2
QCD Phase Diagram
Ø Strong interest in the theoretical calculations which span a broad
(𝜇", T)domain.
3
QCD Phase Diagram
Ø The . /⁄ values are tuned in model calculations to describe the
experimental flow data at different collision energies
Ø Strong interest in the theoretical calculations which span a broad
(𝜇", T)domain.
Iu.A. Karpenko , et al.PRC 91, 064901 (2015)
4
STARPRL 112, 162 301 (2014)
v Investigate signatures for the first-order phase transition
ØStrong interest in the experimental measurements which span a broad (𝜇", T)domain.
QCD Phase Diagram
5
STARPRL 112, 162 301 (2014)
v Investigate signatures for the first-order phase transition
v Search for critical fluctuations
STAR PRL 112, 032 302 (2014)
ØStrong interest in the experimental measurements which span a broad (𝜇", T)domain.
QCD Phase Diagram
6
Azimuthal anisotropic flow
6
Ø Comprehensive set of flow measurements are important to study;ü Differentiate between initial-state models
q Initial-state eccentricity & its fluctuations
7
Azimuthal anisotropic flow
7
Ø Comprehensive set of flow measurements are important to study;ü Differentiate between initial-state models
q Initial-state eccentricity & its fluctuations
ü Transport coefficients (. /⁄ , etc)q Pin down the temperature dependence of the transport
coefficients
8
Azimuthal anisotropic flow
8
Ø Comprehensive set of flow measurements are important to study;ü Differentiate between initial-state models
q Initial-state eccentricity & its fluctuations
ü Transport coefficients (. /⁄ , etc)q Pin down the temperature dependence of the transport
coefficients
ü Detailed flow measurements could aid ongoing efforts
to search for the critical end point(CEP)
9
Azimuthal anisotropic flow
9
Dipole asymmetry
Asymmetry in initial geometry → Final state momentum anisotropy (flow)
𝑑𝑁𝑑𝜑4 = 1 + 29𝑣;
<
;
cos(𝜑 − Ψ;)
10
Azimuthal anisotropic flow
10
Dipole asymmetry
Asymmetry in initial geometry → Final state momentum anisotropy (flow)
𝑑𝑁𝑑𝜑4 = 1 + 29𝑣;
<
;
cos(𝜑 − Ψ;)
Ø The flow harmonic coefficients 𝑣; are influenced by eccentricities(𝜀;)[and their fluctuations], the speed of sound cC(µ", 𝑇), and transport
coefficients FC, GC, …
6
STAR Detector at RHICØ TPC detector mainly get
used in the current analysis
Ø Collected data for Au+Au at different 𝑠JJ� by STAR detector at RHIC
will be presented
Two-particle correlation function 𝐶r Δ𝜑 = 𝜑O − 𝜑P ,
𝐶𝑟 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑 and 𝑣;SP = ∑ UV WX YZC(;WX)�[\
∑ UV WX�[\
Azimuthal anisotropy measurements
Correlation function
12
Flow
Two-particle correlation function 𝐶r Δ𝜑 = 𝜑O − 𝜑P ,
