1 Measurements of flow harmonics with the event plane and cumulant methods from the ATLAS experiment Quark Matter 2012 - 2012-08-17 – Washington DC Tomasz Bold, AGH UST Krakow for the ATLAS Collaboration
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 ATLAS-CONF-2012-117 • Flow measurements with cumulants – Method description – Two and four particle cumulants differential measurement – Comparison between the experiments – Integrated results ATLAS-CONF-2012-118 – Fluctuations ATLAS - cumulant method - integrated flow
3 Event plane method and integrated v 2 • 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 v 2 by number of particles int = ∑ ∑ ∑ ∑ c c v 2 N ik v 2 ik / N ik in bins of p T and η k i k i – corrected by efficiency c (1 − f ik )/ ε ik c = N ik and fake rates N ik ATLAS - cumulant method - integrated flow
4 v 2 {EP} integrated down to very low-p T Reaching low p T reduces uncertainty on the integrated v 2 no assumptions about the spectra and v 2 at low p T In practice 0.16 • N ch drops down 2 v ATLAS Simulation p > 500 MeV HIJING at very low- p T (<0.1 GeV) 0.14 Preliminary T p > 200 MeV Pb+Pb s =2.76 TeV • v 2 (p T ) also drops T 0.12 NN | |<2 � p > 150 MeV T 0.1 p > 100 MeV inclusion of ~0 GeV T 0.08 p > 50 MeV particles not needed/ T 0.06 p > 30 MeV necessary if sufficiently low p T T no min p cut 0.04 T can be reached 0.02 ratio 1.3 1.2 +0.4 0.1 GeV ~5% 1.1 1 0.2 GeV ~20% 0 20 40 60 80 100 Centrality[%] ATLAS - cumulant method - integrated flow
5 Means to reliably reach p T ~0 Three tracking techniques • Pixel tracklets built from 2 hits in first two layers of pixel detector and vertex position – without solenoid magnetic field, p T >0.03 GeV fully efficient p T >0.1 GeV – no p T measurement • Pixel tracks built from hits (3 in the barrel) in the Pixel only - with magnetic field, p T >0.1 GeV • ID tracks (Pixels + SCT) for crosscheck - with magnetic field, p T >0.5 GeV ATLAS - cumulant method - integrated flow
6 Pixel tracklets performance • Tracklets reach down 6 [a.u.] 10 1.4 0-10% 0-10% 1.2 4 10 ATLAS Simulation to 0.03 GeV , T /dp Preliminary 1 2 10 ch Pb+Pb s =2.76 TeV 0.8 NN dN | � |<1 Solenoid-off stably efficient above 1 0.6 ratio 1 0.4 p T >0.1 GeV 0.5 0.2 5 [a.u.] 1.4 10 40-50% at the level of ~80% 40-50% 4 10 1.2 3 T 10 /dp 1 2 10 • Efficiency also stable ch 0.8 10 dN 1 0.6 ratio with η and centrality 1 N / N 0.4 reco primary 0.5 0.2 • Fake rates grow with 4 1.4 [a.u.] 10 70-80% 70-80% 3 1.2 10 centrality and η region T 2 1 /dp 10 N primary 0.8 ch 10 N dN of | η |>2 excluded matched 1 0.6 N / N ratio matched primary 1 0.4 N / N from the analysis fake reco 0.5 0.2 -1 -2 -1 0 1 2 10 1 � p [GeV] T ATLAS - cumulant method - integrated flow
7 ID tracks (Pixel+SCT) performance • Minimum p T =0.5 GeV fake rate efficiency ID tracks ATLAS Simulation 0-10% 0-10% 0-10% 0<| |<1.0 � 0.1 1 Preliminary 1<| � |<2.0 Pb+Pb s =2.76TeV 2<| |<2.5 0.08 � • Efficiency stable with NN 0.8 0.06 0.6 p T >0.7 GeV also 0.04 0.4 stable with centrality 0.02 0.2 efficiency fake rate 0.05 40-50% 40-50% 40-50% • Fake rate well below 1 0.04 0.8 10% in most central 0.03 0.6 0.02 collisions, affecting 0.4 0.01 mostly low- p T and 0.2 efficiency fake rate 0.05 70-80% 70-80% 70-80% higher η 1 0.04 0.8 0.03 0.6 0.02 0.4 0.01 0.2 1 1 p [GeV] p [GeV] T T ATLAS - cumulant method - integrated flow
8 Pixel tracks performance • Efficiency weakly efficiency fake rate Pixel tracks ATLAS Simulation 0-10% 1 0-10% 0-10% 0<| � |<1.0 Preliminary 1 dependent on p T , 1<| |<2.0 � Pb+Pb s =2.76TeV 0.8 2<| |<2.5 � NN 0.8 0.6 reaching as low as 0.6 0.4 0.4 0.1 GeV 0.2 0.2 efficiency fake rate 0.5 40-50% • Low p T region is 40-50% 40-50% 1 0.4 plagued with fake 0.8 0.3 0.6 tracks, up to 40% in 0.2 0.4 0.1 mid- η 0.2 fake rate efficiency 0.25 70-80% 70-80% 70-80% 1 0.2 0.8 0.15 0.6 0.1 0.4 0.05 0.2 -1 -1 10 10 1 1 p [GeV] p [GeV] T T ATLAS - cumulant method - integrated flow
