Niels Bohr Institute - indico.nbi.ku.dk · Angular Correlations 3 For very peripheral collisions or when triggered with a high-p t charged particle the dominant contribution to two

Angular Correlations

1

Raimond SnellingsUtrecht University

7-11-2011

Niels Bohr Institute

Angular Correlations at the LHC

2

q6

-10

12

34 d6-5-4-3

-2-101 2 3 4

0.99

1

1.01

1.02

0-1%

q6

-10

12

34 d6-5-4

-3-2-10 12 3 4

1

1.02

0-5%

q6

-10

12

34 d6-5-4-3

-2-10 1 23 4

0.98

1

1.02

1.04

0-10%

q6

-10

12

34 d6-5-4

-3-2-10 1 2 3 4

0.95

1

1.05

1.1

10-20%

q6

-10

12

34 d6-5-4-3

-2-101 2 3 4

1

1.1

20-30%

q6

-10

12

34 d6-5-4

-3-2-10 12 3 4

0.9

1

1.1

1.2

30-40%

q6

-10

12

34 d6-5-4-3

-2-10 1 23 4

0.9

1

1.1

1.2

40-50%

q6

-10

12

34 d6-5-4

-3-2-10 1 2 3 4

0.9

1

1.1

50-60%

q6

-10

12

34 d6-5-4-3

-2-101 2 3 4

0.9

1

1.1

60-70%

q6

-10

12

34 d6-5-4

-3-2-10 12 3 4

0.9

1

1.1

1.2

70-80%

q6

-10

12

34 d6-5-4-3

-2-10 1 23 4

0.8

1

1.2

1.4

80-90%

ATLAS Preliminary

-1bµ Ldt = 8 0 < 3 GeVb

T, pa

T2 < p

Contributions to the two-particle ΔΦ,Δη angular correlation

come from anisotropic flow, jets, resonances,

HBT, etc

C(��⌘) ⌘ Nmixed

Nsame

d2Nsame

/d��d�⌘

d2Nmixed

/d��d�⌘

Angular Correlations

3

For very peripheral collisions or when triggered with a high-pt charged particle the dominant contribution to two particle angular correlations is due to

jet-correlationsMore central heavy-ion collisions

look very very different!

[rad]!"0

24

#"-1

01

)#

", !

"C

(

0

2

4

6-8, 0-20%a

T 8-15, pt

Tp

Pb-Pb 2.76 TeV

) < 5!"0 < C(zoomed to

q6

-10

12

34 d6-5-4-3

-2-10 1 23 4

0.8

1

1.2

1.4

80-90%

4

q6

-10

12

34 d6-5-4

-3-2-10 12 3 4

1

1.02

0-5%

0.98

1.02

1.04

ATLAS

ATLAS

q6

-10

12

34 d6-5-4-3

-2-101 2 3 4

0.99

1

1.01

1.02

0-1%

q6

-10

12

34 d6-5-4

-3-2-10 12 3 4

1

1.02

0-5%

q6

-10

12

34 d6-5-4-3

-2-10 1 23 4

0.98

1

1.02

1.04

0-10%

q6

-10

12

34 d6-5-4

-3-2-10 1 2 3 4

0.95

1

1.05

1.1

10-20%

q6

-10

12

34 d6-5-4-3

-2-101 2 3 4

1

1.1

20-30%

q6

-10

12

34 d6-5-4

-3-2-10 12 3 4

0.9

1

1.1

1.2

30-40%

q6

-10

12

34 d6-5-4-3

-2-10 1 23 4

0.9

1

1.1

1.2

40-50%

q6

-10

12

34 d6-5-4

-3-2-10 1 2 3 4

0.9

1

1.1

50-60%

q6

-10

12

34 d6-5-4-3

-2-101 2 3 4

0.9

1

1.1

60-70%

q6

-10

12

34 d6-5-4

-3-2-10 12 3 4

0.9

1

1.1

1.2

70-80%

q6

-10

12

34 d6-5-4-3

-2-10 1 23 4

0.8

1

1.2

1.4

80-90%

ATLAS Preliminary

-1bµ Ldt = 8 0 < 3 GeVb

T, pa

T2 < p

ATLAS

measure anisotropic flow

4

• since the common symmetry plane cannot be measured event-by-event, we measure quantities which do not depend on it’s orientation: multi-particle azimuthal correlations

