[PPT] - Measurements of flow harmonics with the event plane and cumulant PowerPoint Presentation

SLIDE 1

Measurements of flow harmonics with the event plane and cumulant methods from the ATLAS experiment

Tomasz Bold, AGH UST Krakow for the ATLAS Collaboration

1

Quark Matter 2012 - 2012-08-17 – Washington DC

SLIDE 2

Topics covered

Integrated flow measurement using the Event

Plane method

– Method description and justification – Three tracking techniques and their performance – Comparison of the measurements – Elliptic flow scaling

Flow measurements with cumulants

– Method description – Two and four particle cumulants differential measurement – Comparison between the experiments – Integrated results – Fluctuations

ATLAS - cumulant method - integrated flow

2

ATLAS-CONF-2012-118 ATLAS-CONF-2012-117

SLIDE 3

Event plane method and integrated v2

Event Plane method

– for each event estimate the event plane angle and resolution

using FCal 3.2<|η|<4.8

– correlate tracks with EP angle

using ID |η|<2.5
Integration: weight differential v2

by number of particles in bins of pT and η

– corrected by efficiency and fake rates

ATLAS - cumulant method - integrated flow

3

v2

int =

Nik

c i

∑

k

∑

v2ik / Nik

c i

∑

k

∑

Nik

c = Nik c (1− fik)/εik

SLIDE 4

2

v

0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

ATLAS Simulation Preliminary =2.76 TeV

NN

s Pb+Pb |<2

|

> 500 MeV

T

p > 200 MeV

T

p > 150 MeV

T

p > 100 MeV

T

p > 50 MeV

T

p > 30 MeV

T

p cut

T

no min p

Centrality[%] 20 40 60 80 100

ratio

1 1.1 1.2 1.3

+0.4

v2{EP} integrated down to very low-pT

Reaching low pT reduces uncertainty on the integrated v2  no assumptions about the spectra and v2 at low pT

ATLAS - cumulant method - integrated flow

4

0.1 GeV  ~5% 0.2 GeV  ~20%

In practice

Nch drops down

at very low-pT (<0.1 GeV)

v2 (pT) also drops

 inclusion of ~0 GeV particles not needed/ necessary if sufficiently low pT can be reached HIJING

SLIDE 5

Means to reliably reach pT~0 Three tracking techniques

Pixel tracklets built from

2 hits in first two layers of pixel detector and vertex position

– without solenoid magnetic field, pT>0.03 GeV fully efficient pT>0.1 GeV – no pT measurement

ATLAS - cumulant method - integrated flow

5

Pixel tracks built from hits (3 in the barrel) in the Pixel only
with magnetic field, pT>0.1 GeV
ID tracks (Pixels + SCT) for crosscheck
with magnetic field, pT>0.5 GeV

SLIDE 6

0.2 0.4 0.6 0.8 1 1.2 1.4

0-10%

0.2 0.4 0.6 0.8 1 1.2 1.4

40-50%

primary

/ N

reco

N

2
1

1 2

0.2 0.4 0.6 0.8 1 1.2 1.4

70-80%

primary

/ N

matched

N

reco

/ N

fake

N

[a.u.]

T

/dp

ch

dN 1

2

10

4

10

6

10

0-10% ATLAS Simulation Preliminary =2.76 TeV

NN

s Pb+Pb |<1 Solenoid-off

|

ratio 0.5 1 [a.u.]

T

/dp

ch

dN 1 10

2

10

3

10

4

10

5

10

40-50%

ratio 0.5 1 [a.u.]

T

/dp

ch

dN 1 10

2

10

3

10

4

10

70-80%

primary

N

matched

N [GeV]

T

p

1

10 1

ratio 0.5 1

Pixel tracklets performance

Tracklets reach down

to 0.03 GeV, stably efficient above pT>0.1 GeV at the level of ~80%

Efficiency also stable

with η and centrality

Fake rates grow with

centrality and η region

f |η|>2 excluded

from the analysis

ATLAS - cumulant method - integrated flow

6

SLIDE 7

ID tracks (Pixel+SCT) performance

Minimum pT=0.5 GeV
Efficiency stable with

pT>0.7 GeV also stable with centrality

Fake rate well below

10% in most central collisions, affecting mostly low-pT and higher η

ATLAS - cumulant method - integrated flow

7 efficiency

0.2 0.4 0.6 0.8 1

0-10% Simulation ATLAS Preliminary =2.76TeV

NN

s Pb+Pb

efficiency

0.2 0.4 0.6 0.8 1

40-50%

[GeV]