9 Consistency between measurements 2 v ATLAS 0.14 Preliminary Pb+Pb • Varied lower 0.12 s =2.76TeV NN | |<1 � integration limit of 0.1 ID tracks Pixel pixel tracks 0.08 tracks Pixel measurement, 0.06 tracklets to match: 0.04 Tracklets ( 0.1 GeV ) 0.02 0-10% 10-20% 20-30% 30-40% 40-50% 50-60% 60-70% 70-80% ID tracks ( 0.5 GeV ) 0 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 0.2 0.4 • Consistent results p [GeV] T,0 for v 2 and v 2 ( η ) 0.14 ATLAS Preliminary Pb+Pb s =2.76TeV 0.12 NN • Weak η ID tracks 0.5<p <5 GeV 0.1 0.1 0.1 0.1 T Pixel tracks 0.5<p <5 GeV 0.08 T 2 Pixel tracks 0.1<p <5 GeV v dependence can be T 0.06 Pixel tracklets p >0.03 GeV T 0.04 observed 0.02 0-10% 10-20% 20-30% 30-40% 0.14 0.12 0.1 0.1 0.1 0.1 2 0.08 v 0.06 0.04 0.02 40-50% 50-60% 60-70% 70-80% -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 -2 -1 0 1 2 � � � � ATLAS - cumulant method - integrated flow
10 Uncertainties Number of sources in the overall uncertainty considered [%] [%] [%] Pixel tracks p >0.1 GeV Tracklets | � |<1 ID tracks p > 0.5 GeV T sys sys 30 T sys Total Total 30 Total 30 � Centrality � Centrality � Centrality N-P hemisperes Track selection 20 Track selection Sine term N-P hemispheres 20 20 Closure N-P hemispheres Fakes uncertainty Charge +/- Charge +/- 10 Sine term Sine term 10 10 Closure Closure 0 0 0 -10 ATLAS Preliminary ATLAS Preliminary ATLAS Preliminary Pb+Pb -20 -10 Pb+Pb -10 Pb+Pb s =2.76TeV s =2.76TeV NN s =2.76TeV NN NN 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 0 10 20 30 40 50 60 70 80 centrality percentile centrality percentile centrality percentile In case of low- p T measurements dominant source is the MC test (closure) contribution All other contributions at the level of 1-2% ATLAS - cumulant method - integrated flow
11 Comparison to CMS 2 40-50% v 0.12 0.14 ATLAS Preliminary ATLAS Preliminary Pb+Pb s =2.76TeV Pb+Pb s =2.76 TeV NN NN 0.12 0.1 0.1 0.08 0.08 2 0.06 v 0.06 ATLAS tracklets p >0.03 GeV 0.04 T ATLAS tracklets B-off, p >0.03 GeV, | |<1 � ATLAS Pixel tracks 0.1<p <5 GeV T 0.04 T ATLAS tracklets B-off, p >0.03 GeV, | |<1 ATLAS 0.1<p <5 GeV, | |<1 � � ATLAS Pixel tracks 0.2<p <5 GeV 0.02 T T T ATLAS 0.1<p <5 GeV, | |<1 � CMS 0.3<p <3 GeV, | |<0.8 ATLAS Pixel tracks 0.3<p <5 GeV T � 0.02 CMS 0.3<p <3 GeV, | |<0.8 � T T T CMS 0.3<p <3 GeV 0 T 0 10 20 30 40 50 60 70 80 -2 -1 0 1 2 centrality percentile � Agreement when the Measurement is sensitive to integration threshold the low- p T tuned to match one from CMS ( 0.3 GeV ) ATLAS - cumulant method - integrated flow
12 v 2 scaling properties 0.1 0.1 0.1 2 v 3-15% 15-25% 25-50% 0.09 v 2 (| η |-y beam ) 0.09 0.09 CMS 2.5-15% ATLAS Preliminary 0.08 0.08 0.08 ATLAS Pixel tracklets ATLAS tracklets 0.07 0.07 0.07 CMS CMS extrapolated to 0.06 0.06 0.06 PHOBOS Hit based PHOBOS Track based 0.05 0.05 0.05 p T =0 from 0.3 GeV ATLAS & CMS Pb+Pb 0.04 0.04 0.04 s =2.76 TeV NN 0.03 0.03 0.03 PHOBOS 0.02 0.02 0.02 Au+Au s =200 GeV 0.01 0.01 0.01 NN 0.08 2 v ATLAS Preliminary -8 -6 -4 -2 0 -8 -6 -4 -2 0 -8 -6 -4 -2 0 0.06 20-30% | |-y | |-y | |-y � � � beam beam beam 0.04 0.02 ATLAS CMS ALICE 0 v 2 ( √ s NN ) ATLAS Pixel tracklets STAR PHOBOS -0.02 PHENIX compatible with ALICE and CMS NA49 -0.04 CERES E877 EOS -0.06 E895 FOPI -0.08 3 2 4 1 10 10 10 10 s (GeV) NN ATLAS - cumulant method - integrated flow
13 Cumulant method • Why to use it? – v 2 harmonic measured with Event Plane folds in the non- flow contributions: jets, resonance decays, ... – In the 2k -th cumulant v 2 {2k} non-flow contributions involving <2k particles are invisible – Numerically difficult nested loops over particles O (N 2k ) 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<p T <12 GeV , | η |<2.5 – v 2 {2} 0-80%, v 2 {4} 5-70% ATLAS - cumulant method - integrated flow
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