Measurement of top quark polarisation in t t ¯ events with the ATLAS detector in proton-proton collisions at √

ATLAS-CONF-2012-133 17September2012

ATLAS NOTE

ATLAS-CONF-2012-133

September 17, 2012

Measurement of top quark polarisation in t t ¯ events with the ATLAS detector in proton-proton collisions at √

s = 7 TeV

The ATLAS Collaboration

Abstract

This note presents a measurement of the top quark polarisation in

events using the lep- ton plus jets final state, where one

boson decays leptonically and the other hadronically.

The decay of the

pair is fully reconstructed using a likelihood method in order to calcu- late the rest frame of the leptonically decaying top quark. A template fit to the distribution of lepton polar angles in the parent top quark’s rest frame is used to extract the fraction of positively polarised top quarks. The full 2011 ATLAS 7 TeV centre of mass energy

colli- sions dataset from the LHC (4.66 fb

) is used to perform the measurement. The fraction of positively polarised top quarks is found to be

0.470± 0.009(stat)

(syst), compatible with the Standard Model prediction of

0.5.

c

Copyright 2012 CERN for the benefit of the ATLAS Collaboration.

Reproduction of this article or parts of it is allowed as specified in the CC-BY-3.0 license.

1 Introduction

Discovered in 1995 by the experiments CDF and D0 at the Tevatron collider [1, 2], the top quark is the heaviest elementary particle known today. Its large mass of m

173.2

0.9 GeV [3] and short lifetime of about 0.5× 10

s [4] make it an interesting particle to study. In the Standard Model (SM), top quarks are produced unpolarised because of parity conservation in QCD and the unpolarised initial state, but some models beyond the SM (BSM) can result in a measurable polarisation of the top quark. In particular, models that predict the top quark forward-backward asymmetry to be larger than the SM prediction, as was seen by the Tevatron experiments [5–8], have di

erent predictions of the top quark polarisation [9].

Recently, the CMS Collaboration has also made public a measurement of top quark polarisation in the dilepton channel [10].

This note presents a measurement of the top quark polarisation in single lepton t¯ t events. Due to the top quark’s short lifetime, it decays before it hadronises. Therefore the spin information of the top quark is conserved and it is possible to extract it from the decay products of the W boson. The top quark polarisation is measured by studying the polar angle of the charged lepton in the parent top quark’s rest frame. The distribution of the polar angle,

, for any daughter particle labeled i with respect to a quantisation axis is given by

W(cos

)

1

cos

(1)

where

represents the degree of polarisation along this axis and

is the spin analysing power [11]. The spin analysing powers of the decay products vary as a function of particle type. At the tree level, charged leptons are predicted to have a spin analysing power of one (α

1). They therefore have the largest sensitivity to the top quark’s spin state. Here the product of

and

is measured. It should be noted that if anomalous couplings are present, the spin analysing power of particles changes independently of the polarisation. The helicity basis of the top quark is used to determine the quantisation axis. This corresponds to choosing the quantisation axis as the parent top quark’s momentum direction in the t¯ t centre of mass frame.

A full reconstruction of the t¯ t system is required in order to calculate cos

. A likelihood fit is used to determine the neutrino momentum and the assignment of final state jets to the top and antitop quark decays. To measure the polarisation of the top quarks, a fit of the reconstructed cos

distribution is performed using signal templates created from simulated signal events, corresponding to positive and negative polarisation ( 1

cos

) and ( 1

cos

) combined with templates for background events. The result of the fit is the fraction of positively polarised top quarks f , which is defined by:

1

2 f (1

cos

)

1

2 (1

f )(1

cos

)

1

2 (1

cos

(2)

and is related to the asymmetry by:

f

1

2

N(cos

0)

N(cos

0)

N(cos

0)

N(cos

0)

(3) The degree of polarisation can be put in terms of the fraction f by the relation:

α_`p=

2 f

1. (4)

2 Data and Simulated Samples

The analysis in this note is performed using the full 2011 7 TeV centre of mass energy pp collision dataset

collected by the ATLAS detector. ATLAS is a multipurpose particle detector at the CERN Large Hadron

Collider and is described in full detail in Ref. [12]. The detector is roughly cylindrical and consists of

an inner tracking detector inside a 2 T solenoidal magnet with coverage over the pseudorapidity range

|η| <

2.7

, electromagnetic and hadronic calorimeters with a range

4.9, and muon spectrometers inside a toroidal magnetic field over a range

2.7.

