 dET
π R2 τ0 dy
~ 5 −15
GeV
fm3
η
y
s
dE
~ σρ L kT2
dx
Color charge
scattering centers
~ λTcs ≡ ( KR )Tcs
K=
x
Radiative:
⎛
⎛ ∂ε Bj ⎞ ⎞
⎜ P = ρ² ⋅⎜
⎟ ⎟⎟
∂
ρ
⎜
⎝
⎠ s/ρ ⎠
⎝
ε=
λ
R
y2 − x2
y +x
2
Range of Color
Force
2
Primary Control Parameters
Obtain
ρ and q
η
via RAA
measurements
T3
~ 1.25
s
qˆ
Scattering Power
Of Medium
Density of
Scattering centers
Flow and jet suppression measurements are important
probes for transport coefficients
Roy A. Lacey, Stony Brook University, 2010
3
How are transport coefficients obtained
from data?
Issues
Data precision
• Role of non-flow
• Role of fluctuations
• Initial conditions (ε2,4) ?
• Tf and δf ?
• Temp dependence of η & ζ.
9 EOS
• Interdependency of
transport coefficients (η & ζ)
• Hadronic vs. plasma
viscosity
• Valid pT range of hydro
9
Comparisons to
model calculations
(eg. viscous hydro,
jet quenching, etc)
Model inspired
Fits to Data
Critical path issues are common to all methodologies
Challenge Æ find invaluable experimental
constraints which can help resolve these issues
Roy A. Lacey, Stony Brook University, 2010
4
Data
Issues:
¾different experimental measurements (diff. experiments)
¾results from different methods
¾ precision of each measurement ?
¾ which data set to use ?
Comprehensive measurements/comparisons lend good insights!
Roy A. Lacey, Stony Brook University, 2010
5
TPC
FTPC
ZDC/SMD
FTPC
ZDC/SMD
η
STAR
ZDC/SMD
BBC/MPC
|η| < 1.3
2.5 <|η|< 4.0
|η| > 6.3
Central Arms
BBC/MPC
ZDC/SMD
η
RXN
RXN
1.0<|η|<2.8
PHENIX
|η|<0.35
3.1<|η|<3.7
3.1<|η|<3.9
Measurements allow
detailed comparisons
PHOBOS
|η| > 6.6
EP
EP
η = 0-1.6
η
2.05<|η|<3.2
Roy A. Lacey, Stony Brook University, 2010
6
Extensive anisotropy Data
arXiv:1003.5586
i = RXN io , l = MPC N , m = BBCS
High precision double differential measurements
Roy A. Lacey, Stony Brook University, 2010
7
Central Arms
Data Precision
RXN
arXiv:1003.5586
BBC/MPC
New RXN
detector
RXN
BBC/MPC
3.1 < η BBC < 3.9
3.1 < η MPC < 3.9
1.5 < η RXNi < 2.8
1.0 < η RXNo < 1.5
1.0 < η RXNio < 2.8
Event planes
¾No evidence for significant η-dependent non-flow contributions
Results from different methods should Not be used as a
measure of systematic error!
Roy A. Lacey, Stony Brook University, 2010
8
Consistency of higher harmonics
Central Arms
RXN
RXN
BBC/MPC
BBC/MPC
PHENIX Preliminary
PHENIX Preliminary
Consistent results for v4 / v2 2 ratio using
measurements with respect to the different event planes
Note increase
Roy A. Lacey, Stony Brook University, 2010
9
EP: 1.0<|η|<2.8
from PHOBOS QM06 proc. J. Phys. G34 S887 (2007)
EP{1}
EP{2}
η
EP: 3.1<|η|<3.7
PHOBOS EP: 2.05<|η|<3.2
Overall good agreement between differential flow measurements
Roy A. Lacey, Stony Brook University, 2010
10
V2{EP} – standard EP method
EP-Star
V2{EP2} – modified EP method
EP-Star
Roy A. Lacey, Stony Brook University, 2010
11
Agreement between RHIC
measurements!
EP
9There is good agreement between experiments
9 Consideration of fluctuations important when
comparing different methods
The results from different methods should Not be
used as a measure of systematic error!
Roy A. Lacey, Stony Brook University, 2010
12
Remarkable scaling (& scaling violations)
has been observed for flow
They lend profound insights, as well as constraints for
straightforward estimates of transport coefficients!
Roy A. Lacey, Stony Brook University, 2010
13
Universal scaling of harmonic flow at RHIC
v2 scaling
Baryon
s
Meson
s
Phys. Rev. Lett. 98,
162301 (2007)
v4 scaling
Universal scaling
KET & nq (nq2) scaling
validated for v2 (v4)
Æ Partonic flow
Roy A. Lacey, Stony Brook University, 2010
14
Flow scales across centrality
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
PHENIX Preliminary
KET & nq (nq2) scaling validated for v2 as
a function of centrality
Roy A. Lacey, Stony Brook University, 2010
15
Scaling constrains η/s
Demir et al
η/s from hadronic phase
is very large 10-12x(1/4π)
No room for such values!
