Niseem Magdy

Niseem MagdySTAR Collaboration

Stony Brook University

[email protected]

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



𝒏


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





𝒕

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



𝒏


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





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





𝒕


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





𝒕


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


0 0.1 0 1

2


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


0 0.1 0 1

2


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.


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


18

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