The analysis presented here uses all components of the ATLAS detector in order to identify the physics objects involved. Jet reconstruction requires both the calorimeters and the tracking system, and the tracking system is particularly important for the identification of jets from b-quarks. Electrons are also identified and reconstructed using the tracking and calorimeter systems. Muons are identified and reconstructed using the tracking system and muon spectrometers. The data analysed here have been collected using triggers that require a single electron or muon in the event. The total integrated luminosity used is 4.66

0.08 fb

.

Samples of simulated events are used to model both the signal t¯ t processes as well as many of the background processes. A number of different Monte Carlo generators are used for this purpose; for each sample a full simulation in G

4 [13] of the ATLAS detector response is performed, and the same reconstruction software as used for data is used to process the events [14]. Signal t¯ t events are produced by the next-to-leading order (NLO) generator MC@NLO [15] with the NLO parton density functions (PDF) set CT10 [16]. Parton showering is modelled with HERWIG [17], and JIMMY [18]

is used to model the underlying event. Backgrounds from single top quark and diboson production are determined using simulation. MC@NLO is used to model single top quark production in the s-channel and the W

t channel and AcerMC [19] is used to model single top quark production in the t-channel.

The ALPGEN [20] generator is used for single W and Z boson production with associated jets, and is interfaced to HERWIG and JIMMY for parton showering and underlying event modeling. Diboson samples are produced with HERWIG alone. Each simulated signal or background event is overlaid with additional pp collisions; the distribution of the number of collisions is reweighted to match the distribution observed in data.

In order to study the systematic uncertainty on the modelling of the signal, other simulated samples are used that di

er from the nominal sample. An uncertainty due to possible limitations in the implemen- tation of t¯ t production in the generators is determined by comparing POWHEG [21] and MC@NLO using the same parton showering and underlying event description. The effects of initial and final state radia- tion and colour reconnection are evaluated with parameter changes in the A

MC generator. The parton shower description is studied using the di

erence between POWHEG combined with PYTHIA [22] or HERWIG. The effects of uncertainty in the top quark mass are evaluated by adjusting the it in MC@NLO.

3 Event Selection and Background Estimation

3.1 Object and Event Selection

The selection of top quark pair events involves the use of many different physics objects. Charged leptons, jets, and the missing transverse momentum from neutrinos are all present in the decay topology of these events. Event selection begins by placing requirements on the reconstruction of these objects to classify them as “good” as defined in the following.

To be selected, electrons and muons must possess sufficient transverse momentum, pass detector quality cuts, and be isolated from additional energy deposits in the detector. For electrons, the calorime- ter cluster must be in the range

2.47, excluding a transition region of the detector from 1.37

1.52. Their transverse energy must be greater than 25 GeV. Quality cuts optimised to

1In the right-handed ATLAS coordinate system, the pseudorapidityηis defined asη = −ln[tan(θ/2)], where the polar angleθis measured with respect to the LHC beamline. The azimuthal angleφis measured with respect to thex-axis, which points towards the centre of the LHC ring. Thez-axis is parallel to the anti-clockwise beam viewed from above. Transverse momentum and energy are defined aspT=psinθandET=Esinθ, respectively.

separate good electrons from jet backgrounds are imposed [23]. The electrons must also pass isolation requirements on the calorimeter energy deposits and track transverse momentum in cones

of

R

0.2 and

R

0.3 respectively, where each cut has been optimised for 90% efficiency. Muons are recon- structed by matching muon spectrometer information with inner detector tracking. Selected muons must lie within the range

2.5 and have p

20 GeV. There are quality requirements imposed on the num- ber of hits in different tracking systems. The muons are required to be isolated by cuts on the transverse calorimeter energy and transverse momentum of tracks in cones of

R

0.2 and

R

0.3.

Jets are reconstructed from calorimeter energy deposits using the anti-k

algorithm [24]. They are required to be in the range

2.5 and have p

25 GeV [25]. These jets are also required to be compatible with the primary vertex in an event using the tracks associated to the jet. The background from W plus jets events is strongly suppressed by the requirement of a b-tagged jet, therefore it is essential to identify such jets. A neural network algorithm is used that combines the jet kinematics and the output of three other tagging algorithms that are based on tracks associated to the jet and on the reconstruction of secondary vertices [26]. A threshold is chosen for which simulated jets from b-quarks have 70%

e

ciency; jets passing this threshold are considered “b-tagged” [27, 28].