• assuming that only correlations with the symmetry plane are present - not a very good assumption (jets, resonances, etc)!

hhein(�1��2)ii = hhein(�1� n�(�2� n))ii= hhein(�1� n)ihe�in(�2� n)ii= hv2ni

hvni = hhein(�1� n)ii

Can we isolate the flow?• flow is a collective effect

• flow “factorizes”

• <vivj>/<vj> = <vivk>/<vk>

• correlate particles separated in rapidity

• correlate particles separated in pt

• multi-particle correlation

• build cumulants

5

Collective Motion

6

p+pA+A independent # of p+p

A+A collective behavior

tests if we are dealing with a common symmetry plane!

multi-particle correlations• for detectors with uniform acceptance 2nd and 4th

cumulant are given by:

7

we got rid of two particle nonflow correlations!

we can remove nonflow order by order

Borghini, Dihn and Ollitrault, PRC 64, 054901 (2001)

8

v2 from cumulants M

etho

d us

ed :

A.B

iland

zic,

R.S

nelli

ngs,

S. V

olos

hin,

Ph

ys.R

ev. C

83 (2

011)

044

913

centrality percentile0 10 20 30 40 50 60 70 80

> 1

)η

Δ (* b

Q aQ

0

5

10

-310×

= 2.76 TeVNNsALICE Preliminary, Pb-Pb events at

charged hadrons


QC

{4}

-60

-40

-20

0

-610×


QC

{6}

0

0.5

1

1.5

-610×


QC

{8}

-0.1

-0.05

0

-610×

cumulants show behavior as expected when correlations are dominated by collective flow

QC{2} = v2{2}QC{4} = �v4{4}QC{6} = 4v6{6}

QC{8} = �33v8{8}

What about p-p?

9

Multiplicity (uncorr.)0 10 20 30 40 50 60

QC

{2}

0

0.01

0.02

0.03 = 0.052vData (7 TeV)


QC

{4}

0

0.2

0.4

0.6

0.8

-310=

ALICE preliminary

ALICE preliminary

)b()a(

remember QC{2} = v2, QC{4} = -v4

the 2 and 4-particle correlations decrease with increasing number of particles produced which is typical behavior of correlations involving only few particles

the 4-particle cumulant, QC{4}, even has the wrong sign compared to true flow!

What about p-p?

10


QC{2

}

0

0.01

0.02

0.03

PythiaPhojet

= 0.052vData (7 TeV)


QC{4

}

0

0.2

0.4

0.6

0.8

-310!

ALICE preliminary

ALICE preliminary

(a) (b)

remember QC{2} = v2, QC{4} = -v4

models like PYTHIA and PHOJET have the correct sign for the correlations and capture the general trends observed in p-p

no evidence for elliptic flow in this multiplicity range

11

The Perfect Liquid

The system produced at the LHC behaves as a very low viscosity fluid (a perfect fluid), constraints dependence of η/s versus temperature

K. A

amod

t et a

l. (A

LICE

Col

labo

ratio

n)

PRL

105,

252

302

(201

0)

(GeV)NNs

1 10 210 310 410

2v

-0.08

-0.06

-0.04

-0.02

0

0.02

0.04

0.06

0.08

ALICESTARPHOBOSPHENIXNA49CERESE877EOSE895FOPI

Flow Analysis Methods

12

flow analysis methods have different sensitivity to

nonflow and fluctuations

I focus on the cumulants

excellent opportunity to study flow fluctuations and from these get a handle on initial conditions!