T

p 1

efficiency

0.2 0.4 0.6 0.8 1

70-80%

fake rate

0.02 0.04 0.06 0.08 0.1

0-10% 0-10% ID tracks |<1.0

0<|

|<2.0

1<|

|<2.5

2<|

fake rate

0.01 0.02 0.03 0.04 0.05 40-50% 40-50%

[GeV]

T

p 1 fake rate

0.01 0.02 0.03 0.04 0.05 70-80% 70-80%

SLIDE 8

Pixel tracks performance

Efficiency weakly

dependent on pT, reaching as low as 0.1 GeV

Low pT region is

plagued with fake tracks, up to 40% in mid-η

ATLAS - cumulant method - integrated flow

8 efficiency

0.2 0.4 0.6 0.8 1

0-10% Simulation ATLAS Preliminary =2.76TeV

NN

s Pb+Pb

efficiency

0.2 0.4 0.6 0.8 1

40-50%

[GeV]

T

p

1

10 1

efficiency

0.2 0.4 0.6 0.8 1

70-80%

fake rate

0.2 0.4 0.6 0.8 1

0-10% 0-10% Pixel tracks |<1.0

0<|

|<2.0

1<|

|<2.5

2<|

fake rate

0.1 0.2 0.3 0.4 0.5 40-50% 40-50%

[GeV]

T

p

1

10 1 fake rate

0.05 0.1 0.15 0.2 0.25 70-80% 70-80%

SLIDE 9

0.2 0.4

2

v

0.02 0.04 0.06 0.08 0.1 0.12 0.14

0-10%

ATLAS Preliminary Pb+Pb =2.76TeV

NN

s |<1

|

ID tracks Pixel tracks Pixel tracklets

0.2 0.4 10-20% 0.2 0.4 20-30% 0.2 0.4 30-40% 0.2 0.4 40-50% 0.2 0.4 50-60% 0.2 0.4 60-70% 0.2 0.4 70-80%

[GeV]

T,0

p

2

v

0.02 0.04 0.06 0.08 0.1 0.12 0.14

0-10% Preliminary ATLAS

=2.76TeV

NN

s Pb+Pb <5 GeV

T

ID tracks 0.5<p <5 GeV

T

Pixel tracks 0.5<p <5 GeV

T

Pixel tracks 0.1<p >0.03 GeV

T

Pixel tracklets p

2
1

1 2

2

v

0.02 0.04 0.06 0.08 0.1 0.12 0.14

40-50%

0.1

10-20%

2
1

1 2

0.1

50-60%

0.1

20-30%

2
1

1 2

0.1

60-70%

0.1

30-40%

2
1

1 2

0.1

70-80%

Consistency between measurements

Varied lower

integration limit of pixel tracks measurement, to match:

Tracklets (0.1 GeV) ID tracks (0.5 GeV)

Consistent results

for v2 and v2(η)

Weak η

dependence can be

bserved

ATLAS - cumulant method - integrated flow

9

SLIDE 10

Uncertainties

Number of sources in the overall uncertainty considered

ATLAS - cumulant method - integrated flow

10

In case of low-pT measurements dominant source is the MC test (closure) contribution All other contributions at the level of 1-2%

centrality percentile 0 10 20 30 40 50 60 70 80 [%]

sys

20
10

10 20 30 |<1

Tracklets |

Total Centrality N-P hemisperes Sine term Closure

ATLAS Preliminary Pb+Pb =2.76TeV

NN

s

centrality percentile 10 20 30 40 50 60 70 80 [%]

sys

10

10 20 30 >0.1 GeV

T

Pixel tracks p Total Centrality Track selection N-P hemispheres Fakes uncertainty Charge +/- Sine term Closure

Preliminary ATLAS Pb+Pb =2.76TeV

NN

s

centrality percentile 10 20 30 40 50 60 70 80 [%]

sys

10

10 20 30 > 0.5 GeV

T

ID tracks p Total Centrality Track selection N-P hemispheres Charge +/- Sine term Closure

