Niseem MagdySTAR Collaboration

Stony Brook University

niseem.abdelrahman@stonybrook.edu

2

Directed flow

2

Ø The rapidity-odd directed flow v"#$$ develops along the direction of the impact parameter and is an odd function of pseudorapidity.

Ø The rapidity-even directed flow v"%&%'stems from initial-state fluctuations acting in concert with hydrodynamic-like expansion

Dipole asym

metry

STAR, PRL 101 252301 (2008)

Ø The magnitude of v"%&%'is sensitive to:ü Initial-state eccentricity & its fluctuationsü Transport coefficients () *⁄ , etc) but with less

sensitivity than for higher order harmonics.

Ø The v"%&%'constitutes a new set of experimental constraints that can help to:ü Differentiate between initial-state modelsü Pin down the temperature dependence of the

transport coefficients.

PRL 108, 252302 (2012)

Ø Collected data for different systems at 𝑠--� ≈ 200 GeV;

Au + AuU + U Cu + Au Cu + Cu d + Au p + Au

3

STAR Detector at RHIC

Ø TPC detector covers |𝜂| < 1

Ø Collected data for Au+Au at different 𝑠--�

Au + Au

Flow

𝑯𝑩𝑻

𝑫𝒆𝒄𝒂𝒚

𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏

Di−jets

Two particle correlation function 𝐶r Δ𝜑 ,

𝐶𝑟 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑 and 𝑣'_ = ∑ ab cd efg('cd)�jk

∑ ab cd�jk

𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆

𝑛 > 1𝑣'' = 𝑣's𝑣't +𝛿*v#bw

𝑛 = 1𝑣"" = 𝑣"s𝑣"t +𝛿x#'y

Non-flow

Azimuthal anisotropy measurements Correlation

function

4Charge

Flow

Non-flow

Non-flow suppression is needed

𝑣"" = 𝑣"s𝑣"t +𝛿x#'y𝑛 = 1

𝑣"" 𝑝{s, 𝑝{w = 𝑣"%&%' 𝑝{

s 𝑣"%&%' 𝑝{

w − 𝐶𝑝{s𝑝{

w

ØGood simultaneous fit ( |}

'$~~1.1) obtained with fit function Eq(1)

Øv""characteristic behavior gives a good constraint for 𝒗𝟏𝒆𝒗𝒆𝒏 𝐩𝐓 extraction5

arXiv:1203.0931arXiv:1203.3410arXiv:1208.1874arXiv:1208.1887arXiv:1211.7162

1

Long range non-flow suppression

𝑣"" Eq(1) represents NxM matrix which we fit with N+1 parameters

𝑴𝒐𝒎

𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏

𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆

-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)

𝑪 ∝ 𝟏 < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 >�

STAR Preliminary

ØThe characteristic behavior of 𝑣"%&%' 𝑝{ agrees with hydrodynamic expectations.

The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻 at 200 GeV and 0%-10% centrality

6

𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻

𝒕

𝜂 < 1and|Δ𝜂| > 0.7Long range non-flow suppression

𝑴𝒐𝒎

𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏

𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆

Dipolar nature requires that ∫ $-$��

𝑝{ 𝑣"%&%' = 0��

0

0.04

0.08

0 1 2 3

veven

1

pT(GeV/c)

Au+Au200 GeV0%-10%

HydroSTAR Preliminary

HydroE.Retinskaya , et al.

PRL 108, 252302 (2012)

ØThe characteristic behavior of 𝑣"%&%' 𝑝{ shows a weak centrality dependence

The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻 and the momentum conservation parameter 𝐶 at 200 GeV

7

𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻

𝒕

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 ∝ 𝟏 < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 >�

8

Rapidity-even dipolar flow

𝒗𝟏𝒆𝒗𝒆𝒏 𝐶𝑒𝑛𝑡

𝒗𝟏𝒆𝒗𝒆𝒏 𝑠--�

𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

ØSimilar characteristic behavior of 𝑣"%&%' 𝑝{ at all energies

Ø𝑣"%&%' 𝑝{ agrees with hydrodynamic calculations at 200 GeV

The extracted 𝑣"%&%' 𝑝{ at all BES energies

9

𝜂 < 1and|Δ𝜂| > 0.7Beam energy 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

1/<Mult>

×102

ØFor different energies

ü 𝑣"%&%' increases as collisions become more peripheral

The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 𝐶𝑒𝑛𝑡 and the momentum conservation parameter at different beam energies

10

𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻

𝒕

𝜂 < 1and|Δ𝜂| > 0.7Beam energy dependence of 𝑣"%&%'

STAR Preliminary

0

0.01

0 0.01 0.02

0

0.01

C(√

s NN

)