The sum of all energy deposits in the calorimeters determines the missing transverse momentum, E

[29]. The procedure used treats deposits appropriately depending on their association with a re- constructed object, and adds them in a vector sum along with a correction for muons. For signal events, the E

is likely to originate from a neutrino from the W decay producing the reconstructed charged lepton. The transverse mass of the W candidate is given by:

m

2p

(`) p

(ν)[1

cos(φ

)]. (5) Based on the selected objects, top quark pair events are selected to have a single charged lepton with many jets and missing transverse momentum:

•

Exactly one good electron or muon, matching their respective single lepton trigger

•

At least four good jets

•

Missing transverse momentum and high transverse mass including the lepton:

–

Electron channel - E

30 GeV and m

30 GeV

Muon channel - E

20 GeV and E

m

60 GeV

•

At least one jet tagged as a b-quark jet 3.2 Estimation of Backgrounds

Two major classes of backgrounds are considered; those with “real” leptons and those with “fake” lep- tons. Backgrounds from real leptons consist of vector boson production and single top production. Single top, Z plus jets, and diboson production are estimated from simulation. Events from simulated W plus jets production are used only to predict the shape of observable distributions, while the expected number of events is based on a measurement of the lepton charge asymmetry in data [30].

Backgrounds with fake leptons originate from multi-jet production. The contribution is estimated using a matrix method applied to the data; it is described in more detail in Ref. [31]. The matrix method estimates the number of events with a fake lepton by comparing the number of events with a lepton passing “loose” and “tight” selection criteria, where the main di

erence is that tight corresponds to the full selection and loose does not require the leptons to be isolated. These numbers are used along with

2∆R= p

∆φ²+ ∆η²

information about the efficiency of real lepton and fake lepton events categorised as loose to also pass the tight selection in order to estimate the yield and the shape of event distributions for fake lepton events passing the full selection. The efficiency for real leptons is measured using Z

events, and the fake efficiency is measured in a sample requiring the presence of a jet and low missing transverse momentum.

By combining the background estimation with simulated signal t¯ t samples, a prediction for the num- ber of data events is obtained. In Table 1, this expectation is compared to the number of data events separately in the electron and muon channels. Comparisons for the number of b-tagged jets and m

can be found in Fig. 1.

Table 1: Number of selected data events and estimated sample composition for the two lepton plus jets channels, specifying whether data-driven (DD) or pure Monte Carlo (MC) methods are used for the estimation of the yields. The uncertainties are broken down into statistical and systematic uncertainties.

e

jets

jets W

jets (DD) 2400

50

4500

60

Fake Leptons (DD) 1600

40

2000

20

Z

jets (MC) 450

10

440

10

Single Top (MC) 1180

10

1950

10

Diboson (MC) 47

1

74

2

Total (non-t¯ t) 5700

60

8900

60

t¯ t

jets (MC) 14200

30

23600

30

t¯ t dilep (MC) 2000

10

2900

10

t¯ t total (MC) 16100

30

26500

40

Total Expected 21900

70

35000

70

Observed 22019 37967

4 Event Reconstruction

To measure the polarisation of the top quark in the lepton plus jets final state, the lepton and neutrino from the Wboson decay and the b-quark are needed to reconstruct the kinematics of the semi-leptonically decaying top. The lepton is measured directly, but the neutrino and b-quark must be inferred from the full event reconstruction. Since the t¯ t centre of mass frame is needed to determine the quantisation axis, the correct assignment of jets on the hadronic side is necessary. The full event reconstruction is based on a kinematic fit of the full decay chain to the reconstructed objects in the event; this method has also been used for other ATLAS top quark studies [30, 32, 33].

