Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
1
Celebrating Joe’s Journey
“you have done it all – excellent forefront research,
classroom teaching, mentoring, major administrative duties
and extensive service to the community. Moreover, you have
been a perceptive voice of civility when arguments have
become heated, a quality that has served to benefit our
science greatly”
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
2
Celebrating Joe’s Journey
“Most of all that I have fully appreciated is his unfailing
enthusiasm and dedication which have been a hallmark in
all of his endeavors. One more thing is his constant drive to
excel and set a higher goal than ordinarily achieved, in order
to remain in the forefront of contemporary research.”
“Prof. Natowitz and his wife Karin gave my family
(includes my wife Honglian Chen) a great help not
only in work but also in life. After I came back to
China, Prof. Natowitz continues to support my
group.”
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
3
Celebrating Joe’s Journey
Two Reminders:
“Age
is only a number, a cipher
for the records. A man can't
retire his experience. He
must use it.”
I.
p
II.
Bernard Baruch
“We don’t stop playing
because we grow old; we
grow old because we stop
playing.”
- George Bernard Shaw
We look forward to many more years of good science from you!
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University,
June 25, 2013
4
“The piano is able to communicate the subtlest universal truths
by means of wood, metal and vibrating air”
Kenneth Miller
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
5
A Current Focus of our Field
Quantitative study of the QCD phase diagram
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
 Necessary for the CEP?
A major current focus is the characterization of the QGP produced
at RHIC and the LHC, as well as a search for the CEP at RHIC
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University,
June 25, 2013
6
Current Strategy
Exploit system size and the energy density lever arm
(𝛍𝐁 ,T) at freezeout
Energy scan
 LHC  access to high T and small 𝝁𝑩
 RHIC  access to different systems and
a broad domain of the (𝛍𝐁 ,T)-plane
RHICBES to LHC  ~360 𝒔𝑵𝑵 increase
 LHC + BES  access to an even
broader domain of the (𝛍𝐁 ,T)-plane
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook
University, June 25, 2013
7
Essential Questions
Lacey et. al, Phys.Rev.Lett.98:092301
 (T, 𝛍𝐁 )-dependence of transport
coefficients 𝒄𝒔 ,
𝜼
𝒔
?
 The role of system size and
fluctuations?
 Location of phase boundaries?
 Indications for a CEP?
At the CEP or close to it, anomalies in
the dynamic properties of the medium
can drive abrupt changes in transport
coefficients
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook
University, June 25, 2013
8
An Essential Question
Song et al
η
 Does the value of 𝒔 depend on the initial geometry
model or the method of extraction?
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
9
Take home message
The acoustic nature of flow leads to specific scaling patterns
which :
I.
Give profound mechanistic insight on viscous damping
II.
Provide constraints for
 (𝛍𝐁 ,T) and R dependence of the viscous coefficients
 Hints for a possible critical point?
 initial state geometry and its fluctuations
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook
University, June 25, 2013
10
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 
 3s T
Staig & Shuryak arXiv:1008.3139
Yield(f) =2 v2 cos[2(fY2]
Crucial parameters  , cs ,  /s,  f, T f
Initial Geometry characterized by many
shape harmonics (εn)  drive vn
dN 

 1  2 vn cos  n f  Y n   
df 
n 1

Initial eccentricity (and its attendant fluctuations) εn drive
momentum anisotropy vn with specific viscous modulation
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
11
Scaling properties of flow
(II) Scaling properties of flow
Acoustic viscous modulation of vn
 2 2 t 
 T  t , k   exp 
k
  T  0 
3 s T 
Initial Geometry characterized by many
shape harmonics (εn)  drive vn
dN 

 1  2 vn cos  n f  Y n   
df 
n 1

k n/R
Staig & Shuryak arXiv:1008.3139
Scaling expectations:
n2 dependence
vn ( pT )
n
 exp    n
2

