Conjectured Phase Diagram
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Transcript of Conjectured Phase Diagram
Acoustic scaling of anisotropic flow in shape-engineered events: implications for extraction (μB,T) of the QGP
Roy A. LaceyStony Brook University
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p
Conjectured Phase Diagram
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Quantitative study of the QCD phase diagram
Roy A. Lacey, Stony Brook University, April 24th, 2014
Interest
Location of the critical End point (CEP)
Location of phase coexistence lines
Properties of each phaseAll are fundamental to the phase
diagram of any substanceSpectacular achievement:Validation of the crossover transition leading to the QGP Necessary for the CEP?
A Current Focus of our Field
Extraction of the ()-dependence of transport coefficients is central to the heavy ion programs at RHIC and the LHC
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LHC access to high T and small RHIC access to different systems anda broad domain of the (,T)-plane
Exploit system size and beam energy lever arm
Roy A. Lacey, Stony Brook University, April 24th, 2014
Energy scan
Current Strategy
LHC + BES access to an even broader domain of the (,T)-plane
(,T) at freeze-out
RHICBES to LHC 360 increase
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Essential Questions
At the CEP or close to it, anomalies inthe dynamic properties of the medium can drive abrupt changes in transport
coe cientsffi
Lacey et. al, Phys.Rev.Lett.98:092301 (2007)
()-dependence of transport coefficients , , etc? The role of system size and fluctuations? Location of phase boundaries? Indications for a Critical EndPoint (CEP)?
Anisotropic flow is an invaluable probe
Lacey et. al, arXiv:0708.3512 (2008)
(η/s)RHIC estimates – QM2009 Excellent Convergence on the magnitude of η/s at RHIC
Roy A. Lacey, Stony Brook University, April 24th, 2014
4πη/s ~ 1 - 2
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Reminder
Status QuoA major uncertainty in theextraction of η/s stems from Incomplete knowledge of the Initial-state eccentricity model
εn – η/s interplay?
T dependence of η/s? μB dependence of η/s? Possible signal for CEP?
Subsequently
Song et al
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Status Quo
Status QuoA major uncertainty in theextraction of η/s stems from Incomplete knowledge of the Initial eccentricity?
εn – η/s interplay?
New methodology and constraints required
Luzum et al. arXiv 0804.4015
15-20%ε2 difference
2x η/s difference
η/s is a property of the medium and should not
depend on initial geometry!This is NOT an uncertainty; It is a failure of the method of
extraction
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Improved Methodology
Higher harmonics provide important constraints!
4πη/s for LHC plasma ~ 2
arXiv:1301.5893Bjoern Schenke et. al.
Can we find methodologies and constraintswhich are insensitive to the initial-state geometry?
Roy A. Lacey, Stony Brook University, April 24th, 20148
The acoustic nature of flow leads to specific scaling patterns which :
I. Give profound mechanistic insight on viscous damping
II. Provide constraints for
initial state geometry and its fluctuations Extraction of the specific viscosity
(,T) dependence of the viscous coefficients Hints for a possible critical point?
Essential message
Significant and important recent development in the field!
s/
P ² Bj
, , /s, f, Ts fc
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3
1 1
~ 5 45
TBj
dER dyGeVfm
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Idealized Geometry
2 2
2 2
y x
y x
Crucial parametersActual collision profiles are not smooth,
due to fluctuations!Initial Geometry characterized by many
shape harmonics (εn) drive vn
Initial eccentricity (and its attendant fluctuations) εn drive momentum anisotropy vn with specific viscous modulation
22, exp 03
tT t k k Ts T
Acoustic viscous modulation of vn
Staig & Shuryak arXiv:1008.3139
Isotropic p
Anisotropic p
Yield(f) =2 v2 cos[2(fY2]
The Flow Probe
1
1 2 cosn nn
dN v nd
ff
Y
Roy A. Lacey, Stony Brook University, April 24th, 2014
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n nv
22, exp 03
tT t k k Ts T
Acoustic viscous modulation of vn
Staig & Shuryak arXiv:1008.3139
/k n R
Scaling expectations:
2( ) expn T
n
v p n
2
2 2
( ) exp ( 4)( )n T n
T
v p nv p
ln n
n
vR
vn is related to v2 System size dependencen2 dependence
Each of these scaling expectations can been validatedη/s , ’
Initial Geometry characterized by many shape harmonics (εn) drive vn
Scaling properties of flow
Roy A. Lacey, Stony Brook University, April 24th, 2014
t R
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Demonstration of acoustic scaling
What do we learn from these scaling patterns?
Roy A. Lacey, Stony Brook University, April 24th, 2014
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A B
Geometric fluctuations included Geometric quantities constrained by multiplicity density.
