2
Directed flow
2
The rapidity-odd directed flow v1πππ develops
along the direction of the impact parameter
and is an odd function of pseudorapidity.
The rapidity-even directed flow v1ππ£ππ 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 v1ππ£ππ is sensitive to:
Initial-state eccentricity & its fluctuations
Transport coefficients ( Ξ€π π , etc) but with less
sensitivity than for higher order harmonics.
The v1ππ£ππ 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 π ππ β 200 GeV;
Au + AuU + U Cu + Au Cu + Cu d + Au p + Au
3
STAR Detector at RHIC
TPC detector covers |π| < 1
Collected data for Au+Au at different π ππ
Au + Au
Flow
π―π©π»
π«ππππ
π΄ππππππππͺπππππππππππ
Diβjets
Two particle correlation function πΆr Ξπ ,
πΆπ Ξπ = ππ/πΞπ and π£πn =ΟΞπ πΆπ Ξπ cos(π Ξπ)
ΟΞπ πΆπ Ξπ
πΊππππ β ππππππ³πππ β πππππ
π > 1π£ππ = π£π
ππ£ππ + πΏπ βπππ‘
π = 1π£11 = π£1
ππ£1π + πΏππππ
Non-flow
Azimuthal anisotropy measurements
Correlation
function
4
Charge
Flow
Non-flo
w
Non-flow suppression is needed
π£11 = π£1ππ£1
π + πΏππππ π = 1
π£11 πππ , ππ
π‘ = π£1ππ£ππ ππ
π π£1ππ£ππ ππ
π‘ β πΆ πππ ππ
π‘
Good simultaneous fit (π2
πππ~ 1.1) obtained with fit function Eq(1)
v11characteristic behavior gives a good constraint for ππππππ π©π extraction
5
arXiv:1203.0931
arXiv:1203.3410
arXiv:1208.1874
arXiv:1208.1887
arXiv:1211.7162
1
Long range non-flow suppression
π£11 Eq(1) represents NxM matrix which we fit with N+1 parameters
π΄πππππππ
πͺππππππππππ
π
π³πππ β πππππ
-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)πͺ β ΰ΅π < ππ»
π >< π΄πππ >
STAR Preliminary
The characteristic behavior of π£1ππ£ππ ππ agrees with hydrodynamic
expectations.
The extracted ππππππ ππ» at 200 GeV and 0%-10% centrality
6
π―ππ ππ»π, ππ»
π = ππππππ ππ»
π ππππππ ππ»
π β πͺ ππ»π ππ»
π
π < 1 and |Ξπ| > 0.7Long range non-flow suppression
π΄πππππππ
πͺππππππππππ
π
π³πππ β πππππ
Dipolar nature requires that 0β ππ
πππππ π£1
ππ£ππ= 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
π£1ππ£ππ ππ shows a weak centrality
dependence
The extracted ππππππ ππ» and the momentum conservation
parameter πΆ at 200 GeV
7
π―ππ ππ»π, ππ»
π = ππππππ ππ»
π ππππππ ππ»
π β πͺ ππ»π ππ»
π
π < 1 and |Ξπ| > 0.7Long range non-flow suppression
π΄πππππππ
πͺππππππππππ
π
π³πππ β πππππ
STAR Preliminary
0 0 0.01
0.02
0 0.004
0.008
C
1/<Mult>
Au+Au200 GeV
The momentum conservation
parameter πΆ scales as < π΄πππ >βπ
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 π£1ππ£ππ ππ data shows
π£1ππ£ππ ππ centrality dependent
STAR Preliminary
πͺ β ΰ΅π < ππ»π >< π΄πππ >
8
Rapidity-even dipolar flow
ππππππ πΆπππ‘
ππππππ π ππ
ππππππ ππ»
Similar characteristic behavior of π£1ππ£ππ ππ at all energies
π£1ππ£ππ ππ agrees with hydrodynamic calculations at 200 GeV
The extracted π£1ππ£ππ ππ at all BES energies
9
π < 1 and |Ξπ| > 0.7Beam energy dependence of π£1
ππ£ππ
STAR Preliminary
π―ππ ππ»π, ππ»
π = ππππππ ππ»
π ππππππ ππ»
π β πͺ ππ»π ππ»
π
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>
Β΄10 2
For different energies
π£1ππ£ππ increases as collisions become more peripheral
The extracted ππππππ πΆπππ‘ and the momentum conservation parameter
at different beam energies
10
π―ππ ππ»π, ππ»
π = ππππππ ππ»
π ππππππ ππ»
π β πͺ ππ»π ππ»
π
π < 1 and |Ξπ| > 0.7Beam energy dependence of π£1
ππ£ππ
STAR Preliminary
0
0.01 0 0.01
0.02
0 0.01
C(ΓsNN)
1/<Mult>
(b)
πͺ β ΰ΅π < ππ»π >< π΄πππ >
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
π£1ππ£ππ shows a weak centrality dependence
Momentum conservation parameter πΆ scales as ππ’ππ‘ β1
|π£1ππ£ππ| shows similar values to π£3 at 0.4 < ππ < 0.7(πΊππ/π)
The extracted ππππππ vs π ππ at 0%-10% centrality
11
π―ππ ππ»π, ππ»
π = ππππππ ππ»
π ππππππ ππ»
π β πͺ ππ»π ππ»
π
π < 1 and |Ξπ| > 0.7Beam energy dependence of π£1
ππ£ππ
STAR Preliminary
P.BoΕΌek
PLB 717 287-290 (2012)
-0.02
-0.01 0
0.01
0.02
10 100
ΓsNN (GeV)
vn
Au+Au0%-10%
0.4< pT < 0.7(GeV/c)
v even1v3
Ξ΅3 > Ξ΅1
π£3 has larger viscous effect than π£1ππ£ππ
12
ππππππ ππΆβ
ππππππ ππ»
Rapidity-even dipolar flow
Au + AuU + U Cu + Au Cu + Cu d + Au p + Au
π£π measurements for different systems are sensitive to system shape (νπ),
dimensionless size (π π) and transport coefficients Ξ·
s,ΞΆ
s, β¦ .