vn is related to v2
vn ( pT )  n
  exp    (n 2  4) 
v2 ( pT )  2
System size dependence
 v    
ln  n  
R
 n 
Each of these scaling expectations has been validated
 Reflects acoustic modulation NOT super horizon modulation
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
12
 A quick review of the data?
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook
University, June 25, 2013
13
Anisotropy Measurements
ATLAS data - Phys. Rev. C86, 014907 (2012) & ATLAS-CONF-2011-074
High precision double differential measurements obtained for
higher harmonics at RHIC and the LHC.
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
14
Anisotropy Measurements
arXiv:1305.3341
STAR - Phys.Rev.C86, 014904 (2012); Phys.Rev.C86, 054908 (2012)
CMS - Phys.Rev.C87, 014902 (2013)
 An extensive set of measurements now span a broad range
of beam energies (T, 𝛍𝐁 ).
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
15
Anisotropy Measurements
High precision double differential measurements obtained for
identified particle species at RHIC and the LHC.
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
16
 Do the wealth of anisotropy measurements show a
consistent scaling pattern?
 What do we learn from these scaling patterns?
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
17
Acoustic Scaling – n2
ATLAS data - Phys. Rev. C86, 014907 (2012)
vn ( pT )
n
  exp    n 2 
arXiv:1301.0165
 Characteristic n2 viscous damping validated
 Characteristic 1/(pT)α dependence of extracted β values validated
Constraint for η/s and δf
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
18
vn ( pT )
n
1
Data and calculated points from CMS PAS HIN-12-011
(a)
4
0
(b) Pb+Pb @ 2.76 TeV
s
0
1
2.5
-1
ln(vn/ n)
  exp    n 2 
0.150
(c)
0.1%
Data
0.125
-2
0.100
-3
-4
0.075
-5
Viscous Hydro
-6
0.050
0
10
20
30
40
n
0
10
20
30
2
2
n2
n
40
0
1
2
3
s
scaling validated in viscous hydrodynamics;
calibration  4πη/s ~ 2
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
19
Flow is partonic & Acoustic?
arXiv:1211.4009
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
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
20
Scaling properties of flow
Acoustic Scaling – Ratios
vn PID scaling
Expectation validated: v n ( KET ) ~ v n2 /2 or
vn
(nq ) n /2
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
21
Scaling properties of flow
𝟏
Acoustic Scaling –
𝑹
 vn    
ln   
R
 n 
0.25
ATLAS Pb+Pb @ 2.76 TeV
pT = 2-3 GeV/c
v2
0.20
0.15
Centrality
5-70%
0.10
 Eccentricity change alone is not sufficient
To account for the Npart dependence of vn
0
100 200 300
Transverse size (𝑹 ) influences viscous damping
Npart
 Characteristic 𝟏/𝑹 scaling prediction is
non-trivial
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
400
22
Scaling properties of flow
Acoustic Scaling –
𝟏
𝑹
 v    
ln  n  
R
 n 
 Characteristic 𝟏/𝑹 viscous damping validated
at RHIC & the LHC
 A further constraint for η/s
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
23
Song et al
η
 Does the value of 𝒔 depend on the initial geometry
model or the method of extraction?
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
24
 v    
ln  n  
R
 n 
(a)
s)QGP (b)
MC-Glauber
0
1
2
3
ln(v2/ 2)
-1
2.0
(c)
Data
MC-KLN
1.5
-2
1.0
-3
0.5
-4
Viscous Hydro
0.5
1.0 1.5
-1
1/R (fm )
Viscous Hydro
0.0
0.5
1.0
1.5
-1
1/R (fm )
2.0 0
1
4
2
/s
3
Characteristic 𝟏/𝑹 viscous damping validated in
viscous hydrodynamics; calibration  4πη/s ~ 1.3
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
25
Acoustic Scaling – 1/R
Compare system size @ RHIC
 v    
ln  n  
R
 n 
Au+Au 0.2 TeV
(PHENIX)
ln(v2/ 2)
-0.4
Cu+Cu 0.2 TeV
(STAR)
pT = 1.19 GeV/c
pT = 1.79 GeV/c
pT = 0.79 GeV/c
0.0
-0.4
-0.8
-0.8
-1.2
-1.2
Slope difference
encodes viscous -1.6
coefficient
difference
-1.6
-2.0
0.0
ln(v2/ 2)
0.0
-2.0
0.5
1.0
1.5
0.5 1.0 1.5
-1
1/R (fm )
0.5
1.0
1.5
 Viscous coefficient larger for more dilute system
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
26
Scaling properties of flow
Acoustic Scaling –
7.7 GeV
𝟏
𝑹
𝑺𝒄𝒂𝒍𝒊𝒏𝒈 𝒇𝒐𝒓 𝒕𝒉𝒆 𝑩𝒆𝒂𝒎 𝑬𝒏𝒆𝒓𝒈𝒚 𝑺𝒄𝒂𝒏
19.6 GeV
39 GeV
62.4 GeV
 vn    
ln   
R
 n 
200 GeV
2.76 TeV
 Characteristic 𝟏/𝑹 viscous
damping validated across
beam energies
 First experimental indication
for η/s variation in the
𝑻, 𝝁𝑩 -plane
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
27
Summary
Acoustic scaling observed for flow
They lend profound mechanistic insights, as well as new
constraints for transport coefficients and the initial state
What do we learn?
 Flow is acoustic – “as it should be”
Obeys the dispersion relation for sound propagation (n2, (n2-4),
𝟏/𝑹 )  constraints for ε, β, and δf
 Clear system size dependence of β  sensitive to dilution!
 Scaling across systems  including very asymmetric
systems
Characteristic dependence of β [η/s(T)] on beam energy 
constraints for:
(T, 𝛍𝐁 )-dependence η/s
η/s @ LHC larger than at RHIC
 Indication for CEP??
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
28
End
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
29
Essential Questions
Luzum et al. arXiv 0804.4015
 LHC  access to high T and small 𝝁𝑩
 RHIC  access to different systems and
a broad domain of the (𝛍𝐁 ,T)-plane
RHICBES to LHC  ~360 𝒔𝑵𝑵 increase
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
30
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
31
Recent Accomplishments & Near-term Opportunities
Geometry
Phys. Rev. C 81, 061901(R) (2010)
B
A
 n  cos n f  n* 
LR
L ~  R
arXiv:1203.3605
σx & σy  RMS widths of density distribution
 Geometric fluctuations included
 Geometric quantities constrained by multiplicity density.
Workshop on Nuclear Dynamics and Thermodynamics, Roy A. Lacey, Stony Brook University, June 25, 2013
32