1/<Mult>

(b)

𝑪 ∝ 𝟏 < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 >�

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

ü 𝑣"%&%' shows a weak centrality dependence

ü Momentum conservation parameter 𝐶 scales as 𝑀𝑢𝑙𝑡 �"

Ø|𝑣"%&%'| shows similar values to 𝑣� at 0.4 < 𝑝{ < 0.7(𝐺𝑒𝑉/𝑐)

The extracted 𝒗𝟏𝒆𝒗𝒆𝒏 vs 𝑠--� at 0%-10% centrality

11

𝐯𝟏𝟏 𝒑𝑻𝒂, 𝒑𝑻𝒕 = 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒂 𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

𝒕 − 𝑪𝒑𝑻𝒂𝒑𝑻

𝒕

𝜂 < 1and|Δ𝜂| > 0.7Beam energy dependence of 𝑣"%&%'

STAR Preliminary

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-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

Øε� > ε"

ü 𝑣� has larger viscous effect than 𝑣"%&%'

12

𝒗𝟏𝒆𝒗𝒆𝒏 𝑁av𝒗𝟏𝒆𝒗𝒆𝒏 𝒑𝑻

Rapidity-even dipolar flow

Au + AuU + U Cu + Au Cu + Cu d + Au p + Au

Ø 𝑣' measurements for different systems are sensitive to system shape (𝜀'), dimensionlesssize(𝑅𝑇) and transport coefficients §

g, ¨g, … .

𝒍𝒏𝒗𝒏𝜺𝒏

∝ −𝑨𝜼𝒔 𝑵𝑪𝒉 �𝟏/𝟑

Even Harmonic 𝒗𝟐 Odd Harmonic 𝒗𝟑A𝑡𝑡ℎ𝑒𝑠𝑎𝑚𝑒 )*and 𝑁av �"/�

𝒗𝒏 𝒅𝒓𝒊𝒗𝒆𝒏𝒃𝒚

𝜺𝒏 +… 𝜺𝟑 ∝𝟏𝑵�

PRC 88, 044915 (2013)E. Shuryak and I. Zahed

𝜺𝟐 scalingisneeded

ExpectationsØ Odd harmonics are system

independent

Ø Even harmonics are system

dependent13

𝑣'/∈'∝ 𝑒�¹()*

'}º{) 𝑆~ 𝑅𝑇 �~ 𝑁av then 𝑅𝑇~ 𝑁av "/�

B.Schenke , et al.PRC89, 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.PRC89, 064908(2014)

𝑣"%&%'vs𝑝{ at different 𝑁av for all systems

Ø The efficiency corrections for NÃÄ have applied for Au+Au and U+U collisions.Ø Within the experimental uncertainties 𝑣"%&%'shows similar trends and

magnitudes for all systems.Ø 𝑣"%&%' is system independent.

14

STAR Preliminary

𝑣"%&%'fordifferentsystems𝜂 < 1and|Δ𝜂| > 0.7𝒍𝒏

𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁av �𝟏/𝟑

0

0.1

0 1 2

vev

en

1

⟨ Nch ⟩ = 140

(a)

0

0.1

0 1 2

vev

en

1

⟨ Nch ⟩ = 70

(b)U+UAu+AuCu+AuCu+Cu

0

0.1

0 1 2

vev

en

1

⟨ Nch ⟩ = 25

(c)U+UAu+AuCu+AuCu+Cu

d+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/ε

2

(j)

0

0.4

0 1 2

v2/ε

2

(k)

pT(GeV/c)

0

0.4

0 1 2

v2/ε

2

(l)

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 140

(a)

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 70

(b)U+UAu+AuCu+AuCu+Cu

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 25

(c)U+UAu+AuCu+AuCu+Cu

d+Aup+Au

0

0.1

0 1 2

v 3

(d)

0

0.1

0 1 2

v 3

(e)

0

0.1

0 1 2

v 3

(f)

0

0.2

0 1 2

v 2

(g)

0

0.2

0 1 2

v 2

(h)

0

0.2

0 1 2

v 2

(i)

0

0.4

0 1 2

v 2/ε

2

(j)

0

0.4

0 1 2

v 2/ε

2

(k)

pT(GeV/c)

0

0.4

0 1 2

v 2/ε

2

(l)

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 140

(a)

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 70

(b)U+UAu+AuCu+AuCu+Cu

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 25

(c)U+UAu+AuCu+AuCu+Cu

d+Aup+Au

0

0.1

0 1 2

v 3

(d)

0

0.1

0 1 2

v 3

(e)

0

0.1

0 1 2

v 3

(f)

0

0.2

0 1 2

v 2

(g)

