Niseem MagdySTAR Collaboration

Stony Brook University niseem.abdelrahman@stonybrook.edu

Ø Collected data for different systems;

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

2

STAR Detector at RHIC

Ø TPC detector covers |𝜂| < 1

Flow

𝑯𝑩𝑻

𝑫𝒆𝒄𝒂𝒚

𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏

Di−jets

Two particle correlation function 𝐶r Δ𝜑 ,

𝐶𝑟 Δ𝜑 = 𝑑𝑁/𝑑Δ𝜑 and 𝑣OP = ∑ RS TU VWX(OTU)�\]

∑ RS TU�\]

𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆

𝑛 > 1𝑣OO = 𝑣Oe𝑣Of +𝛿hijSk

𝑛 = 1𝑣ll = 𝑣le𝑣lf +𝛿mjOn

Non-flow

Azimuthal anisotropy measurements Correlation

function

3Charge

Flow

Non-flow

Non-flow suppression is needed

𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆Non−flow

𝑯𝑩𝑻 The 𝛥𝜂 dependence of 𝑣vvs centrality

4

𝑣v

STAR Preliminary

Short range non-flow suppression

Ø The short range non-flow shows 𝛥𝜂 dependence

Ø The short range non-flow reduced using 𝛥𝜂 > 0.7 cut

Ø Wider 𝛥𝜂cuts degrade the statistical certainties

𝑫𝒆𝒄𝒂𝒚

5

𝑣v

STAR Preliminary

𝜂 < 1and|Δ𝜂| > 0.7

Ø The non-flow effect using 𝛥𝜂 > 0.7 cut get reduced

into 1:2% for all systems.

The 𝑣vvs 𝑁Ri for all systems using 𝛥𝜂 > 0.7 cut

Short range non-flow suppression𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆Non−flow

𝑯𝑩𝑻

𝑫𝒆𝒄𝒂𝒚

0 0.02 0.04 0.06 0.08

0.1

200 400 600 800

U+U193 GeV

v2

LSUS

0

0.02

0.04

0.06

0.08

0.1

200 400 600 800

Au+Au200 GeV

0

0.02

0.04

0.06

0.08

0.1

200

Cu+Au200 GeV

0

0.02

0.04

0.06

0.08

0.1

100 200

Cu+Cu200 GeV

0

0.02

0.04

0.06

0.08

0.1

15 30

d+Au200 GeV

p+Au LSp+Au US

0.9

1

1.1

200 400 600

vall2 / vUS

2

0.9

1

1.1

200 400 600

0.9

1

1.1

100 200 300⟨ Nch ⟩

0.9

1

1.1

100 200

0.9

1

1.1

15 30

𝑣ll = 𝑣le𝑣lf +𝛿mjOn𝑛 = 1

𝑣ll 𝑝~e, 𝑝~k = 𝑣l���O 𝑝~

e 𝑣l���O 𝑝~

k − 𝐶𝑝~e𝑝~

k

STAR Preliminary

ØGood simultaneous fit obtained with fit function.

Ø𝐯𝟏𝟏characteristic behavior gives a good constraint for 𝒗𝟏𝒆𝒗𝒆𝒏 𝐩𝐓 extraction.6

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

𝑪 ∝< 𝑴𝒖𝒍𝒕 >�𝟏 1

𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏

Di−jets

𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆 Long range non-flow suppression

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

ØThe characteristic behavior of 𝑣l���O 𝑝~ in good agreement with the hydrodynamics calculations

ØThe momentum conservation parameter 𝐶 scales as 1/<Mult>

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| > 0.7

STAR Preliminary

Long range non-flow suppression𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏

Di−jets

𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆

0

0 0.01 0.02

0

0.004

0.008

C(√s

NN

)

1/<Mult>

Au+Au200 GeV

PRL. 108, 252302378 (2012)