A set of permutations of the selected jets in the event is first made, assigning each jet to be either

one of the two b-quarks from top quark decays or one of the two quarks from the hadronically decaying

Wboson. For each permutation, a likelihood function for the kinematics corresponding to the top quark

decay topology is constructed and maximised, using the energies of the reconstructed particles and the

full momentum of the neutrino as parameters. This kinematic likelihood combines the resolutions for

the jets, charged lepton, and E

with Breit-Wigner functions for the masses of two W bosons and two

top quarks. In addition, the combined probability using the b-tagging efficiency and light quark rejec-

tion factors of the tagging algorithm is calculated for the assignment of jets in that permutation. The

event probability for each permutation is then defined as the product of the kinematic likelihood and the

b-tagging likelihood normalised by the sum of the probabilities over all permutations. The permutation

Events

2000 4000 6000 8000 10000 12000 14000 16000 18000 20000

22000 _Data

t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

Number of b-tagged Jets

1 2 3 4

Ratio

0.5 1 1.5

(a) Electron channelb-tagged jets

Events

5000 10000 15000 20000 25000 30000

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

Number of b-tagged Jets

1 2 3 4

Ratio

0.5 1 1.5

(b) Muon channelb-tagged jets

Events / 10 GeV

1000 2000 3000 4000 5000 6000

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

(W) [GeV]

mT

50 100 150 200 250

Ratio 0.5

1 1.5

(c) Electron channelmT

Events / 10 GeV

1000 2000 3000 4000 5000 6000

7000 ^Datatt

W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

(W) [GeV]

mT

50 100 150 200 250

Ratio 0.5

1 1.5

(d) Muon channelmT

Figure 1: Comparison between data and expectation for the number of b-tagged jets and the m

for the

electron and muon channels. Also shown is the ratio of the data to the expectation. The shaded regions

represent the error on the prediction.

with the highest event probability is chosen and used to interpret both top quark decays in that event. A comparison of the event probability distribution for the best permutation of data and simulation is shown in Fig. 2; the large number of events with values near one correspond to events in which the probabil- ity for one permutation completely dominates all others, while the rest of the distribution corresponds to cases in which two or more permutations have comparable probabilities. Comparisons of the recon- structed kinematic quantities for the b-quark assigned to the leptonically decaying W and the neutrino are shown in Figs. 3 and 4. The expected distribution of cos

is compared with data in Fig. 5, which is obtained after acceptance and e

ciency if one starts with a flat distribution at generator level.

1 10 102

103

104

105

106

Events / 0.04

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

Event Probability 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio 0.8

1 1.2

(a) Electron Channel

1 10 102

103

104

105

106

Events / 0.04

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

Event Probability 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Ratio 0.8

1 1.2

(b) Muon Channel

Figure 2: Comparison between data and expectation of the configuration with the highest event proba- bility. Also shown is the ratio of the data to the expectation. The shaded regions represent the error on the prediction.

5 Polarisation Template Fit

A template fit to the data is performed in the variable cos

, using templates based on fully positively and

negatively polarised top quarks, added to the background expectation to extract a value for the fraction

of positively polarised top quarks. The signal templates are created by reweighting the simulated signal

events so that the generated distributions of cos

are equal to

(1

cos

) and

(1

cos

). Each

of the backgrounds described in Section 3.2 are modelled with a separate template with their individ-

ual normalisation uncertainties treated as systematic uncertainties. A simultaneous extended maximum

likelihood fit to the e

f , the fraction of positively polarised top

quarks. The SM value of no polarisation corresponds to f

0.5. The fit is performed for positively and

negatively charged leptons both separately and jointly. The t¯ t production cross-section is allowed to vary

in order to reduce the influence of normalisation uncertainties on the result. The influence of each source

of systematic uncertainty is evaluated by varying the templates for each uncertainty separately up and

down by one standard deviation and repeating the fit over ensembles of pseudo-data generated from the

data. In the case where an uncertainty is taken as the difference between two points, it is symmetrised

around the nominal value. The width of the distribution over many pseudo-data sets of differences be-

1000 2000 3000 4000 5000 6000 7000 8000

Events / 20 GeV

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

) [GeV]

(bLep

pT

0 50 100 150 200 250 300

Ratio 0.5

1 1.5

(a) Electron Channel

2000 4000 6000 8000 10000 12000

Events / 20 GeV

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

) [GeV]

(bLep

pT

0 50 100 150 200 250 300

Ratio 0.5

1 1.5

(b) Muon Channel

500 1000 1500 2000 2500

Events / 0.24

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

Lep) η(b

-3 -2 -1 0 1 2 3

Ratio 0.5

1 1.5

(c) Electron Channel

500 1000 1500 2000 2500 3000 3500 4000

Events / 0.24

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

Lep) η(b

-3 -2 -1 0 1 2 3

Ratio 0.5

1 1.5

(d) Muon Channel

Figure 3: Comparison of p

and

between the expectation and the data for the b-quark assigned to the

leptonically decaying W boson in the electron and muon channels. Also shown is the ratio of the data to

the expectation. The shaded regions represent the error on the prediction.

