Measurement of event-by event vn Pb-Pbcollisions at NN =2 ...jjiastar/LocalLinks/Soumya_HotQuarks2012.pdfEvent by Event flow measurements 4 Corresponding two - Track distribution in

Measurement of event-by event vn in

Pb-Pb collisions at

√sNN=2.76 TeV with the ATLAS detector

Soumya Mohapatra

Stony Brook UniversityStony Brook University

for the ATLAS Collaboration

Hot Quarks 2012

14-21 October 2012

� Event by event measurement of vn distributions: ATLAS-CONF-2012-114

� ATLAS event-Plane Correlation Note: ATLAS-CONF-2012-049

Flow harmonics2

( )n1 2v cosn

n

dNn

dφ

φ∝ + − Φ∑

2

The importance of fluctuations3

Two-particle cumulant ~ √(<v2>2+σ2)

Four-particle cumulant ~ √(<v >2-σ2)

EP Method in between <v2> and

√(<v2>2+σ2)

3

Measuring the full distribution of EbE vn distribution

completely supercedes these measurements.

Not only do we get the <vn> and σ but also the full

shape of the distribution.

Large amount of information regarding the initial

geometry and hydrodynamic expansion.

Four-particle cumulant ~ √(<v2>2-σ2)

Event by Event flow measurements4

Corresponding two-

Track distribution in

three central events

4

particle correlations

The large acceptance of the ATLAS detector and large multiplicity at LHC makes EbE vn

measurements possible for the first time.

Azimuthal distribution in single event

� Ideal detector:

5

dN

dφ∝1+ vn cos(nφ − nΨn )

n=1

∑ = 1+ vn,x cos(nφ) + vn,y sin(nφ)( )n=1

∑

v = v2 + v

2

vn,x = cos(nφ) , vn,y = sin(nφ)

5

vn = v2

n,x + v2

n,y


� Ideal detector:

6

dN


n=1


∑

v = v2 + v

2


� Correct for acceptance:

6

vn = v2

n,x + v2

n,y

vn,x → vn,x − vdet

n,x

vn,y → vn,y − vdet

n,y


� Ideal detector:

7

dN


n=1


∑

v = v2 + v

2


� Correct for acceptance:

� Correct for efficiency by weighting tracks by

7

vn = v2

n,x + v2

n,y

vn,x → vn,x − vdet

n,x

vn,y → vn,y − vdet

n,y

1

ε η,pT( )

Flow vector distribution & smearing8

2D flow vector distribution


8

Flow vector distribution & smearing9

2D flow vector distribution

vn = v2

n,x + v2

n,y


9

The v2obs will differ from the true v2 due

to finite multiplicity in the events

Determining response function10

vn,y

10

vn,x

� The measured vn vector will fluctuate about the true vector due to finite

number of tracks

� The fluctuation will be a 2D Gaussian

� Response function will be known if the width of the Gaussian fluctuation

can be determined

Determining response function11

vn,y

11

vn,x

� Divide the event into two sub-events with roughly equal number of tracks

� The fluctuation in each sub-event will be √2 times larger than the full

event

� If we take difference between the flow vectors for the two sub-events,

the signal will cancel and we will get the size of the fluctuation

Determining response function� Estimated by the correlation between “symmetric” subevents

12

12

� Response function obtained by integrating out azimuth angle

� Use Bayesian unfolding to correct measured vn distributions

� 2D response function is a 2D Gaussian!

Basic unfolding performance: v2, 20-25%E

ve

nts

410

f=0 as prior

Input=1itrN

=2itrN

=4itrN

=8itrN

=16itrN

=32itrN

=64itrN

=128itrN

=1

28

ite

ra

tio

to

N 1

1.1

13

v2 converges within a few % for Niter=8

small improvements for larger Niter.

13

2v0 0.05 0.1 0.15 0.2

310 >0.5 GeV

T20-25% p

f=0 as prior

ATLAS Preliminary

=2.76 TeVNN

sPb-Pb

-1bµ= 8 intL

2v0 0.05 0.1 0.15 0.2

Ra

0.9

=128iter

Unfolded: ratio to N

Dependence on prior: v4 20-25%14

� Despite different initial distribution, all converge for Niter=64

� Wide prior converges from above, narrow prior converges from below.

14

v2-v4 probability distributions)

2P

(v

-210

-110

1

10

>0.5 GeVT

p

0-1%

5-10%

20-25%

30-35%

40-45%

ATLAS Preliminary

=2.76 TeVNN

sPb-Pb

-1bµ= 8 intL

)3

P(v

-110

1

10

>0.5 GeVT

p

0-1%

5-10%

20-25%

30-35%

40-45%

ATLAS Preliminary

=2.76 TeVNN

sPb-Pb

-1bµ= 8 intL

)4

P(v

1

10

210

>0.5 GeVT

p

0-1%

5-10%

20-25%

30-35%

40-45%

ATLAS Preliminary

=2.76 TeVNN

sPb-Pb

-1bµ= 8 intL

v v v4

15

Main physics result: probability distributions of EbE vn

15

2v0 0.1 0.2

10 40-45%

60-65%

3v0 0.05 0.1

40-45%

55-60%

4v0 0.02 0.04 0.06

-110

40-45% v2 v3

v4

for gaussiandistributions:p(vn ) =vn

σe

−v2n /2σ 2

, σ =2

πvn

Unfolding in different pT ranges: 20-25%)

2P

(v

-210

-110

1

10

>0.5 GeVT

p

>0.5 GeVT

1>p

>1 GeVT

p

20-25%2v

)P

(v)

3P

(v

-110

1

10

ATLAS Preliminary=2.76 TeV

NNsPb-Pb

-1bµ= 8 intL

20-25%3v

)4

P(v

-110

1

10

210 20-25%4v

10

Rescale to the same mean 210 Rescale to the same mean

10

Rescale to the same mean

v v v

16

Distributions for higher pT bin is broader, but they all have ~same

reduced shape

16

Hydrodynamic response ~ independent of pT.