Preliminary ATLAS Pb+Pb =2.76TeV

NN

s

SLIDE 11

Comparison to CMS

Measurement is sensitive to the low-pT

ATLAS - cumulant method - integrated flow

11

Agreement when the integration threshold tuned to match one from CMS (0.3 GeV)

centrality percentile

10 20 30 40 50 60 70 80

2

v

0.02 0.04 0.06 0.08 0.1 0.12

|<1

>0.03 GeV, |

T

ATLAS tracklets B-off, p |<1

<5 GeV, |

T

ATLAS 0.1<p |<0.8

<3 GeV, |

T

CMS 0.3<p ATLAS Preliminary =2.76 TeV

NN

s Pb+Pb

2
1

1 2

2

v

0.02 0.04 0.06 0.08 0.1 0.12 0.14

40-50%

>0.03 GeV

T

ATLAS tracklets p <5 GeV

T

ATLAS Pixel tracks 0.1<p <5 GeV

T

ATLAS Pixel tracks 0.2<p <5 GeV

T

ATLAS Pixel tracks 0.3<p <3 GeV

T

CMS 0.3<p

Preliminary ATLAS

=2.76TeV

NN

s Pb+Pb

|<1

>0.03 GeV, |

T

ATLAS tracklets B-off, p |<1

<5 GeV, |

T

ATLAS 0.1<p |<0.8

<3 GeV, |

T

CMS 0.3<p

SLIDE 12

v2 scaling properties v2(|η|-ybeam) ATLAS Pixel tracklets CMS extrapolated to pT=0 from 0.3 GeV

ATLAS - cumulant method - integrated flow

12

v2(√sNN) ATLAS Pixel tracklets compatible with ALICE and CMS

beam

|-y

|
8
6
4
2

2

v

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

3-15% CMS 2.5-15% ATLAS tracklets CMS PHOBOS Hit based PHOBOS Track based

beam

|-y

|
8
6
4
2

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

15-25%

ATLAS Preliminary

beam

|-y

|
8
6
4
2

0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

25-50%

ATLAS & CMS Pb+Pb =2.76 TeV

NN

s PHOBOS Au+Au =200 GeV

NN

s

(GeV)

NN

s

1 10

2

10

3

10

4

10

2

v

0.08
0.06
0.04
0.02

0.02 0.04 0.06 0.08

Preliminary ATLAS 20-30%

ATLAS CMS ALICE STAR PHOBOS PHENIX NA49 CERES E877 EOS E895 FOPI

SLIDE 13

Cumulant method

Why to use it?

– v2 harmonic measured with Event Plane folds in the non- flow contributions: jets, resonance decays, ... – In the 2k-th cumulant v2{2k} non-flow contributions involving <2k particles are invisible – Numerically difficult  nested loops over particles O(N2k)  Generating Functions of correlations and cumulants used as enabling technique  numerical complexity O(N)

In ATLAS ID tracks used

– Reference flow measured from 0.5<pT<12 GeV, |η|<2.5 – v2{2} 0-80%, v2{4} 5-70%

ATLAS - cumulant method - integrated flow

13

SLIDE 14

The v2{2} systematically above v2{4}  Differences due to non-flow and/or event-by-event fluctuations  At high-pT v2{2} likely determined by the influence of jets

2

v

0.1 0.2

0-5% ATLAS Preliminary = 2.76 TeV

NN

s Pb-Pb

1

b µ 2

int

L | < 1

|

0.1 0.2

{2}

2

v {4}

2

v

5-10%

0.1 0.2

10-20%

0.1 0.2

20-30%

0.1 0.2

30-40%

0.1 0.2

40-50%

5 10

0.2 0.4 0.6

50-60%

5 10

0.2 0.4 0.6

60-70%

[GeV]

T

p

5 10

0.2 0.4 0.6

70-80%

Cumulants results

ATLAS - cumulant method - integrated flow

14

For v2{2} no single major source of uncertainty Uncertainties dominated by statistics for v2{4} for high pT

2 4 6 8 10

2

|/v

2

v

|

0.05 0.1 0.15

Statistical error Systematic error

ATLAS Preliminary 20-30%

{2}

2

v

[GeV]