𝐶𝑟 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑 and 𝑣;SP = ∑ UV WX YZC(;WX)�[\
∑ UV WX�[\
Non-flow
Azimuthal anisotropy measurements
Correlation function
13
Flow
𝑯𝑩𝑻
𝑫𝒆𝒄𝒂𝒚
Two-particle correlation function 𝐶r Δ𝜑 = 𝜑O − 𝜑P ,
𝐶𝑟 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑 and 𝑣;SP = ∑ UV WX YZC(;WX)�[\
∑ UV WX�[\
𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆
𝑛 > 1𝑣;SP = 𝑣;S𝑣;P +𝛿/opVq
Non-flow
Azimuthal anisotropy measurements
Correlation function
14ChargeNon-flow suppression is needed
Flow
𝑯𝑩𝑻
𝑫𝒆𝒄𝒂𝒚
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
Di−jets
Two-particle correlation function 𝐶r Δ𝜑 = 𝜑O − 𝜑P ,
𝐶𝑟 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑 and 𝑣;SP = ∑ UV WX YZC(;WX)�[\
∑ UV WX�[\
𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
𝑛 > 1𝑣;SP = 𝑣;S𝑣;P +𝛿/opVq
𝑛 = 1𝑣~SP = 𝑣~S𝑣~P +𝛿�p;�
Non-flow
Azimuthal anisotropy measurements
Correlation function
15ChargeNon-flow suppression is needed
16
Ø Short-range non-flow effect get reduced using |Δη| > 0.7 cut
The 𝑣�vs centrality at 𝑠JJ� = 200using different 𝛥𝜂 cuts
Short-range non-flow suppression𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆Non−flow𝑯
𝑩𝑻
𝑫𝒆𝒄𝒂𝒚
0
0.02
0.04
0.06
0.08
0.1
20 40 60 80
v2
Au+Au200 GeV|∆η| > 0.3
LSUS
0
0.02
0.04
0.06
0.08
0.1
20 40 60 80
|∆η| > 0.7
0
0.02
0.04
0.06
0.08
0.1
20 40 60 80
|∆η| > 0.9
0.8
0.9
1
1.1
1.2
20 40 60 80
LS/US
0.8
0.9
1
1.1
1.2
20 40 60 80Centrality%
LS/US
0.8
0.9
1
1.1
1.2
20 40 60 80
LS/US
STAR Preliminary
𝑣~SP = 𝑣~S𝑣~P +𝛿�p;�𝑛 = 1
𝑣~~ 𝑝�S, 𝑝�P = 𝑣~���; 𝑝�
S 𝑣~���; 𝑝�
P − 𝐶𝑝�S𝑝�
P
17
arXiv:1203.0931arXiv:1203.3410arXiv:1208.1874arXiv:1208.1887arXiv:1211.7162
1
Long-range non-flow suppression
𝑣~~ in Eq(1) represents NxM matrix which we fit with N+1 parameters
𝑴𝒐𝒎
𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
𝑪 ∝ < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 > �𝟏
𝑣~SP = 𝑣~S𝑣~P +𝛿�p;�𝑛 = 1
ØGood simultaneous fit ( ��
;��~1.1) obtained with Eq. 1
18
arXiv:1203.0931arXiv:1203.3410arXiv:1208.1874arXiv:1208.1887arXiv:1211.7162
1
Long-range non-flow suppression
𝑣~~ in Eq(1) represents NxM matrix which we fit with N+1 parameters
𝑴𝒐𝒎
𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
𝑪 ∝ < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 > �𝟏
-1
0
1
2
1 2 3
v 11
x10-3
Au+Au0-5%
200 GeV
(a)
0.2 < paT < 0.6 (GeV/c)
-1
0
1
2
1 2 3
v 11
1.0 < paT < 1.4 (GeV/c)
(b)
-1
0
1
2
1 2 3
v 11
pbT (GeV/c)
1.4 < paT < 1.8 (GeV/c)
(c)
-1
0
1
2
1 2 3
v 11
1.8 < paT < 2.6 (GeV/c)
(d)
STAR Preliminary
𝑣~~ 𝑝�S, 𝑝�P = 𝑣~���; 𝑝�
S 𝑣~���; 𝑝�
P − 𝐶𝑝�S𝑝�
P
𝑣~SP = 𝑣~S𝑣~P +𝛿�p;�𝑛 = 1
ØGood simultaneous fit ( ��
;��~1.1) obtained with Eq. 1
Øv~~characteristic behavior gives a good constraint for 𝒗𝟏𝒆𝒗𝒆𝒏 𝐩𝐓 extraction19
arXiv:1203.0931arXiv:1203.3410arXiv:1208.1874arXiv:1208.1887arXiv:1211.7162
1
Long-range non-flow suppression
𝑣~~ in Eq(1) represents NxM matrix which we fit with N+1 parameters
𝑴𝒐𝒎
𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
𝑪 ∝ < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 > �𝟏
-1
0
1
2
1 2 3
v 11
x10-3
Au+Au0-5%
200 GeV
(a)
0.2 < paT < 0.6 (GeV/c)
-1
0
1
2
1 2 3
v 11
1.0 < paT < 1.4 (GeV/c)
(b)
-1
0
1
2
1 2 3
v 11
pbT (GeV/c)
1.4 < paT < 1.8 (GeV/c)
(c)
-1
0
1
2
1 2 3
v 11
1.8 < paT < 2.6 (GeV/c)
(d)
STAR Preliminary
𝑣~~ 𝑝�S, 𝑝�P = 𝑣~���; 𝑝�
S 𝑣~���; 𝑝�
P − 𝐶𝑝�S𝑝�
P
ØThe characteristic behavior of 𝑣~���; 𝑝� shows a weak centrality dependence
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻 and the momentum conservation parameter 𝐶 at 𝑠JJ� = 200
20
𝜂 < 1and|Δ𝜂| > 0.7Long-range non-flow suppression
𝑴𝒐𝒎
𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
STAR Preliminary
0
0.04
0.08
0.12
0 1 2 3
veven
1
pT(GeV/c)
Au+Au200 GeV
0%-10%10%-20%20%-30%30%-40%
Ø Fit to 𝑣~���; 𝑝� data shows 𝑣~���; 𝑝� centrality dependent
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒃 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒃 − 𝑪𝒑𝑻𝒂𝒑𝑻
𝒃
ØThe characteristic behavior of 𝑣~���; 𝑝� shows a weak centrality dependence
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻 and the momentum conservation parameter 𝐶 at 𝑠JJ� = 200
21
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒃 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒃 − 𝑪𝒑𝑻𝒂𝒑𝑻
𝒃
𝜂 < 1and|Δ𝜂| > 0.7Long-range non-flow suppression
𝑴𝒐𝒎
𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
STAR Preliminary
0
0 0.01 0.02
0
0.004
0.008
C
1/<Mult>
Au+Au200 GeV
Ø The momentum conservation parameter 𝐶 scales as < 𝑴𝒖𝒍𝒕 >�𝟏
0
0.04
0.08
0.12
0 1 2 3
veven
1
pT(GeV/c)
Au+Au200 GeV
0%-10%10%-20%20%-30%30%-40%
Ø Fit to 𝑣~���; 𝑝� data shows 𝑣~���; 𝑝� centrality dependent
STAR Preliminary
𝑪 ∝ < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 > �𝟏
22
Flow harmonics
𝒗; 𝐶𝑒𝑛𝑡𝒗; 𝜂, 𝑝�
23
Flow harmonics
𝒗; 𝐶𝑒𝑛𝑡
𝒗; 𝑠JJ�
𝒗; 𝜂, 𝑝�
ØSimilar characteristic behavior of 𝑣~���; 𝑝� at all energies
Ø𝑣~���; 𝑝� agrees with hydrodynamic calculations at 200 GeV
ØMomentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
The extracted 𝑣~���; 𝑝� at all BES energies
24
Transverse momentum dependence of 𝑣~���;
STAR Preliminary
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻
𝒕
HydroE.Retinskaya , et al.