STAR Preliminary

0

0.04

0.08

0 1 2 3

veven

1

pT

Au+Au200 GeV0%--10%

Hydro

𝑪 ∝ 𝟏 < 𝒑𝑻𝟐 >< 𝑴𝒖𝒍𝒕 >�

8

Ø Multi-particle correlations also used to further suppress

non-flow

Ø 𝜂 gap between particles in each pair used to suppress the

short-range non-flow

Ø Simultaneous fit used to suppress long-range non-flow

associated with momentum conservation

Non-flow suppression

𝑯𝑩𝑻

𝑫𝒆𝒄𝒂𝒚

𝑴𝒐𝒎𝒆𝒏𝒕𝒖𝒎𝑪𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒐𝒏

Di−jets

𝑺𝒉𝒐𝒓𝒕 − 𝒓𝒂𝒏𝒈𝒆𝑳𝒐𝒏𝒈 − 𝒓𝒂𝒏𝒈𝒆

9

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-3-2-1

0123

0

10

20

30

40

50

60

-2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5-3-2-1

0123

0

10

20

30

40

50

60

70

4 ≡ 𝑒�O �����������

4 ≡ 𝑒�O �����������

Subevent cumulant measures long-range collectivity.

Short-range non-flow dominate

Long-range non-flow dominate

>ch<N20 40 60 80 100 120 140

{4}

2C

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35-310×

PYTHIA 13 TeV<3.0 GeV

T|<2.5 0.3<pη|

<4> from standard from standard22<2>

<4> from 3 subevent from 3 subevent22<2>

Both 4 and 2 2 v

are much smaller with subevent

Three subevent cumulantcan further suppress away-

side jet contribution

In the subevent method, particles are correlated

across all subevents (long-range)

Multi-particle correlations and the non-flow suppression

𝑐v 4 ≡ 4 − 2 2 v

𝒄𝟐 𝟒

𝟐 𝟐 𝟐𝟒

10

Collectivity in small systems

Ø Cr shows similar trend for all systems

Ø 𝑐v 4 shows negative value for different systems

𝜂 < 1and|Δ𝜂| > 0.7

Ø The correlation function Cr for all systems at one 𝑁Ri valueØ 𝑐v{4} vs 𝑁Ri for 4 systems

STAR Preliminary

-0.02

-0.01

0

0.01

0 200 400 600

-0.02

-0.01

0

0.01

c2{4}

x10-3

(g)

⟨Nch⟩

U+UAu+AuCu+Au

d+Au

0.99

1

1.01

-3 -2 -1 0 1 2 3

U+U193 GeV

⟨ Nch ⟩ = 25

Cr

(a)

0.99

1

1.01

-3 -2 -1 0 1 2 3

Au+Au200 GeV

(b)

0.99

1

1.01

-3 -2 -1 0 1 2 3

Cu+Au200 GeV

(c)

0.99

1

1.01

-3 -2 -1 0 1 2 3

Cu+Cu200 GeV

(d)

0.99

1

1.01

-3 -2 -1 0 1 2 3

d+Au200 GeV

(e)

∆ϕ(rad)

0.99

1

1.01

-3 -2 -1 0 1 2 3

p+Au200 GeV

(f)

Three subevent cumulant

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

Ø 𝑣O measurements for different systems are sensitive to system shape (𝜀O), dimensionlesssize(𝑅𝑇) and transport coefficients �

X,  X, … .

𝒍𝒏𝒗𝒏𝜺𝒏

∝ −𝑨𝜼𝒔 𝑵𝑪𝒉 �𝟏/𝟑

Even Harmonic 𝒗𝟐 Odd Harmonic 𝒗𝟑A𝑡𝑡ℎ𝑒𝑠𝑎𝑚𝑒 ¬hand 𝑁Ri �l/­

𝒗𝒏 𝒅𝒓𝒊𝒗𝒆𝒏𝒃𝒚

𝜺𝒏 +… 𝜺𝟑 ∝𝟏𝑵�

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

𝜺𝟐 scalingisneeded

ExpectationsØ 𝑣l���Oand𝑣­ are system

independent

Ø 𝑣v is system dependent

11

𝑣O/∈O∝ 𝑒�µ(¬h

O¶·~) 𝑆~ 𝑅𝑇 ­~ 𝑁Ri then 𝑅𝑇~ 𝑁Ri l/­

PRC89, 064908(2014)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

12

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)

Ø Odd harmonics are system independent.Ø Even harmonics are system dependent.