0

0.2

0 1 2

v 2

(h)

0

0.2

0 1 2

v 2

(i)

0

0.4

0 1 2

v 2/ε

2(j)

0

0.4

0 1 2

v 2/ε

2

(k)

pT(GeV/c)

0

0.4

0 1 2

v 2/ε

2

(l)

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 140

(a)

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 70

(b)U+UAu+AuCu+AuCu+Cu

0

0.1

0 1 2

veven

1

⟨ Nch ⟩ = 25

(c)U+UAu+AuCu+AuCu+Cu

d+Aup+Au

0

0.1

0 1 2

v 3(d)

0

0.1

0 1 2

v 3

(e)

0

0.1

0 1 2

v 3

(f)

0

0.2

0 1 2

v 2

(g)

0

0.2

0 1 2

v 2

(h)

0

0.2

0 1 2

v 2

(i)

0

0.4

0 1 2

v 2/ε

2

(j)

0

0.4

0 1 2

v 2/ε

2

(k)

pT(GeV/c)

0

0.4

0 1 2

v 2/ε

2

(l)

𝑝Æ(GeV/c)

15

𝑣"%&%' vs 𝑁av for all systems

𝒗𝒏𝐟𝐨𝐫𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭𝐬𝐲𝐬𝐭𝐞𝐦𝐬

0.02

0.04

0.06

0.08

0 175 350 525 700

0.02

0.04

0.06

0.08(c)

v2 0.2 < pT(GeV/c) < 4

U+UAu+AuCu+AuCu+Cu

d+Aup+Au

0.01

0.02

0 175 350 525 700⟨ Nch ⟩

(b)

v3 0.2 < pT(GeV/c) < 4

0.01

0.02

0 175 350 525 700

vn

(a)

|veven1 |

0.2 < pT(GeV/c) < 0.9

0

0.01

0 0.02 0.04

C⟨ Nch ⟩-1

Ø Momentum conservation parameter 𝐶 scales asNÃÄ �"for all systems

𝑁av

0.02

0.04

0.06

0.08

0 175 350 525 700

0.02

0.04

0.06

0.08(c)

v2 0.2 < pT(GeV/c) < 4

U+UAu+AuCu+AuCu+Cu

d+Aup+Au

0.01

0.02

0 175 350 525 700⟨ Nch ⟩

(b)

v3 0.2 < pT(GeV/c) < 4

0.01

0.02

0 175 350 525 700

vn

(a)

|veven1 |

0.2 < pT(GeV/c) < 0.9

0

0.01

0 0.02 0.04

C

⟨ Nch ⟩-1

STAR Preliminary

|𝑣"%&%'|

𝜂 < 1and|Δ𝜂| > 0.7𝒍𝒏𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁av �𝟏/𝟑

Ø The efficiency corrections for NÃÄ have applied for Au+Au and U+U collisions.Ø Within the experimental uncertainties 𝑣"%&%'shows similar trends and

magnitudes for all systems.Ø 𝑣"%&%' is system independent.

16

Ø Odd harmonics are system independent.

Ø Even harmonics are system dependent with less dependence

for higher harmonics.

𝑣'for large systems 𝐴 + 𝐵𝒍𝒏

𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁av �𝟏/𝟑 𝑣'vs 𝑝{ at 𝑁av = 270

0

0.1

0 1 2 3

veven

1⟨ NCh ⟩ = 270(a)

U+UAu+AuCu+Au

0

0.1

0.2

0 1 2 3

v 2

(b)

0

0.1

0 1 2 3

v 3

(c)

0

0.05

0 1 2 3

v 4

pT(GeV/c)

(d)

STAR Preliminary

𝜂 < 1and|Δ𝜂| > 0.7

ConclusionComprehensive set of STAR measurements presented for 𝑣"%&%'(𝑝{, Cent%and 𝑠--� ) for several collision systems.

Within the experimental uncertainties, the similar trends and magnitudes of the measured 𝑣"%&%' for different colliding systems at 𝑠--� ~200𝐺𝑒𝑉suggest a comparable viscous coefficient A §

*

17

ØFor 𝐴𝑢 + 𝐴𝑢 beam energy scanü 𝑣"%&%' shows a weak dependence on centrality and beam energyü Within the experimental uncertainties|𝑣"%&%'|( 𝑠--� ) shows a similar

magnitude to 𝑣�suggesting that 𝑣�has larger viscous effect than 𝑣"%&%'

ØFor different systems at similar multiplicity (200𝐺𝑒𝑉) ü Within the experimental uncertainties𝑣"%&%' shows similar trends and

magnitudes for all systemsü 𝑣"%&%' is system independent.

18