Partonic flow dominates!
Hadronic contribution cannot be large
Roy A. Lacey, Stony Brook University, 2010
16
Charm flows and scales
PHENIX Final Run4
PHENIX Preliminary Run7
van Hees et al.
Minimum bias
Au+Au at sNN = 200 GeV
J/ψ v2 still challenged by statistics
9 Strong coupling
9 η/s - estimate
Roy A. Lacey, Stony Brook University, 2010
17
v4/(v2)2 ratio same for different particle
species
V4 = k(v2)2 where k is the same for different particle species
Roy A. Lacey, Stony Brook University, 2010
18
Universal Scaling of flow via
Quarks
v 4,M ( 2KE T )
v 22,M ( 2KE T )
v 4,B ( 2KE T )
v 22,B ( 2KE T )
⎛ 1 1 v 4,q ( 2KE T ) ⎞
≈α ⎜ + × 2
⎜ 4 2 v ( 2KE ) ⎟⎟
2,q
T ⎠
⎝
⎛ 1 1 v 4,q ( 2KE T ) ⎞
≈α ⎜ + × 2
⎜ 3 3 v ( 2KE ) ⎟⎟
2,q
T ⎠
⎝
2
v 2,M ( 2KET ) ≈ v 2,B ( 3KET )
3
⎛ v 4,q ( 2KE T ) ⎞ 1
⎜⎜ 2
⎟⎟ ~
⎝ v 2,q ( 2KE T ) ⎠ 2
Encodes viscosity information
4πη/s ~ 1- 2
Roy A. Lacey, Stony Brook University, 2010
19
V4/(v2)2
Ideal hydro
Estimate Æ 4π(η/s) ~ 1- 2
Roy A. Lacey, Stony Brook University, 2010
20
Scaling constrains η/s
Chaudhuri
Teaney
Viscosity required
for KET scaling Æ Lower Limit ?
Roy A. Lacey, Stony Brook University, 2010
21
New constraint for η/s
Use viscous corrections as a lever
Dusling & Teaney
arXiv:0909.0754
Song & Heinz
arXiv:0712.3715
B ⎛ pT
*
K ( pT ) = K + ⎜
T f ⎜⎝ T f
⎞
⎟⎟
⎠
2 −α
Use viscous corrections dominate for pT > 1 GeV/c
Roy A. Lacey, Stony Brook University, 2010
22
Further constraints for η/s
Geometry
(from model)
Hydro calculations
η
s
Constrained
by data
~ λTcs ≡ ( KR ) T cs
Obtain from fits to data
(viscous correction)
Lattice EOS
Viscous correction influence v2/ε
Strategy Æ quantify viscous Corrections via a
fitting procedure, to obtain K as a function of Npart
k
⎡
⎤
−1
⎥
⎡
⎤
v2 k ( pT ) v2 k ( pT ) ⎢⎢
1
1
dN
⎥ , ⎡ K * ( pT ) ⎤ = ⎢ β ( pT )
=
*
⎣
⎦
S dy ⎥⎦
ε 2k
ε 2 k ⎢ K ( pT ) ⎥
⎣
⎢1 + K
⎥
0
⎣
⎦
B ⎛ pT
*
K ( pT ) = K + ⎜
T f ⎜⎝ T f
Roy A. Lacey, Stony Brook University, 2010
⎞
⎟⎟
⎠
2 −α
23
Flow scales across centrality
PHENIX Preliminary
PHENIX
Preliminary
Similar viscous
corrections for the
same KET selection
PHENIX Preliminary
PHENIX Preliminary
Roy A. Lacey, Stony Brook University, 2010
24
Proofing of the methodology
Methodology successfully proofed – very important
Roy A. Lacey, Stony Brook University, 2010
25
Geometric Quantities
Phys. Rev. C 81, 061901(R) (2010)
A
B
¾ Geometric fluctuations are very important
¾ eccentricity estimates should be constrained by
multiplicity density!
Roy A. Lacey, Stony Brook University, 2010
26
Participant eccentricity & deformation
Phys. Rev. C 81, 061901(R) (2010)
A
B
Au+Au
New experimental constraint for
Distinguishing Glauber and CGC Initial geometry!
Roy A. Lacey, Stony Brook University, 2010
27
k
Knudsen Fits
arXiv:1005.4979
(a)
pT (GeV/c)
CGC
⎡
⎤
−1
⎥
⎡
⎤
v2 k ( pT ) v2 k ( pT ) ⎢⎢
1
1
dN
*
⎥ , ⎡ K ( pT ) ⎤ = ⎢ β ( pT )
=
⎦
ε 2k
ε 2 k ⎢ K * ( pT ) ⎥ ⎣
S dy ⎥⎦
⎣
⎢1 + K
⎥
(b)
0
⎣
⎦
CGC
0.4
2.4-3.6
1.6-2.4
1.2-1.6
0.8-1.2
0.5-0.8
0.6
0.7
<pT> GeV/c
5.40
4.44
0.6
2.95
2.76
0.4
0.2
0.5
v2/ε2
v4/ε4
v2/ε2
0.3
CGC
0.4
0.3
0.2
0.1
0.2
0
0.0
0.0
0
100
200
Npart
300
0
100
200
300
Npart
Excellent simultaneous fits achieved
Viscous corrections grow with pT
100
200
Npart
300
For pT > 3 GeV/c
apparent viscous corrections
decrease with pT
Eccentricity encodes
path length dependence
Roy A. Lacey, Stony Brook University, 2010
28
Viscous Corrections
Onset of suppression!