Borghini, Dihn and Ollitrault, PRC 64, 054901 (2001)

Bilandzic, Snellings and Voloshin, PRC 83, 044913 (2011)

v2n{2} = v̄2n + ⇥2v + �

v2n{4} = v̄2n � ⇥2v

v2n{6} = v̄2n � ⇥2v

v2n{8} = v̄2n � ⇥2v

Flow Fluctuations

13

when (2-particle) nonflow is corrected for or negligible!

in limit of “small” (not necessarily Gaussian) fluctuations

in limit of only (Gaussian) fluctuations

vn{4} = 0

vn{2} =2��v̄n

v2n{2} = v̄2n + �2v

v2n{4} = v̄2n � �2v

v2n{2}+ v2n{4} = 2v̄2n

v2n{2}� v2n{4} = 2�2v

14

v2 versus centrality in ALICE


2v

0

0.05

0.1


(charged hadrons)2v > 0)ηΔ ({2}2v > 1)ηΔ ({2}2v

{4}2v{6}2v{8}2v

Two particle v2 estimates depend on Δη

Higher order cumulant v2 estimates are consistent within

uncertainties

Two particle v2 estimates are corrected for nonflow based on

HIJINGThe estimated nonflow

correction for Δη > 1 is included in the systematic uncertainty


2v

0

0.05

0.1


> 0}d6{2, 2v > 1}d6{2, 2v

corrected > 0}d6{2, 2v corrected > 1}d6{2, 2v

{4}2v

v2 Fluctuations

15

Fluctuations are significant and for more central collisions not in agreement with the eccentricity fluctuations in MC-

Glauber and MC-KLN CGCtune initial conditions? what are the other contributions?

need to compare to full model calculations!

�vn ⇥ [1

2

�v2n{2}� v2n{4}

�]12

�vn

v̄n'

✓v2n{2}� v2n{4}v2n{2}+ v2n{4}

◆ 12

centrality percentile0 5 10 15 20 25 30 35 40 45 50

2vσ

0.02

0.04

0.06


2vσ ≈ 21

)/2)2{4}2 - v2{2}2

((v

centrality percentile0 5 10 15 20 25 30 35 40 45 50

2ε/ 2εσ

or

2v/ 2vσ

0.2

0.4

0.6

0.8

1 = 2.76 TeVNNsALICE Preliminary, Pb-Pb events at

21

))2{4}2 + v2{2}2

)/(v2{4}2 - v2{2}2

ALICE ((v

21

))2{4}2ε + 2{2}2ε)/(2{4}2ε - 2{2}2εMC-KLN ((

21

))2{4}2ε + 2{2}2ε)/(2{4}2ε - 2{2}2εMC-Glauber ((

2ε/ 2ε

σMC-KLN (2.76 TeV)

2ε/ 2ε

σMC-Glauber (64 mb)

16

v2 as function of pt

Elliptic flow as function of transverse momentum does not change much from RHIC to LHC energies, can we understand that?

K. A

amod

t et a

l. (A

LICE

Col

labo

ratio

n)

PRL

105,

252

302

(201

0)

)c (GeV/t

p0 1 2 3 4 5

{4}

2v

0.05

0.1

0.15

0.2

0.25

10-20%20-30%30-40%10-20% (STAR)20-30% (STAR)30-40% (STAR)

17

v2 for identified particles

the mass splitting increased compared to RHIC energies

pion and kaon v2 are described well with hydrodynamic predictions using MC-KLN CGC initial conditions and η/s = 0.2

(GeV/c)t

p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2v

0

0.05

0.1

0.15

0.2

0.25 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at (PHENIX data: Au-Au@200 GeV)

(PHENIX)-K-/ (PHENIX)p

|>1}d6{2, |2

, v±/

|>1}d6{2, |2

, v±K|>1}d6{2, |

2, vp

centrality 20%-40%

RHIC hydroLHC hydro(CGC initial conditions)

/s=0.2)d(

Hydro: Shen, Heinz, Huovinen & Song, arXiv:1105.3226

(GeV/c)t

p0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2

2v

0

0.05

0.1

0.15

0.2

0.25 = 2.76 TeV, Heinz&ShenNNsHydro prediction for Pb-Pb events at /s=0.2dCGC initial conditions,

/

Kp

centrality 20%-40%

RHIC hydroLHC hydro

(GeV/c)t

p0 0.5 1 1.5 2 2.5 3 3.5

2v

0

0.1

0.2

0.3centrality 40%-50%

|>1}d6{2, |2

, v±/|>1}d6{2, |

2, v±K

|>1}d6{2, |2

, vp

hydro LHC(CGC initial conditions)