PRL 108, 252302 (2012)
0
0.1
0 1 2
veven
1(a) Au+Au
200 GeV0-10%
Hydro(η/s = 0.16)
0
0.1
0 1 2
veven
1
62.4 GeV(b)
0
0.1
0 1 2
veven
1
(c)39 GeV
0
0.1
0 1 2
veven
1
(d)27 GeV
0
0.1
0 1 2
19.6 GeV
(e)
0
0.1
0 1 2
pT (GeV/c)
(f)14.5 GeV
0
0.1
0 1 2
11.5 GeV(g)
0
0.1
0 1 2
7.7 GeV(h)
0
1
2
0 0.02 0.04 0 1 2
C
⟨ Mult ⟩-1
×102
Ø𝑣~���; increases weakly as collisions
become more peripheral
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝐶𝑒𝑛𝑡 and the momentum conservation parameter at different beam energies
25
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻
𝒕
Centrality dependence dependence of 𝑣~���;
STAR Preliminary
0
0.01
0.02
10 20 30 40 50 60 70
|v1ev
en|
Centrality%
(a) Au+Au0.4 < pT < 0.7(GeV/c)
200 GeV39 GeV
19.6 GeV
For different beam energies;
Ø𝑣~���; increases weakly as collisions
become more peripheral
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝐶𝑒𝑛𝑡 and the momentum conservation parameter at different beam energies
26
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻
𝒕
Centrality dependence dependence of 𝑣~���;
STAR Preliminary
0
0.01
0 0.01 0.02
0
0.01
C(√
s NN
)
⟨ Mult ⟩-1
(b)
0
0.01
0.02
10 20 30 40 50 60 70
|v1ev
en|
Centrality%
(a) Au+Au0.4 < pT < 0.7(GeV/c)
200 GeV39 GeV
19.6 GeV
STAR Preliminary
𝑪 ∝ < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 > �𝟏
Ø Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
For different beam energies;
27
The extracted 𝑣;¦~ 𝜼 at all BES energies
𝜂 < 1and|Δ𝜂| > 0.7Pseudorapidity dependence of𝑣;¦~
Ø 𝑣; 𝜼 has similar trends for different beam energies.
Ø 𝑣; 𝜼 decreases with harmonic order n.
0
0.02
0.04
0 0.4 0.8
v nAu+Au
200 GeV0-40%
(a)
0
0.02
0.04
0 0.4 0.8
v n
62.4 GeV(b)
0
0.02
0.04
0 0.4 0.8
v n
39 GeV(c) v2/2
v3v4
0
0.02
0.04
0 0.4 0.8
v n
27 GeV(d)
0
0.02
0.04
0 0.4 0.8
19.6 GeV(e)
0
0.02
0.04
0 0.4 0.8
|η|
14.5 GeV(f)
0
0.02
0.04
0 0.4 0.8
11.5 GeV(g)
0
0.02
0.04
0 0.4 0.8
7.7 GeV(h)
STAR Preliminary
28
0
0.1
0.2
0 1 2 3
v nAu+Au200 GeV0-40%
(a)
0
0.1
0.2
0 1 2 3
v n
62.4 GeV(b)
0
0.1
0.2
0 1 2 3
v n
39 GeV(c)v2v3v4v5
0
0.1
0.2
0 1 2 3
v n
27 GeV(d)
0
0.1
0.2
0 1 2 3
19.6 GeV(e)
0
0.1
0.2
0 1 2 3
pT(GeV/c)
14.5 GeV(f)
0
0.1
0.2
0 1 2 3
11.5 GeV(g)
0
0.1
0.2
0 1 2 3
7.7 GeV(h)
The extracted 𝑣;¦~ 𝑝� at all BES energies
𝜂 < 1and|Δ𝜂| > 0.7Transverse momentum dependence of𝑣;¦~
Ø 𝑣; 𝑝� has similar trends for different beam energies.
Ø 𝑣; 𝑝� decreases with harmonic order n.
STAR Preliminary
0
0.04
0 20 40 60
v nAu+Au
200 GeV(a)
0
0.04
0 20 40 60
v n
62.4 GeV(b)
0
0.04
0 20 40 60
v n
39 GeV(c)v2/2
v3v4v5
0
0.04
0 20 40 60
v n
27 GeV(d)
0
0.04
0 20 40 60
19.6 GeV(e)
0
0.04
0 20 40 60
Centrality%
(f) 14.5 GeV
0
0.04
0 20 40 60
11.5 GeV(g)
0
0.04
0 20 40 60
7.7 GeV(h)
The extracted𝑣;¦~ Centrality at all BES energiesCentrality dependence of𝑣;¦~
Ø 𝑣; Centrality has similar trends for different beam energies.