𝑣Ofor large systems 𝐴 + 𝐵

0

0.04

0.08

0 200 400 600

v 2

(a) U+UAu+AuCu+Au

0

0.02

0 200 400 600

v 3

(b)

0

0.01

0 200 400 600

v 4

(c)

0

0.01

0 200 400 600

v 5

⟨ NCh ⟩

(d)

𝜂 < 1and|Δ𝜂| > 0.7𝒍𝒏𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁Ri �𝟏/𝟑

STAR Preliminary STAR Preliminary

𝑣Ovs 𝑝~ at fixed 𝑁Ri = 270 𝑣Ovs 𝑁Ri at fixed 𝑝~[0.2:4 GeV/c]

Ø𝑣l���Oand𝑣­are system independent.

𝑣l���Oand 𝑣­vs𝑝~ at different 𝑁Ri for all systems

Ø𝑣l���Oand 𝑣­show similar trends and magnitudes for all systems.

13

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)

STAR Preliminary

𝒗𝒏𝐟𝐨𝐫𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭𝐬𝐲𝐬𝐭𝐞𝐦𝐬𝜂 < 1and|Δ𝜂| > 0.7𝒍𝒏

𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁Ri �𝟏/𝟑

Ø 𝑣l���Oand𝑣­ show similar trends and magnitudes for all systems.

Ø 𝑣l���Oand𝑣­ are system independent.14

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

𝑵𝑪𝒉

𝑪 ∝< 𝑁Ri >�𝟏

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

𝑣l���Oand 𝑣­vs 𝑁Ri for all systems

𝒗𝒏𝐟𝐨𝐫𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭𝐬𝐲𝐬𝐭𝐞𝐦𝐬𝜂 < 1and|Δ𝜂| > 0.7𝒍𝒏

𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁Ri �𝟏/𝟑

Ø𝑣v is system dependent (shape).

Ø𝑣v show similar trends for all systems.

15

Ø�¶Í¶(𝑝~) for all systems scales to a single curve.

𝑣vvs𝑝~ at different 𝑁Ri for all systems

𝒗𝒏𝐟𝐨𝐫𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭𝐬𝐲𝐬𝐭𝐞𝐦𝐬𝜂 < 1and|Δ𝜂| > 0.7

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 2v 2

/ε2

(l)

STAR Preliminary

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)

𝒍𝒏𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁Ri �𝟏/𝟑

Ø𝑣v show similar trends but different magnitudes for different systems.

Ø𝑣v is system dependent (shape).16

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

𝑣v

𝑵𝑪𝒉

STAR Preliminary

𝑣vvs 𝑁Ri for all systems

𝒗𝒏𝐟𝐨𝐫𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭𝐬𝐲𝐬𝐭𝐞𝐦𝐬𝜂 < 1and|Δ𝜂| > 0.7𝒍𝒏

𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁Ri �𝟏/𝟑

ln �¶Í¶

vs 𝑁Ri �l/­for all systems

Ø�¶Í¶

for all systems scales to a single curve.Ø Similar slopes implies similar viscous coefficient ( A𝜂/𝑠) for all systems.

17

𝒗𝒏𝐟𝐨𝐫𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐭𝐬𝐲𝐬𝐭𝐞𝐦𝐬 𝜂 < 1and|Δ𝜂| > 0.7

STAR Preliminary

0.09

0.3

0.1 0.2 0.3 0.4

v 2/ε

2

⟨ Nch ⟩-1/3

U+UAu+AuCu+AuCu+Cu

p+Aud+Au

0.8

0.9

1

1.1

1.2

1 2 3 4 5 6

Slop

e sys

/ ⟨ S

lope

⟩

⟨ Slope ⟩ U+U Au+Au Cu+Au Cu+Cu

𝒍𝒏𝒗𝒏𝜺𝒏

∝ −𝑨 𝜼/𝒔 𝑁Ri �𝟏/𝟑

ConclusionComprehensive set of STAR measurements presented for

𝑣O(𝑝~, 𝑁Ri ) for several collision systems.

ØScaling the system size;ü The odd harmonics are system independentü The even harmonics are system dependentü

�¶Í¶

for all systems scaled onto one curve to ~15% in slope

At the same energy, the scaling features suggest similar viscous coefficient (A �

h) for different systems.

18

ØNon-flow suppressionü 𝛥𝜂 cut used to suppress the short range non-flowü 𝑐v 4 shows negative value for all presented systems.

19