/s=0.2)d(

= 2.76 TeVNNsALICE preliminary, Pb-Pb events at

18

v2 for identified particles

at small (mt-m0)/nq the scaling in the data resemble the scaling as observed in hydrodynamics

(GeV/c)q)/n0-mt

(m0 0.2 0.4 0.6 0.8 1

q/n 2v

0

0.05

0.1

0.15 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at centrality 10%-20%

|>1}d6{2,|2

, v±/

|>1}d6{2,|2

, v±K

|>1}d6{2,|2

, vp

(GeV/c)q)/n0-mt

(m0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

q/n 2v

0

0.05

0.1

0.15 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at centrality 40%-50%

|>1}d6{2,|2

, v±/

|>1}d6{2,|2

, v±K

|>1}d6{2,|2

, vp

(GeV/c)q)/n0-mt

(m0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

q/n 2v

0

0.05

0.1

0.15 = 2.76 TeV, Heinz&ShenNNsHydro prediction for Pb-Pb events at centrality 40%-50%

hydro/

K hydro

p hydro

hydro LHC(CGC initial conditions)

/s=0.2)d(

Hyd

ro: S

hen,

Hei

nz, H

uovi

nen

& S

ong,

arX

iv:1

105.

3226

19

Initial conditions and vn

6 4 2 0 2 4 66

4

2

0

2

4

6

y(fm)

x(fm)

G. Qin, H. Petersen, S. Bass, and B. Muller

initial spatial geometry not a smooth almond (for which all odd harmonics are zero due to reflection symmetry)

may give rise to higher odd harmonics which give additional independent constraint on the initial conditions!!!

x, b

y z

2⇡

N

dN

d�= 1 +

1X

n=1

2vn cosn(�� n)2⇡

N

dN

d�= 1 +

1X

n=2,4,6,...

2vn cosn(�� R)

20

Shear Viscosity!=0.4 fm/c

-10 -5 0 5 10

x [fm]

-10

-5

0

5

10

y [fm

]

0

100

200

300

400

500

600

" [fm

-4]

!=6.0 fm/c, ideal

-10 -5 0 5 10

x [fm]

-10

-5

0

5

10

y [fm

]

0

2

4

6

8

10

12

" [fm

-4]

!=6.0 fm/c, #/s=0.16

-10 -5 0 5 10

x [fm]

-10

-5

0

5

10

y [fm

]

0

2

4

6

8

10

12

" [fm

-4]

Music, Sangyong Jeon

initial conditions ideal hydro η/s=0 viscous hydro η/s=0.16

0

0.02

0.04

0.06

0.08

0.1

0.12

0 0.5 1 1.5 2 2.5 3

v 3

!/s=0.08

!/s=0.16

pionskaons

protons

p (GeV/c)t

Hydro: Alver, Gombeaud, Luzum & Ollitrault, Phys. Rev. C82 (2010)

Larger η/s clearly smoothes the distributions and suppresses the higher harmonics (e.g. v3)

21

Shear Viscosityη/s = 0

η/s > 0

u1

u2

u3u1 > u2 > u3 shear viscosity will make

them equal and destroy the elliptic flow v2

higher harmonics represent smaller differences which get destroyed more easily, and which, if measurable, makes

them more sensitive probes to η/s

22

Triangular Flow

ALICE Collaboration, arXiv:1105.3865 accepted for PRL

The v3 with respect to the reaction plane determined in the ZDC and with the v2 participant plane is consistent with zero as expected if v3 is due to fluctuations of the initial eccentricity

The v3{2} is about two times larger than v3{4} which is also consistent with expectations based on initial eccentricity fluctuations


0

0.05

0.1

ALICE > 1}ηΔ{2, 2v > 1}ηΔ{2, 3v > 1}ηΔ{2, 4v

{4}3vRPΨ3/v

22Ψ3/ v×100

Alver, Gombeaud, Luzum & Ollitrault, Phys. Rev. C82 034813 (2010)/s=0.08η Glauber 3v

/s=0.16η CGC 3vWe observe significant v3 which compared to v2 has a different centrality dependence

The centrality dependence and magnitude are similar to predictions for MC Glauber with η/s=0.08 but above MC-KLN CGC with η/s=0.16