Ø 𝑣; Centrality decreases with harmonic order n.
STAR Preliminary
16
Ø|𝑣~���;| shows similar values to 𝑣¨ at 0.4 < 𝑝� < 0.7(𝐺𝑒𝑉/𝑐)
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 vs 𝑠JJ� at 0%-10% centrality
30
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻
𝒕
𝜂 < 1and|Δ𝜂| > 0.7Beam-energy dependence of 𝑣~���;
-0.02
-0.01
0
0.01
0.02
10 100
√sNN(GeV)
vn
Au+Au0-10%
0.4< pT < 0.7(GeV/c)veven
1v3
STAR Preliminary
Reflection
Ø|𝑣~���;| shows similar values to 𝑣¨ at 0.4 < 𝑝� < 0.7(𝐺𝑒𝑉/𝑐)
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 vs 𝑠JJ� at 0%-10% centrality
31
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻
𝒕
𝜂 < 1and|Δ𝜂| > 0.7Beam-energy dependence of 𝑣~���;
P.BożekPLB 717, 287-290 (2012)
0 50 100 150 2000
0.2
0.4
0.6
0-5%
5-10%
10-20%
20-30%
ε
2ε
3ε
1ε
partN
Øε¨ > ε~
ü 𝑣¨ has larger viscous damping effect than 𝑣~���;
-0.02
-0.01
0
0.01
0.02
10 100
√sNN(GeV)
vn
Au+Au0-10%
0.4< pT < 0.7(GeV/c)veven
1v3
STAR Preliminary
Reflection
The extracted 𝑣;¦~vs 𝑠JJ� at 0-40% centrality
Beam-energy dependence of𝑣;¦~
Ø 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
Ø 𝑣; 𝑠JJ� decreases with harmonic order n (viscous effects).
STAR Preliminary
18
0
0.01
0.02
0.03
0.04
10 100
√sNN(GeV)
(a)
vn
Au+Au0-40%
v2/2v3v4
33
Summary-I Comprehensive set of flow measurements were studied for Au+Au collision system at all BES energies with one set of
cuts.ØFor n > 1;
ü 𝑣; decreases with harmonic order n.
ØFor n = 1;
34
Summary-I Comprehensive set of flow measurements were studied for Au+Au collision system at all BES energies with one set of
cuts.ØFor n > 1;
ü 𝑣; decreases with harmonic order n.
ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ØFor n = 1;
35
Summary-I Comprehensive set of flow measurements were studied for Au+Au collision system at all BES energies with one set of
cuts.ØFor n > 1;
ü 𝑣; decreases with harmonic order n.
ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ØFor n = 1;
36
Summary-I Comprehensive set of flow measurements were studied for Au+Au collision system at all BES energies with one set of
cuts.ØFor n > 1;
ü 𝑣; decreases with harmonic order n.
ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ØFor n = 1;ü Similar characteristic behavior of 𝑣~���; 𝑝� at all energies.
37
Summary-I Comprehensive set of flow measurements were studied for Au+Au collision system at all BES energies with one set of
cuts.ØFor n > 1;
ü 𝑣; decreases with harmonic order n.
ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ØFor n = 1;ü Similar characteristic behavior of 𝑣~���; 𝑝� at all energies.
ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
38
Summary-I Comprehensive set of flow measurements were studied for Au+Au collision system at all BES energies with one set of
cuts.ØFor n > 1;
ü 𝑣; decreases with harmonic order n.
ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ØFor n = 1;ü Similar characteristic behavior of 𝑣~���; 𝑝� at all energies.
ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
ü |𝑣~���;| shows similar values to 𝑣¨ (larger viscous effect for 𝑣¨)
39
Summary-I Comprehensive set of flow measurements were studied for Au+Au collision system at all BES energies with one set of
cuts.ØFor n > 1;
ü 𝑣; decreases with harmonic order n.
ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ØFor n = 1;ü Similar characteristic behavior of 𝑣~���; 𝑝� at all energies.
ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
ü |𝑣~���;| shows similar values to 𝑣¨ (larger viscous effect for 𝑣¨)
ØMore information could be extracted from 𝑣; measurements via the acoustic ansatz
Ø 𝑣; measurements are sensitive to system shape (𝜀;), size(𝑅𝑇) and transport coefficients F
C, GC, … .
40
arXiv:1305.3341Roy A. Lacey, et al.
arXiv:1601.06001Roy A. Lacey, et al.
PRC 84, 034908 (2011)P. Staig and E. Shuryak.
PRC 88, 044915 (2013)E. Shuryak and I. Zahed
Acoustic ansatz
Ø 𝑣; measurements are sensitive to system shape (𝜀;), size(𝑅𝑇) and transport coefficients F
C, GC, … .
41
arXiv:1305.3341Roy A. Lacey, et al.
arXiv:1601.06001Roy A. Lacey, et al.
PRC 84, 034908 (2011)P. Staig and E. Shuryak.
PRC 88, 044915 (2013)E. Shuryak and I. Zahed
Acoustic ansatz
Ø Acoustic ansatz
ü Sound attenuation in the viscous matter reduces the magnitude of 𝑣;.
Ø 𝑣; measurements are sensitive to system shape (𝜀;), size(𝑅𝑇) and transport coefficients F
C, GC, … .
42
𝑆~ 𝑅𝑇 ¨~ 𝑁Uo then 𝑅𝑇~ 𝑁Uo²³
arXiv:1305.3341Roy A. Lacey, et al.
arXiv:1601.06001Roy A. Lacey, et al.
PRC 84, 034908 (2011)P. Staig and E. Shuryak.
PRC 88, 044915 (2013)E. Shuryak and I. Zahed
Acoustic ansatz
Ø Acoustic ansatz
ü Sound attenuation in the viscous matter reduces the magnitude of 𝑣;.Ø Anisotropic flow attenuation,
�´µ´∝ 𝑒�¶;� ,𝛽 ∝ F
/ ~¸�
Ø From macroscopic entropy considerations
Ø 𝑣; measurements are sensitive to system shape (𝜀;), size(𝑅𝑇) and transport coefficients F
C, GC, … .
𝒍𝒏 𝒗𝒏𝜺𝒏
∝ −𝒏𝟐 𝜷» 𝑵𝑪𝒉�𝟏𝟑 where 𝜷» ∝ 𝜼
𝒔
43
𝑆~ 𝑅𝑇 ¨~ 𝑁Uo then 𝑅𝑇~ 𝑁Uo²³
arXiv:1305.3341Roy A. Lacey, et al.
arXiv:1601.06001Roy A. Lacey, et al.
PRC 84, 034908 (2011)P. Staig and E. Shuryak.
PRC 88, 044915 (2013)E. Shuryak and I. Zahed
Acoustic ansatz
Ø Acoustic ansatz
ü Sound attenuation in the viscous matter reduces the magnitude of 𝑣;.Ø Anisotropic flow attenuation,
�´µ´∝ 𝑒�¶;� ,𝛽 ∝ F
/ ~¸�
Ø From macroscopic entropy considerations
Ø We can rewrite Eq(i)
Ø At the same centrality we have
𝒍𝒏 𝒗𝒏𝟏/𝒏
𝒗𝟐𝟏/𝟐 ∝ − 𝒏 − 𝟐 𝜷» 𝑵𝑪𝒉
�𝟏𝟑 where 𝜷» = 𝑨 𝜼𝒔 1.7
1.8
1.9
10 100⟨ N
ch ⟩1/
3
√sNN(GeV)
Au-Au0-40%
where A is constant
Ø 𝑣; measurements are sensitive to system shape (𝜀;), size(𝑅𝑇) and transport coefficients F
C, GC, … .