1000 2000 3000 4000 5000 6000 7000 8000 9000

Events / 20 GeV

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

) [GeV]

ν

T( p

0 50 100 150 200 250 300

Ratio 0.5

1 1.5

(a) Electron Channel

2000 4000 6000 8000 10000 12000 14000

Events / 20 GeV

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

) [GeV]

ν

T( p

0 50 100 150 200 250 300

Ratio 0.5

1 1.5

(b) Muon Channel

1000 2000 3000 4000 5000 6000 7000 8000

Events / 40 GeV

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

) [GeV]

ν

z( p

-500 -400 -300 -200 -100 0 100 200 300 400 500

Ratio 0.5

1 1.5

(c) Electron Channel

2000 4000 6000 8000 10000 12000

Events / 40 GeV

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

) [GeV]

ν

z( p

-500 -400 -300 -200 -100 0 100 200 300 400 500

Ratio 0.5

1 1.5

(d) Muon Channel

Figure 4: Comparison of neutrino p

and p

between the expectation and the data in the electron and

muon channels. Also shown is the ratio of the data to the expectation. The shaded regions represent the

error on the prediction.

500 1000 1500 2000 2500

Events / 0.1

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

l) θ cos(

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Ratio 0.8

1 1.2

(a) Electron channel

500 1000 1500 2000 2500 3000 3500 4000

Events / 0.1

Data t t W+jets Single top Z+jets Diboson Fake Leptons

Syst. Unc.

⊕ Stat L dt = 4.66 fb-1

∫

= 7 TeV s

ATLAS Preliminary

l) θ cos(

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

Ratio 0.8

1 1.2

(b) Muon Channel

Figure 5: Nominal expected distributions of cos

compared to data for the electron and muon channels after event reconstruction but before performing the template fit. Also shown is the ratio of the data to the expectation. The shaded regions represent the error on the prediction.

tween the central fit values and the up and down results is taken as the systematic uncertainty in that parameter. Systematic uncertainties arising from the same source are treated as being correlated between different samples.

6 Sources of Systematic Uncertainty

The systematic uncertainties evaluated in this analysis originate from the detector response to the physics objects and the modelling of the signal and background processes. For each source of uncertainty the e

ect on both the normalisation and the shape of the cos

template is evaluated. The uncertainties are discussed in more detail below and summarised in Table 3.

6.1 Experimental Uncertainties

The uncertainties involved in the reconstruction and identification of the charged lepton, jets, and missing

transverse momentum are all evaluated. These include the uncertainties in the determination of the

kinematics of the objects involved, as well as the e

ciency to reconstruct and identify them. This

includes both resolution uncertainties and calibration scale uncertainties. Calibration scale uncertainties

for jets from b-quarks and other jets are treated separately. The e

ect of systematic uncertainties on all

objects is also propagated into the calculation of the missing energy. The missing transverse energy is

also affected by uncertainties originating from energy deposits that are unassociated with objects. Events

with detector uncertainties taken into account are then fit with the likelihood procedure and reconstructed

as usual to produce alternate signal and background templates. For the e

ciency uncertainties the new

weights are used to create alternate templates. The systematic uncertainty that has the largest effect on

the polarisation fraction measurement is the determination of the energy scale of the selected jets, which

a

ects both the signal and background normalisations as well as the signal shape.

6.2 Signal Modelling

Theoretical uncertainties on t¯ t production in simulation include uncertainties on the generator used to produce t¯ t events, the description of initial and final state radiation, the description of colour reconnec- tion, and the modelling of fragmentation. These are evaluated by modifying the generation and simu- lation procedures used to model the signal using the programs described in Section 2. The di

erences between generators are evaluated by comparing results obtained using the nominal MC@NLO sample with POWHEG when both are interfaced to HERWIG. The effects of initial and final state radiation are evaluated using a pair of signal samples generated with A

MC and PYTHIA using di

erent parton showering parameters that have been constrained by the measurement in Ref. [34]. Colour reconnection is also evaluated using the difference between different PYTHIA tunes combined with the A

MC gen- erator. The fragmentation uncertainty is evaluated using the di

erence between samples generated with POWHEG and interfaced to either HERWIG or PYTHIA. The uncertainty on the cos

distribution due to each of these sources is evaluated separately and propagated to the analysis.