23

Triangular Flow

(GeV/c)q)/n0-mt

(m0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

q/n 3v

-0.01

0

0.01

0.02

0.03

0.04

0.05

0.06 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at

centrality 10%-20%

±/ {2}3v± K{2}3v

p {2}3v

(GeV/c)t

p0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

3v

0

0.05

0.1

0.15

0.2 = 2.76 TeVNNsALICE preliminary, Pb-Pb events at

centrality 10%-20%

±/ {2}3v± K{2}3v

p {2}3v

The behavior of v3 as function of pt for pions, kaons and protons shows the same features as observed for v2

(the mass splitting, the crossing of the pions with protons at intermediate pt)

24

Geometry and Harmonics

(GeV/c)Tp0 0.5 1 1.5 2 2.5 3 3.5 4

nv

0

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

1 v2 v3 v4 v5 v6 v

Au+Au 200 GeV (b = 0 fm)

G-L Ma and X-N Wang, arXiv:1011.5249v2

0 1 2 3 4 5

nv

0

0.1

0.2

0.3

(a)Centrality 30-40%{2}2v{2}3v{2}4v{2}5v

/s = 0.0)η (2v/s = 0.08)η (2v/s = 0.0)η (3v/s = 0.08)η (3v

0 1 2 3 4 5

nv

0

0.05

0.1

(b)Centrality 0-5%

{2}2v

{2}3v

{2}4v

{2}5v

)c (GeV/t

p0 1 2 3 4 5

nv

0

0.05

0.1 (c)Centrality 0-2%{2}2v{2}3v

{2}4v{2}5v

ALIC

E Collaboration, arX

iv:1105.3865 accepted for PRL

For central collisions at intermediate pt the higher harmonics v3 and v4 cross v2 and become the dominant harmonics

For more central collisions this occurs already at lower pt

25

Geometry

(rad.)φΔ-1 0 1 2 3 4

)φΔ

C(

0.9920.9940.9960.998

11.0021.0041.0061.008

1.01

< 3.0t,trig2.0 < p < 2.0t,assoc1.0 < p

| < 0.8ηCentrality 0-1%, || > 1ηΔ|

| > 1}ηΔ{2, |2,3,4,5v

ALI

CE

Col

labo

ratio

n, a

rXiv

:110

5.38

65 a

ccep

ted

for

PRL

0 1 2 3 4 5

nv

0

0.1

0.2

0.3

(a)Centrality 30-40%{2}2v{2}3v{2}4v{2}5v

/s = 0.0)! (2v/s = 0.08)! (2v/s = 0.0)! (3v/s = 0.08)! (3v

0 1 2 3 4 5

nv

0

0.05

0.1

(b)Centrality 0-5%

{2}2v

{2}3v

{2}4v

{2}5v

)c (GeV/t

p0 1 2 3 4 5

nv

0

0.05

0.1 (c)Centrality 0-2%{2}2v{2}3v

{2}4v{2}5v

We observe a doubly-peaked structure in the azimuthal correlation function opposite to the trigger particle before the subtraction of v2

The red line shows the sum of the measured anisotropic flow Fourier coefficients. The flow coefficients give a natural explanation of the observed correlation structure known as the Mach cone and ridge

C(��) ⌘ Nmixed

Nsame

dNsame

/d��

dNmixed

/d��

ALI

CE

Col

labo

ratio

n, a

rXiv

:110

5.38

65

Conclusions• Anisotropic flow measurements provided strong constraints on

the properties of hot and dense matter produced at RHIC and LHC energies and have lead to the new paradigm of the QGP as the so called perfect liquid

• At the LHC we observe even stronger flow than at RHIC which is expected for almost perfect fluid behavior

• The first measurements of v3, v4 and v5 have recently been made at RHIC and the LHC and indicate that these flow coefficients behave as expected from fluctuations of the initial spatial eccentricity (geometry!) and a created system which has a small η/s

• provide new strong experimental constraints on η/s and initial conditions

26

Thanks

27

Documents

Niels Bohr Institute - indico.nbi.ku.dk · Angular Correlations 3 For very peripheral collisions or when triggered with a high-p t charged particle the dominant contribution to two