𝒍𝒏 𝒗𝒏𝜺𝒏
∝ −𝒏𝟐 𝜷» 𝑵𝑪𝒉�𝟏𝟑 where 𝜷» ∝ 𝜼
𝒔
44
𝑆~ 𝑅𝑇 ¨~ 𝑁Uo then 𝑅𝑇~ 𝑁Uo²³
arXiv:1305.3341Roy A. Lacey, et al.
arXiv:1601.06001Roy A. Lacey, et al.
PRC 84, 034908 (2011)P. Staig and E. Shuryak.
PRC 88, 044915 (2013)E. Shuryak and I. Zahed
Acoustic ansatz
Ø Acoustic ansatz
ü Sound attenuation in the viscous matter reduces the magnitude of 𝑣;.Ø Anisotropic flow attenuation,
�´µ´∝ 𝑒�¶;� ,𝛽 ∝ F
/ ~¸�
Ø From macroscopic entropy considerations
Ø We can rewrite Eq(i)
Ø At the same centrality we have
𝒍𝒏 𝒗𝒏𝟏/𝒏
𝒗𝟐𝟏/𝟐 ∝ − 𝒏 − 𝟐 𝜷» 𝑵𝑪𝒉
�𝟏𝟑 where 𝜷» = 𝑨 𝜼𝒔
𝒍𝒏 𝒗𝒏𝟏/𝒏
𝒗𝟐𝟏/𝟐 𝑵𝑪𝒉
𝟏𝟑(𝒏−𝟐)�𝟏= 𝜷»»
1.7
1.8
1.9
10 100⟨ N
ch ⟩1/
3
√sNN(GeV)
Au-Au0-40%
where A is constant
45
Viscous coefficient
ØThe viscous coefficient shows a non-monotonic behavior with beam-energy
𝜷»» = 𝒍𝒏 𝒗𝒏𝟏/𝒏
𝒗𝟐𝟏/𝟐 𝑵𝑪𝒉
𝟏𝟑 𝒏 − 𝟐 �𝟏 = 𝑨𝜼𝒔
STAR PreliminarySTAR Preliminary
0.4
0.8
1.2
10 100
0.4
0.8
1.2
√sNN(GeV)
(b)
β′ ′
n = 3n = 4
0
0.01
0.02
0.03
0.04
10 100
√sNN(GeV)
(a)
vn
Au+Au0-40%
v2/2v3v4
ConclusionComprehensive set of STAR measurements presented for
𝑣;(𝑝�, 𝜂, Centrality𝑎𝑛𝑑 𝑠JJ� ) for Au+Au collisions.
46
ØFor 𝑣;:ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ConclusionComprehensive set of STAR measurements presented for
𝑣;(𝑝�, 𝜂, Centrality𝑎𝑛𝑑 𝑠JJ� ) for Au+Au collisions.
47
ØFor 𝑣;:ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
ConclusionComprehensive set of STAR measurements presented for
𝑣;(𝑝�, 𝜂, Centrality𝑎𝑛𝑑 𝑠JJ� ) for Au+Au collisions.
48
ØFor 𝑣;:ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ConclusionComprehensive set of STAR measurements presented for
𝑣;(𝑝�, 𝜂, Centrality𝑎𝑛𝑑 𝑠JJ� ) for Au+Au collisions.
49
ØFor 𝑣;:ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ü |𝑣~���;| shows similar values to 𝑣¨ (larger viscous effect for 𝑣¨)
ConclusionComprehensive set of STAR measurements presented for
𝑣;(𝑝�, 𝜂, Centrality𝑎𝑛𝑑 𝑠JJ� ) for Au+Au collisions.
50
ØFor 𝑣;:ü 𝑣; 𝑝�, 𝜂, Centrality indicates a similar trend for different beam energies.
ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �~
ü 𝑣; 𝑠JJ� shows a monotonic increase with beam-energy.
ü |𝑣~���;| shows similar values to 𝑣¨ (larger viscous effect for 𝑣¨)
The viscous coefficient (𝑨 𝜼𝒔), is non-monotonic versus
the collision-energy with an apparent minimum near ~15 GeV.
51
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