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2
Directed flow
2
The rapidity-odd directed flow v1𝑜𝑑𝑑 develops
along the direction of the impact parameter
and is an odd function of pseudorapidity.
The rapidity-even directed flow v1𝑒𝑣𝑒𝑛 stems
from initial-state fluctuations acting in
concert with hydrodynamic-like expansion
Dip
ole asy
mm
etry
STAR, PRL 101 252301 (2008)
The magnitude of v1𝑒𝑣𝑒𝑛 is sensitive to:
Initial-state eccentricity & its fluctuations
Transport coefficients ( Τ𝜂 𝑠 , etc) but with less
sensitivity than for higher order harmonics.
The v1𝑒𝑣𝑒𝑛 constitutes a new set of experimental
constraints that can help to:
Differentiate between initial-state models
Pin down the temperature dependence of the
transport coefficients.
PRL 108, 252302 (2012)
Collected data for different systems at 𝑠𝑁𝑁 ≈ 200 GeV;
Au + AuU + U Cu + Au Cu + Cu d + Au p + Au
3
STAR Detector at RHIC
TPC detector covers |𝜂| < 1
Collected data for Au+Au at different 𝑠𝑁𝑁
Au + Au
Flow
𝑯𝑩𝑻
𝑫𝒆𝒄𝒂𝒚
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏
Di−jets
Two particle correlation function 𝐶r Δ𝜑 ,
𝐶𝑟 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑 and 𝑣𝑛n =σΔ𝜑 𝐶𝑟 Δ𝜑 cos(𝑛 Δ𝜑)
σΔ𝜑 𝐶𝑟 Δ𝜑
𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
𝑛 > 1𝑣𝑛𝑛 = 𝑣𝑛
𝑎𝑣𝑛𝑏 + 𝛿𝑠ℎ𝑜𝑟𝑡
𝑛 = 1𝑣11 = 𝑣1
𝑎𝑣1𝑏 + 𝛿𝑙𝑜𝑛𝑔
Non-flow
Azimuthal anisotropy measurements
Correlation
function
4
Charge
Flow
Non-flo
w
Non-flow suppression is needed
𝑣11 = 𝑣1𝑎𝑣1
𝑏 + 𝛿𝑙𝑜𝑛𝑔 𝑛 = 1
𝑣11 𝑝𝑇𝑎 , 𝑝𝑇
𝑡 = 𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇
𝑎 𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇
𝑡 − 𝐶 𝑝𝑇𝑎 𝑝𝑇
𝑡
Good simultaneous fit (𝜒2
𝑛𝑑𝑓~ 1.1) obtained with fit function Eq(1)
v11characteristic behavior gives a good constraint for 𝒗𝟏𝒆𝒗𝒆𝒏 𝐩𝐓 extraction
5
arXiv:1203.0931
arXiv:1203.3410
arXiv:1208.1874
arXiv:1208.1887
arXiv:1211.7162
1
Long range non-flow suppression
𝑣11 Eq(1) represents NxM matrix which we fit with N+1 parameters
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎
𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐
𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
-1 0 1 2 1 2 3
v11
x10 -3Au+Au0%-5%200 GeV
(a) 0.2 < p aT < 0.6 (GeV/c)
-1 0 1 2 1 2 3
v1 1
1.0 < p aT < 1.4 (GeV/c)
(b)
-1 0 1 2 1 2 3
v1 1
p bT (GeV/c) 1.4 < p aT < 1.8 (GeV/c)
(c)
-1 0 1 2 1 2 3
v1 1
1.8 < p aT < 2.6 (GeV/c)
(d)𝑪 ∝ ൗ𝟏 < 𝒑𝑻
𝟐 >< 𝑴𝒖𝒍𝒕 >
STAR Preliminary
The characteristic behavior of 𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇 agrees with hydrodynamic
expectations.
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻 at 200 GeV and 0%-10% centrality
6
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻
𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪 𝒑𝑻𝒂 𝒑𝑻
𝒕
𝜂 < 1 and |Δ𝜂| > 0.7Long range non-flow suppression
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎
𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐
𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
Dipolar nature requires that 0∞ 𝑑𝑁
𝑑𝑝𝑇𝑝𝑇 𝑣1
𝑒𝑣𝑒𝑛= 0
0
0.04
0.08 0 1
2 3
veven1
pT (GeV/c)
Au+Au200 GeV0%-10%
HydroSTAR Preliminary
Hydro
E.Retinskaya , et al.