*cosn nn f
Phys. Rev. C 81, 061901(R) (2010)
arXiv:1203.3605
σx & σy RMS widths of density distribution
Geometric quantities for scalingGeometry
Roy A. Lacey, Stony Brook University, April 24th, 2014
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Relationship between initial and freeze-out geometry
Roy A. Lacey, Stony Brook University, April 24th, 2014
exquisitely demonstrated via HBT measurement
t R
Femtoscopic measurements
R and mT scaling of the full set of HBT data Similar expansion dynamics Larger expansion rates at the LHC
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exquisitely demonstrated via HBT measurement for several systems
t R
R (fm)1 2
Rin
v (fm
)
0
4
8
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16Pb+Pb 2.76 TeVp+Pb 5.02 TeV
0.2 <kT<0.3 GeV/c
R (fm)0.0 0.5 1.0 1.5 2.0 2.5
Rsi
de (f
m)
0
2
4
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82.76 TeV Pb+Pb - ALICE200 GeV Au+Au - PHENIX200 GeV Au+Au - STAR200 GeV d+Au - PHENIX
kT~ 0.4 GeV/c
(a) (b)
ALICE
Femtoscopic measurements arXiv:1404.5291
Relationship between initial and freeze-out geometry
Larger expansion rate at the LHC
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Npart
0 100 200 300 400v 2
0.10
0.15
0.20
0.25pT = 2-3 GeV/c
ATLAS Pb+Pb @ 2.76 TeV
Centrality 5-70%
ln n
n
vR
Characteristic scaling prediction is non-trivial
Eccentricity change alone is not sufficientTo account for the Npart dependence of vn
Transverse size ( ) influences viscous damping
Acoustic Scaling –
Scaling properties of flow
Roy A. Lacey, Stony Brook University, April 24th, 2014
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ln n
n
vR
Acoustic Scaling –
Characteristic viscous damping validated at RHIC & the LHC A further constraint for η/s
Scaling properties of flow
Roy A. Lacey, Stony Brook University, April 24th, 2014
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ln n
n
vR
Characteristic a
The relative magnitude of vn provides an important constraint!
Scaling properties of flow
Roy A. Lacey, Stony Brook University, April 24th, 2014
η/s Viscous hydrodynamics can be used for calibration
- Viscous Hydrodynamics
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Shape-engineered events
Roy A. Lacey, Stony Brook University, April 24th, 2014
Note characteristic anti-correlation predicted for v3(q2) in mid-central events
Shape fluctuations lead toa distribution of the Q vector
at a fixed centrality
Cuts on qn should change the magnitudes , , at a given centrality due to fluctuations
These magnitudes can influence scaling
Crucial constraint for initial-geometry models
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Shape-engineered events
Cuts on qn should change the magnitudes , , at a given centrality due to fluctuations
Roy A. Lacey, Stony Brook University, April 24th, 2014
ALICE data
q2(Lo)
q2(Hi)
Viable models for initial-state fluctuations should still scale
Shape fluctuations lead toa distribution of the Q vector
at a fixed centrality
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Acoustic Scaling of shape-engineered events
Scaling properties of flow
Roy A. Lacey, Stony Brook University, April 24th, 2014
Characteristic viscous damping validated for different event shapes at the same centrality A further constraint for initial fluctuations model and η/s
Song et al
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Characteristic viscous damping validated in viscous hydrodynamics; calibration 4πη/s ~
Extracted η/s value insensitive to initial conditions
η/s show 100% uncertainty due to “uncertainty” about the initial geometry
η/s is a property of the medium and should not depend on initial geometryThis is NOT an uncertainty; It is an incorrect method of extraction
Extraction of η/s ln n
n
vR
Slope sensitive to 4η/s
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n2 scaling validated in experiment and viscous hydrodynamics;
calibration 4πη/s ~ 2Note agreement with Schenke et al.
2( )expn T
n
v pn
n20 10 20 30 40
ln(v
n/ n)
-6
-5
-4
-3
-2
-1
0
1
012.5
s0 1 2 3
0.050
0.075
0.100
0.125
0.1504s
n20 10 20 30 40
Data
(a) (b) (c)Pb+Pb @ 2.76 TeV
0.1%
Viscous Hydro
arXiv:1301.0165 & CMS PAS HIN-12-011
Slope sensitive to η/s
Extraction of η/s
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Anisotropy Measurements
An extensive set of measurements now span a broad range of beam energies ().
STAR - Phys.Rev.C86, 014904 (2012); Phys.Rev.C86, 054908 (2012) CMS - Phys.Rev.C87, 014902 (2013)
arXiv:1305.3341
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ln n
n
vR
Characteristic viscous damping validated across beam energies
First experimental indication for η/s variation in the -plane
7.7 GeV 19.6 GeV 39 GeV 62.4 GeV 200 GeV
2.76 TeV
Acoustic Scaling –
Scaling properties of flow
Roy A. Lacey, Stony Brook University, April 24th, 2014
HBT should show complimentary
signals for similar
Lacey et. al. Phys. Rev. Lett. 112, 082302
Flow is acoustic – “as it should be” Obeys the dispersion relation for sound propagation
(n2 & ) constraints for 4πη/s & viable initial-state models
4πη/s for RHIC plasma ~ 1 ~ my 2006 estimate4πη/s for LHC plasma ~ 2Extraction insensitive to initial geometry model
Characteristic dependence of viscous coefficient β” on beam energy give constraints for:
()-dependence η/s Indication for CEP??
Scaling properties of anisotropic flow lend profound mechanistic insights, as well as new constraints for
transport coefficients
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What do we learn?
Summary
Roy A. Lacey, Stony Brook University, April 24th, 2014
End
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