arXiv:1005.4979
CGC
4π
η
s
~ 1.1 ± .1
Glauber
4π
η
s
Plasma viscosity is > 0
~ 2.1 ± .2
B
K =K+
Tf
*
⎛ pT
⎜⎜
⎝ Tf
⎞
⎟⎟
⎠
2 −α
⎫
⎪
α =2
⎪
T f ~165 ± 11 MeV
⎪
⎪
c s ~ 0.47 ± .03 c (lattice) ⎬
⎪
ζ
⎪
is small
s
⎪
⎪
λ ~ 0.2-0.3 fm
⎭
¾Quadratic dependence of δf
¾ Breakdown of hydrodynamic ansatz for K* ~ 1
¾Onset of jet suppression
Roy A. Lacey, Stony Brook University, 2010
29
• KET/nq< 1GeV – soft physics
Hydrodynamic flow
•Interplay soft-hard 3.0 < pT< 5
GeV/c ?
•Hard dominates: pT> 5 GeV/c
Roy A. Lacey, Stony Brook University, 2010
30
Temperature dependence
of η/s
G. Denicol et al
v2
pT
Relaxation time limits η/s
to small values
Roy A. Lacey, Stony Brook University, 2010
31
Scaling properties of RAA
Several issues
• Data precision
•Path Length dependence
• Anomalous suppression
• etc
Roy A. Lacey, Stony Brook University, 2010
32
Jet Suppression
R AA =
Yield AA
⟨ N binary ⟩ AA Yield pp
direct γ
Inclusive hadron suppression is pervasive, but does not
give an unambiguous constraint for q̂
Roy A. Lacey, Stony Brook University, 2010
33
Universal Scaling of RAA
Motivating Idea!
Beer Lambert’s law
T=
I1
= e −ε Lc
I0
ln(T ) = −ε cL
R AA =
Yield AA
⟨ N binary ⟩ AA Yield pp
L
ln(T)
Radiation energy loss
Dead cone effect
L
Phys. Lett. B519, 199 (2001)
Straightforward validation tests as a function of pT and L
Roy A. Lacey, Stony Brook University, 2010
34
Scaling of Jet Quenching
Phys.Rev.C80:051901,2009
Phys.Rev.Lett.103:142302,2009
Minimum L
Requirement
i.e. no corona
quenching
GeV 2
qˆ ~ 1
fm
Scaling also validated for different system size etc!
Roy A. Lacey, Stony Brook University, 2010
35
Scaling of Jet Quenching
- System size
Similar scaling found
For different collision
systems.
“Profound” Value Æ global simplification
Æ Focus on essential variables
Roy A. Lacey, Stony Brook University,
2010
36
Scaling of Jet Quenching Reaction plane dependence
Phys.Rev.C80:051901,2009
Phys.Rev.Lett.103:142302,2009
Estimates From slope
GeV 2
qˆ ~ 1
fm
η
⎛
T3 ⎞
4π ~ 4π ⎜1.25 ⎟ ~ 1.4
s
qˆ ⎠
⎝
Automatic accounting of high-pT v2
Further validation of path length scaling!
Very important but no new information!
Roy A. Lacey, Stony Brook University, 2010
37
Is Jet Quenching Anomalous?
Phys.Rev.Lett.103:142302,2009
Different
Minimum L
Requirement
i.e. no corona
quenching
Quenching compatible with anisotropy
Æ Anomalous quenching?
Future B & D measurements (RAA & v2)
at high pT will help!
Roy A. Lacey, Stony Brook University, 2010
38
Is Jet Quenching Anomalous?
Phys.Rev.Lett.103:142302,2009
π
e±
2
v2 > v
Quenching compatible with anisotropy
Æ Anomalous quenching?
Future B & D measurements (RAA & v2)
at high pT will help!
Roy A. Lacey, Stony Brook University, 2010
39
summary
Phys.Rev.Lett.98:092301,2007
Relaxation time
Koide et al
η
⎫
⎪
GeV 2
s
qˆ ~ 1
⎪⎪ Strong
λ ~ 0.2 − 0.3 fm ⎬
fm
Coupling!
T f ~165 ± 11 MeV ⎪
For both light partons and
⎪
heavy quarks
c s ~ 0.47 ± 0.03 c ⎪⎭
The fluid which leads to large collective flow
is also responsible for strong jet quenching
4π
∼ 1− 2
Roy A. Lacey, Stony Brook University, 2010
40
End
Roy A. Lacey, Stony Brook University, 2010
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