PRL 108, 252302 (2012)
The characteristic behavior of
𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇 shows a weak centrality
dependence
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻 and the momentum conservation
parameter 𝐶 at 200 GeV
7
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻
𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪 𝒑𝑻𝒂 𝒑𝑻
𝒕
𝜂 < 1 and |Δ𝜂| > 0.7Long range non-flow suppression
𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎
𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐
𝒏
𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆
STAR Preliminary
0 0 0.01
0.02
0 0.004
0.008
C
1/<Mult>
Au+Au200 GeV
The momentum conservation
parameter 𝐶 scales as < 𝑴𝒖𝒍𝒕 >−𝟏
0
0.04
0.08
0.12 0 1
2 3
veven1
pT (GeV/c)
Au+Au200 GeV
0%-10%
10%-20%
20%-30%
30%-40%
Fit to 𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇 data shows
𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇 centrality dependent
STAR Preliminary
𝑪 ∝ ൗ𝟏 < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 >
8
Rapidity-even dipolar flow
𝒗𝟏𝒆𝒗𝒆𝒏 𝐶𝑒𝑛𝑡
𝒗𝟏𝒆𝒗𝒆𝒏 𝑠𝑁𝑁
𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
Similar characteristic behavior of 𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇 at all energies
𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇 agrees with hydrodynamic calculations at 200 GeV
The extracted 𝑣1𝑒𝑣𝑒𝑛 𝑝𝑇 at all BES energies
9
𝜂 < 1 and |Δ𝜂| > 0.7Beam energy dependence of 𝑣1
𝑒𝑣𝑒𝑛
STAR Preliminary
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻
𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪 𝒑𝑻𝒂 𝒑𝑻
𝒕
Hydro
E.Retinskaya , et al.
PRL 108, 252302 (2012)
0 0.1
0 1
2
veven1
(a)Au+Au200 GeV0%-10%
Hydro(h/s = 0.16)
0
0.1
0 1
2
veven1
62.4 GeV
(b)
0 0.1
0 1
2
veven1
(c)39 GeV
0 0.1
0 1
2
veven1
(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
1/<Mult>
´10 2
For different energies
𝑣1𝑒𝑣𝑒𝑛 increases as collisions become more peripheral
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝐶𝑒𝑛𝑡 and the momentum conservation parameter
at different beam energies
10
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻
𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪 𝒑𝑻𝒂 𝒑𝑻
𝒕
𝜂 < 1 and |Δ𝜂| > 0.7Beam energy dependence of 𝑣1
𝑒𝑣𝑒𝑛
STAR Preliminary
0
0.01 0 0.01
0.02
0 0.01
C(ÖsNN)
1/<Mult>
(b)
𝑪 ∝ ൗ𝟏 < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 >
STAR Preliminary
0
0.01
0.02
10 20
30 40
50 60
70
|v1even
|
Centrality%
(a)Au+Au
0.4 < pT < 0.7(GeV/c)
200 GeV39 GeV
19.6 GeV
𝑣1𝑒𝑣𝑒𝑛 shows a weak centrality dependence
Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 −1
|𝑣1𝑒𝑣𝑒𝑛| shows similar values to 𝑣3 at 0.4 < 𝑝𝑇 < 0.7(𝐺𝑒𝑉/𝑐)
The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 vs 𝑠𝑁𝑁 at 0%-10% centrality
11
𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻
𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
𝒕 − 𝑪 𝒑𝑻𝒂 𝒑𝑻
𝒕
𝜂 < 1 and |Δ𝜂| > 0.7Beam energy dependence of 𝑣1
𝑒𝑣𝑒𝑛
STAR Preliminary
P.Bożek
PLB 717 287-290 (2012)
-0.02
-0.01 0
0.01
0.02
10 100
ÖsNN (GeV)
vn
Au+Au0%-10%
0.4< pT < 0.7(GeV/c)
v even1v3
ε3 > ε1
𝑣3 has larger viscous effect than 𝑣1𝑒𝑣𝑒𝑛
12
𝒗𝟏𝒆𝒗𝒆𝒏 𝑁𝐶ℎ
𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻
Rapidity-even dipolar flow
Au + AuU + U Cu + Au Cu + Cu d + Au p + Au
𝑣𝑛 measurements for different systems are sensitive to system shape (휀𝑛),
dimensionless size (𝑅𝑇) and transport coefficients η
s,ζ
s, … .