0.3

3v0 0.05 0.1 0.15

)3

P(v

-110

1

10

4v0 0.02 0.04 0.06 0.08

)4

P(v

-110

1

10

2v0 0.1 0.2 0.3

)2

P(v

-210

-110

1 )P

(v

v2 v3 v4

Comparison to Event-plane vn values17

v2σ 2

17

σ 2 / v2

for gaussian fluctuations :σ n / vn ≈ 0.523


v2σ 2

18

σ 2 / v2



v2σ 2

19

σ 2 / v2



v3σ 3

20

σ 3 / v3


Comparison to Event-plane vn values

v2 v3 v4

21

21

Measuring the hydrodynamic response: v2

For Glauber and CGC mckln

)2

P(v

1

10

20-1% v

>0.5 GeVT

data p


NNsPb-Pb

-1bµ= 8 intL

-110

1

10

25-10% v

>0.5 GeVT

data p


NNsPb-Pb

-1bµ= 8 intL

-110

1

10

220-25% v

>0.5 GeVT

data p


NNsPb-Pb

-1bµ= 8 intL

0-1% 5-10% 20-25%

22

22Both models fail describing p(v2) across the full centrality range

0 0.02 0.04 0.06

-110

T

2∈Glauber 0.36

2∈MC-KLN 0.31

0 0.05 0.1 0.15

10 T

2∈Glauber 0.46

2∈MC-KLN 0.30

0 0.05 0.1 0.15 0.2

-210

T

2∈Glauber 0.41

2∈MC-KLN 0.29

2v0 0.1 0.2

)2

P(v

-210

-110

1

10

230-35% v

>0.5 GeVT

data p

2∈Glauber 0.36

2∈MC-KLN 0.28

ATLAS Preliminary

=2.76 TeVNN

sPb-Pb -1

bµ= 8 intL

2v0 0.1 0.2 0.3

-210

-110

1

10

240-45% v

>0.5 GeVT

data p

2∈Glauber 0.32

2∈MC-KLN 0.26

ATLAS Preliminary

=2.76 TeVNN

sPb-Pb -1

bµ= 8 intL

2v0 0.1 0.2 0.3

-310

-210

-110

1

10

255-60% v

>0.5 GeVT

data p

2∈Glauber 0.24

2∈MC-KLN 0.22

ATLAS Preliminary

=2.76 TeVNN

sPb-Pb -1

bµ= 8 intL

30-35% 40-45% 55-60%

Two-plane correlations 23

Also see Li Yan’s talk in this session

Three-plane correlations 24

Also see Li Yan’s talk in this session

Summary

� Measured event-by-event probability distribution of v2-v4 in various

centrality bins.

� The v2 distribution is radial projection of 2D Gaussian in most

central events.

� But significant deviation is seen for >5%

� For v3, v4 the distributions are consistent with 2D Gaussian for all

centralities

25

centralities

� The reduced shape of vn distributions has no pT dependence �

hydro response independent of pT

� p(v2) is inconsistent with p(ε2) from Glauber &MC-KLN model.

� Also measured a large set of two and three-plane correlations

� Both measurements are the first of their kind.

� Provide direct constraints on the hydrodynamic response to initial geometry

fluctuations. 25

BACKUP SLIDES

ATLAS Detector27

EM Calorimeters

-4.9<η<4.9

� Tracking coverage : |η|<2.5

� FCal coverage : 3.2<|η|<4.9 (used to determine Event Planes)

� For reaction plane correlations use entire EM calorimeters (-4.9 <η< 4.9 )

|η|<2.5

Inner detector

3.2<|η|<4.9Forward Calorimeter (Fcal)

Soumya Mohapatra Stony Brook University ATLAS Collaboration

Basic unfolding performance: v2, 20-25%28

v2 converges within a few % for Niter=8

small improvements for larger Niter.

28


29


30

EbE distributions31

EbE distributions32

Unfolding for Half ID33

Bayesian unfolding

� Unfolding implemented using RooUnfold package

– True (“cause” c or vn) vs measured distribution (“effect” e or vnobs)

Denote response function

– Unfolding matrix M is determined via iterative procedure

34

– Unfolding matrix M is determined via iterative procedure

– Prior, c0, can be chosen as input vnobs distribution or it can be chosen to be

closer to the truth by a simple rescaling according to the EP vn

34

Measuring the two-plane correlations

-4.9<η<-0.5 0.5<η<4.9-0.5<η<0.5

Ψn is measured here Ψm is measured here

35

� Correlations are measured using EM+Forward calorimerers (-4.9<η<-4.9)

� If Ψn is measured in negative half (-4.9<η<-0.5), then Ψm is measured in

positive half of calorimeters (and vice versa).

� Thus same particles are not used in measuring both Ψn and Ψm.

� Removes auto-correlation

� There is a ∆η gap of 1 units between the two halves to remove any non-

flow correlations

Measuring the three-plane correlations

-2.7<η<-0.5 0.5<η<2.7

Ψn Ψm

Ψk

-4.8<η<-3.3 3.3<η<4.8

36

� Ψn ,Ψm and Ψk are measured in different parts of the calorimeter.

� Thus same particles are not used in measuring any of the Ψ’s.

� Thus there is no auto-correlation

� There is a ∆η gap between any two of the detectors

� Event mixing is used to remove detector effects

Documents

Measurement of event-by event vn Pb-Pbcollisions at NN =2 ...jjiastar/LocalLinks/Soumya_HotQuarks2012.pdfEvent by Event flow measurements 4 Corresponding two - Track distribution in