The largest e

ect in signal modelling comes from the uncertainty of the top quark mass, which is about 1 GeV. It is evaluated using seven different signal templates with altered top quark masses between 165 GeV and 180 GeV. The full analysis is repeated at each point, and the results are used to perform a linear fit of the dependence of f on the top quark mass. The change in f over a range of

is combined with the absolute variation of the nominal result from the best fit trend, used to quantify the uncertainty in the determination of the fitted dependence, and the total is used to estimate an overall uncertainty on f due to the uncertainty in the top quark mass.

6.3 Background Modelling

The uncertainty on the normalisation of the various background components is included in the polar- isation fit. For the largest backgrounds the e

ect of systematic uncertainties is also propagated to the template shapes. For W plus jets production, the overall normalisation is varied according to the resid- ual uncertainty after the rescaling based on measured charge asymmetry. In addition, the W plus jets template is varied in shape and normalisation by reweighting events based on both the uncertainty in the associated heavy quark production flavor fractions and the parameters of the simulation of extra jets. For the estimate of events with fake leptons, the templates are varied according to the uncertainties in the evaluation of the real and fake e

ciencies.

7 Results and Conclusions

7.1 Template Fit Results

A simultaneous fit to the electron plus jets and muon plus jets data yields:

f

0.470

0.009(stat)

(syst), (6) which is equivalent to a value of

of:

α_`p=−0.060±

0.018(stat)

(syst). (7) A summary of the systematic uncertainties on the measurement of f is presented in Table 3 for the combined flavour fit.

In Table 2 the fractions obtained from fits to data samples containing only a single lepton flavour

and/or charge are reported. The observed cos

distribution in the muon plus jets and the electron plus

jets channels are shown in Fig 6, and are overlaid with the best-fit prediction of the template model,

as well as the predictions for fully positive and negative polarisation. All of the individual results are

consistent with each other within the uncertainties.

7.2 Conclusion

A first measurement by the ATLAS Collaboration of the top quark polarisation in t¯ t production has been presented. The full 2011 data, with an integrated luminosity of 4.66 fb

has been used to analyse t¯ t decays in the lepton plus jets final state. The result of the template fit yields a value for the fraction of positively polarised top quarks of,

f

0.470

0.009(stat)

(syst). (8)

This value agrees with the Standard Model prediction of f

0.5. The largest sources of uncertainty on

this measurement come from the determination of the jet energy scale and the e

ect of the top quark mass

on the signal modelling. The result assumes that the cos

distributions for positively and negatively

charged leptons are the same. This is equivalent to the assumption of CP conservation in the production

mechanism forcing

so that

. The analysis was repeated separately for

events with positively and negatively charged leptons and the results are found to be fully consistent with

each other within the quoted uncertainties.

Table 2: Results for the fractional contribution of positively polarised top quarks to the event sample for the e

jets,

jets and combined channel, as well as for the study of only positively or negatively charged leptons. Statistical and systematic uncertainties are included.

Channel f

e

jets 0.456

0.015(stat)

(syst)

jets 0.480

0.011(stat)

(syst)

`+

jets 0.470

0.009(stat)

(syst) e

jets positive charge 0.460

0.022(stat)

(syst)

jets positive charge 0.495

(stat)

(syst)

`+

jets positive charge 0.481

0.013(stat)

(syst) e

jets negative charge 0.450

0.021(stat)

(syst)

jets negative charge 0.466

0.015(stat)

(syst)

`+

jets negative charge 0.459

0.012(stat)

(syst)

l) θ cos(

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

Entries / 0.1

0 500 1000 1500 2000

2500 Data

Fit αp=0 αp=+1 αp=-1 ATLAS Preliminary

L dt = 4.66 fb-1

∫

=7 TeV s

(a) Electron Channel

l) θ cos(

-1 -0.8-0.6-0.4-0.2 0 0.2 0.4 0.6 0.8 1

Entries / 0.1

0 500 1000 1500 2000 2500 3000 3500 4000

Data Fit αp=0 αp=+1 αp=-1 ATLAS Preliminary

L dt = 4.66 fb-1

∫

=7 TeV s

(b) Muon Channel

Figure 6: Result of the separate electron and muon fits compared to data in each channel; the maximal

fit templates (α

Table 3: Summary of the systematic uncertainties on f in the lepton plus jets final state. The jet recon- struction is dominated by the energy scale uncertainty, while the signal modeling is dominated by the uncertainty in the top quark mass.