T

p

2 4 6 8 10

0.05 0.1 0.15 Centrality cuts Sine term >0

<0 vs
Track selection
vs h

+

h MC closure

{4}

2

v

SLIDE 15

5 10

2

v

0.1 0.2

{2}

2

ATLAS: v {2}

2

ALICE: v {2}

2

CMS: v

ATLAS Preliminary 40-50%

[GeV]

T

p 5 10

0.1 0.2

Event Plane

2

ATLAS: v Event Plane

2

CMS: v

5 10

0.1 0.2

{4}

2

ATLAS: v {4}

2

ALICE: v {4}

2

CMS: v

Comparison of v2{2}, v2{4}, v2{EP} Good agreement between LHC experiments

– v2{4} agrees very well – v2{2} a bit off at high-pT between ATLAS and CMS

The v2{EP} lies between v2{2} and v2{4}

ATLAS - cumulant method - integrated flow

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SLIDE 16

2

v

0.05 0.1

0-5% ATLAS Preliminary = 2.76 TeV

NN

s Pb-Pb

1

b µ 2

int

L < 12 GeV

T

0.5 < p

0.05 0.1

{2}

2

v {4}

2

v 5-10%

0.05 0.1

10-20%

0.05 0.1

20-30%

0.05 0.1

30-40%

0.05 0.1

40-50%

2
1

1 2

0.05 0.1

50-60%

2
1

1 2

0.05 0.1

60-70%

2
1

1 2

0.05 0.1

70-80%

Pseudorapidity dependence integrated flow

The difference observed in the differential measurement propagates to the integrated ones

ATLAS - cumulant method - integrated flow

16

centrality percentile

0-10% 10-20% 20-30% 30-40% 40-50% 50-60% 60-70% 70-80% 2

v 0.05 0.1 0.15

{2}

2

v {4}

2

v

ATLAS Preliminary = 2.76 TeV

NN

s Pb-Pb | < 1

|
1

b µ 2

int

L < 12 GeV

T

0.5 < p

SLIDE 17

centrality percentile

1

% 1

2

% 2

3

% 3

4

% 4

5

% 5

6

% 6

7

% 7

8

%

>

2

<v

2

v

0.2

0.4 0.6 0.8

2

4

2

+v

2

v

2

4

2

v

2

v

ATLAS Preliminary < 12 GeV

T

|<1 0.5 < p

|

Glauber MC )

1
4/

Gaussian distribution (

Event-by-event fluctuations Difference between v2{2} and v2{4} may also measure the fluctuations of eccentricity

ATLAS - cumulant method - integrated flow

17

σ 2 v2 = v2{2}2 − v2{4}2 v2{2}2 + v2{4}2

A. Voloshin, A. Poskanzer, A. Tang, A. Wang

arXiv:0708.0800

2 4 6

>

2

<v

2

v

0.2

0.4 0.6 0.8 1

5-10% 10-20% 20-30% 30-40%

ATLAS Preliminary

2

4

2

+v

2

v

2

4

2

v

2

v |<1

|

[GeV]

T

p

2 4 6 0.2 0.4 0.6 0.8 1

40-50% 50-60% 60-70%

W. Broniowski, M. Rybczynski, P. Bozek

arXiv:0710.5731

In the 5-10% bin independent of pT

less central collisions and higher pT  stronger pT dependence

Evolution with centrality  compares well with the GLISSANDO model for central collisions

SLIDE 18

Summary

Integrated v2 flow harmonic measured using the EP method

– three tracking techniques used to reach pT down to ~0.03 GeV no extrapolation required! – lower pT leads to reduced integrated v2

The v2(η) consistent with CMS and extrapolation of scaling trend

found at RHIC

The v2(√sNN)  agreement with ALICE and CMS
Differential v2 flow harmonic was measured

using 2 and 4 particles cumulants – results compatible with CMS and ALICE – clearly observed suppression v2{2}  v2{4} – v2{2} > v2{EP} > v2{4}

Event-by-event elliptic flow fluctuations ~40%

– independent of pT only in 5-10% bin, weak pT dependence up to ~1.5 GeV

ATLAS - cumulant method - integrated flow

18