πππππΊπ
β βπ¨πΌ
ππ΅πͺπ
βπ/π
Even Harmonic ππ Odd Harmonic ππAπ‘ π‘βπ π ππππ
π and ππΆβ
β1/3
πππ πππππ ππ
πΊπ + β¦ πΊπ βπ
π΅
PRC 88, 044915 (2013)E. Shuryak and I. Zahed
πΊπ scaling is needed
Expectations Odd harmonics are system
independent
Even harmonics are system
dependent13
π£π/βπ β πβ π΄ (ππ π2
π π) π ~ π π 3 ~ ππΆβ then π π~ ππΆβ1/3
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)
π£1ππ£ππ vs ππ at different ππΆβ for all systems
The efficiency corrections for NCh have applied for Au+Au and U+U collisions.
Within the experimental uncertainties π£1ππ£ππ shows similar trends and
magnitudes for all systems.
π£1ππ£ππ is system independent.
14
STAR Preliminary
π£1ππ£ππ for different systems
π < 1 and |Ξπ| > 0.7πππππΊπ
β βπ¨ πΌ/π ππΆββπ/π
0 0.1
0 1
2
veven1Γ‘ Nch Γ± = 140 (a) 0 0.1
0 1
2
vev en
1
Γ‘ Nch Γ± = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1
0 1
2
vev en1
Γ‘ Nch Γ± = 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
veven1Γ‘ Nch Γ± = 140 (a) 0 0.1 0
1 2
veven1Γ‘ Nch Γ± = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1 0 1
2
veven1Γ‘ Nch Γ± = 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
veven1Γ‘ Nch Γ± = 140 (a) 0 0.1 0
1 2
veven1Γ‘ Nch Γ± = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1 0 1
2
veven1Γ‘ Nch Γ± = 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
veven1Γ‘ Nch Γ± = 140 (a) 0 0.1 0
1 2
veven1Γ‘ Nch Γ± = 70 (b)U+UAu+AuCu+AuCu+Cu
0 0.1 0 1
2
veven1Γ‘ Nch Γ± = 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)
πT (GeV/c)
15
π£1ππ£ππ vs ππΆβ for all systems
ππ ππ¨π« ππ’ππππ«ππ§π π¬π²π¬πππ¦π¬
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
Γ‘ Nch Γ±
(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
Γ‘ Nch Γ± -1
Momentum conservation
parameter πΆ scales as
NChβ1for all systems
ππΆβ
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
Γ‘ Nch Γ±
(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
CΓ‘ Nch Γ± -1
STAR Preliminary
|π£1ππ£ππ|
π < 1 and |Ξπ| > 0.7πππππΊπ
β βπ¨ πΌ/π ππΆββπ/π
The efficiency corrections for NCh have applied for Au+Au and U+U collisions.
Within the experimental uncertainties π£1ππ£ππ shows similar trends and
magnitudes for all systems.
π£1ππ£ππ is system independent.
16
Odd harmonics are system
independent.
Even harmonics are system
dependent with less dependence
for higher harmonics.
π£πfor large systems π΄ + π΅ππ
πππΊπ
β βπ¨ πΌ/π ππΆββπ/π π£π vs ππ at ππΆβ = 270
0
0.1
0
1
2
3
veven1
Γ‘ N
Ch Γ± =
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
π < 1 and |Ξπ| > 0.7
ConclusionComprehensive set of STAR measurements presented for
π£1ππ£ππ(ππ, Cent% and π ππ) for several collision systems.
Within the experimental uncertainties, the similar trends and
magnitudes of the measured π£1ππ£ππ for different colliding systems at
π ππ ~ 200 πΊππ suggest a comparable viscous coefficient AΞ·
π
17
For π΄π’ + π΄π’ beam energy scan π£1
ππ£ππ shows a weak dependence on centrality and beam energy
Within the experimental uncertainties |π£1ππ£ππ|( π ππ) shows a similar
magnitude to π£3 suggesting that π£3 has larger viscous effect than π£1ππ£ππ
For different systems at similar multiplicity (200 πΊππ) Within the experimental uncertainties π£1
ππ£ππ shows similar trends and
magnitudes for all systems
π£1ππ£ππ is system independent.
18