𝒍𝒏𝒗𝒏𝜺𝒏
∝ −𝑨𝜼
𝒔𝑵𝑪𝒉
−𝟏/𝟑
Even Harmonic 𝒗𝟐 Odd Harmonic 𝒗𝟑A𝑡 𝑡ℎ𝑒 𝑠𝑎𝑚𝑒𝜂
𝑠and 𝑁𝐶ℎ
−1/3
𝒗𝒏𝒅𝒓𝒊𝒗𝒆𝒏 𝒃𝒚
𝜺𝒏 + … 𝜺𝟑 ∝𝟏
𝑵
PRC 88, 044915 (2013)E. Shuryak and I. Zahed
𝜺𝟐 scaling is needed
Expectations Odd harmonics are system
independent
Even harmonics are system
dependent13
𝑣𝑛/∈𝑛 ∝ 𝑒− 𝐴 (𝜂𝑠𝑛2
𝑅𝑇) 𝑆 ~ 𝑅𝑇 3 ~ 𝑁𝐶ℎ then 𝑅𝑇~ 𝑁𝐶ℎ1/3
B.Schenke , et al.
PRC 89, 064908 (2014)
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
B.Schenke , et al.
PRC 89, 064908 (2014)
𝑣1𝑒𝑣𝑒𝑛 vs 𝑝𝑇 at different 𝑁𝐶ℎ for all systems
The efficiency corrections for NCh have applied for Au+Au and U+U collisions.
Within the experimental uncertainties 𝑣1𝑒𝑣𝑒𝑛 shows similar trends and
magnitudes for all systems.
𝑣1𝑒𝑣𝑒𝑛 is system independent.
14
STAR Preliminary
𝑣1𝑒𝑣𝑒𝑛 for different systems
𝜂 < 1 and |Δ𝜂| > 0.7𝒍𝒏𝒗𝒏𝜺𝒏
∝ −𝑨 𝜼/𝒔 𝑁𝐶ℎ−𝟏/𝟑
0 0.1
0 1
2
veven1á Nch ñ = 140 (a) 0 0.1
0 1
2
vev en
1
á Nch ñ = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1
0 1
2
vev en1
á Nch ñ = 25 (c)U+UAu+AuCu+AuCu+Cud+Aup+Au
0 0.1
0 1
2
v3
(d) 0 0.1 0 1
2
v3
(e)
0 0.1 0 1
2
v3
(f)
0 0.2
0 1
2
v2
(g) 0 0.2 0 1
2
v2
(h)
0 0.2 0 1
2
v2
(i)
0 0.4 0 1 2 v2/e2
(j)
0 0.4 0 1 2 v2/e2
(k)pT (GeV/c)
0 0.4 0 1 2 v2/e2
(l) 0 0.1
0 1
2
veven1á Nch ñ = 140 (a) 0 0.1 0
1 2
veven1á Nch ñ = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1 0 1
2
veven1á Nch ñ = 25 (c)U+UAu+AuCu+AuCu+Cud+Aup+Au
0 0.1
0 1
2
v3 (d) 0 0.1 0 1
2
v3 (e) 0 0.1 0 1
2
v3 (f)
0 0.2
0 1
2
v2 (g) 0 0.2 0 1
2
v2 (h) 0 0.2 0 1
2
v2 (i)
0 0.4 0 1 2 v2/e2 (j) 0 0.4 0 1 2 v2 /e2 (k)pT (GeV/c)
0 0.4 0 1 2 v2 /e2 (l)
0 0.1
0 1
2
veven1á Nch ñ = 140 (a) 0 0.1 0
1 2
veven1á Nch ñ = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1 0 1
2
veven1á Nch ñ = 25 (c)U+UAu+AuCu+AuCu+Cud+Aup+Au
0 0.1
0 1
2
v3 (d) 0 0.1 0 1
2
v3 (e) 0 0.1 0 1
2
v3 (f)
0 0.2
0 1
2
v2 (g) 0 0.2 0 1
2
v2 (h) 0 0.2 0 1
2
v2 (i)
0 0.4 0 1 2 v2/e2 (j) 0 0.4 0 1 2 v2 /e2 (k)pT (GeV/c)
0 0.4 0 1 2 v2 /e2 (l)
0 0.1
0 1
2
veven1á Nch ñ = 140 (a) 0 0.1 0
1 2
veven1á Nch ñ = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1 0 1
2
veven1á Nch ñ = 25 (c)U+UAu+AuCu+AuCu+Cud+Aup+Au
0 0.1
0 1
2
v3 (d) 0 0.1 0 1
2
v3 (e) 0 0.1 0 1
2
v3 (f)
0 0.2
0 1
2
v2 (g) 0 0.2 0 1
2
v2 (h) 0 0.2 0 1
2
v2 (i)
0 0.4 0 1 2 v2/e2 (j) 0 0.4 0 1 2 v2 /e2 (k)pT (GeV/c)
0 0.4 0 1 2 v2 /e2 (l)
𝑝T (GeV/c)
15
𝑣1𝑒𝑣𝑒𝑛 vs 𝑁𝐶ℎ for all systems
𝒗𝒏 𝐟𝐨𝐫 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭 𝐬𝐲𝐬𝐭𝐞𝐦𝐬
0.02
0.04
0.06
0.08
0 175
350 525
700
0.02
0.04
0.06
0.08(c)
v20.2 < pT (GeV/c) < 4
U+UAu+AuCu+AuCu+Cu
d+Aup+Au
0.01
0.02
0 175
350 525
700
á Nch ñ
(b)
v30.2 < pT (GeV/c) < 4
0.01
0.02
0 175
350 525
700
vn
(a)
|v even1 |
0.2 < pT (GeV/c) < 0.9
0
0.01 0 0.02
0.04
C
á Nch ñ -1
Momentum conservation
parameter 𝐶 scales as
NCh−1for all systems
𝑁𝐶ℎ
0.02 0.04 0.06 0.08 0 175 350 525 700 0.02 0.04 0.06 0.08(c)v20.2 < pT (GeV/c) < 4 U+UAu+AuCu+AuCu+Cud+Aup+Au
0.01 0.02 0 175 350 525 700
á Nch ñ
(b)v30.2 < pT (GeV/c) < 4
0.01 0.02 0 175 350 525 700
vn (a)|v even1 |0.2 < pT (GeV/c) < 0.9
0 0.01 0 0.02 0.04
Cá Nch ñ -1
STAR Preliminary
|𝑣1𝑒𝑣𝑒𝑛|
𝜂 < 1 and |Δ𝜂| > 0.7𝒍𝒏𝒗𝒏𝜺𝒏
∝ −𝑨 𝜼/𝒔 𝑁𝐶ℎ−𝟏/𝟑
The efficiency corrections for NCh have applied for Au+Au and U+U collisions.
Within the experimental uncertainties 𝑣1𝑒𝑣𝑒𝑛 shows similar trends and
magnitudes for all systems.
𝑣1𝑒𝑣𝑒𝑛 is system independent.
16
Odd harmonics are system
independent.
Even harmonics are system
dependent with less dependence
for higher harmonics.
𝑣𝑛for large systems 𝐴 + 𝐵𝒍𝒏
𝒗𝒏𝜺𝒏
∝ −𝑨 𝜼/𝒔 𝑁𝐶ℎ−𝟏/𝟑 𝑣𝑛 vs 𝑝𝑇 at 𝑁𝐶ℎ = 270
0
0.1
0
1
2
3
veven1
á N
Ch ñ =
270
(a)
U+
UA
u+
Au
Cu+
Au
0
0.1
0.2
0
1
2
3
v2
(b)
0
0.1
0
1
2
3
v3
(c)
0
0.05
0
1
2
3
v4
pT(G
eV
/c)
(d)
STAR Preliminary
𝜂 < 1 and |Δ𝜂| > 0.7
ConclusionComprehensive set of STAR measurements presented for
𝑣1𝑒𝑣𝑒𝑛(𝑝𝑇, Cent% and 𝑠𝑁𝑁) for several collision systems.
Within the experimental uncertainties, the similar trends and
magnitudes of the measured 𝑣1𝑒𝑣𝑒𝑛 for different colliding systems at
𝑠𝑁𝑁 ~ 200 𝐺𝑒𝑉 suggest a comparable viscous coefficient Aη
𝑠
17
For 𝐴𝑢 + 𝐴𝑢 beam energy scan 𝑣1
𝑒𝑣𝑒𝑛 shows a weak dependence on centrality and beam energy
Within the experimental uncertainties |𝑣1𝑒𝑣𝑒𝑛|( 𝑠𝑁𝑁) shows a similar
magnitude to 𝑣3 suggesting that 𝑣3 has larger viscous effect than 𝑣1𝑒𝑣𝑒𝑛
For different systems at similar multiplicity (200 𝐺𝑒𝑉) Within the experimental uncertainties 𝑣1
𝑒𝑣𝑒𝑛 shows similar trends and
magnitudes for all systems
𝑣1𝑒𝑣𝑒𝑛 is system independent.
18