Source

f

Lepton reconstruction

-0.003 Jet reconstruction

-0.028 E

reconstruction

0.001 -0.003 Signal modelling

-0.012

W

-0.004

Fake lepton shape

0.004 -0.005

Monte Carlo background cross section

-0.002

Template statistical uncertainty

-0.004

Total systematic

-0.032

References

[1] CDF Collaboration, F. Abe et al., Observation of top quark production in pp collisions, Phys. Rev. ¯ Lett.

(1995) 2626–2631, arXiv:hep-ex/9503002 [hep-ex].

[2] D0 Collaboration, S. Abachi et al., Observation of the top quark, Phys. Rev. Lett.

(1995) 2632–2637, arXiv:hep-ex/9503003 [hep-ex].

[3] CDF Collaboration, D0 Collaboration, T. Aaltonen et al., Combination of the top-quark mass measurements from the Tevatron collider, arXiv:1207.1069 [hep-ex].

[4] D0 Collaboration, V. M. Abazov et al., An Improved determination of the width of the top quark, Phys. Rev. D85 (2012) 091104, arXiv:1201.4156 [hep-ex].

[5] D0 Collaboration, V. M. Abazov et al., Forward-backward asymmetry in top quark-antiquark production, Phys. Rev. D84 (2011) 112005, arXiv:1107.4995 [hep-ex].

[6] D0 Collaboration, V. M. Abazov et al., Measurement of Leptonic Asymmetries and Top Quark Polarization in t¯ t Production, arXiv:1207.0364 [hep-ex].

[7] CDF Collaboration, T. Aaltonen et al., Study of the Top Quark Production Asymmetry and Its Mass and Rapidity Dependence in the Full Run II Tevatron Dataset, Conf. Note 10807 (2012) . [8] CDF Collaboration, T. Aaltonen et al., Combined result of the Forward Backward Asymmetry in

Top Pair Production from Lepton Plus Jet and Di-lepton Channels Using Data up to 5.3 f b

, Conf. Note 10584 (2011) .

[9] D. Krohn, T. Liu, J. Shelton, and L.-T. Wang, A Polarized View of the Top Asymmetry, Phys. Rev.

D84 (2011) 074034, arXiv:1105.3743 [hep-ph].

[10] CMS Collaboration, Measurement of the top polarization in the dilepton final state, CMS PAS TOP-12-016 (2012) .

[11] A. Brandenburg, Z. Si, and P. Uwer, QCD corrected spin analyzing power of jets in decays of polarized top quarks, Phys.Lett. B539 (2002) 235–241, arXiv:hep-ph/0205023 [hep-ph].

[12] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, J. Inst.

(2008) S08003.

[13] S. Agostinelli et al., Geant4: A Simulation Toolkit, Nucl. Instr. and Meth. A506 (2003) 250.

[14] ATLAS Collaboration, The ATLAS Simulation Infrastructure, Eur. Phys. J. C

(2010) 823, arXiv:1005.4568 [physics.ins-det].

[15] S. Frixione and B. R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP

(2002) 029, arXiv:hep-ph/0204244 [hep-ph].

[16] H.-L. Lai et al., New parton distributions for collider physics, Phys. Rev. D82 (2010) 074024, arXiv:1007.2241 [hep-ph].

[17] G. Corcella et al., HERWIG 6: An Event generator for hadron emission reactions with interfering

gluons (including supersymmetric processes), JHEP

(2001) 010, arXiv:hep-ph/0011363

[hep-ph].

[18] J. Butterworth et al., Multiparton Interactions in Photoproduction at HERA, Z. Phys. C72 (1996) 637.

[19] B. P. Kersevan and E. Richter-Was, The Monte Carlo Event Generator AcerMC version 3.5 with interfaces to PYTHIA 6.4, HERWIG 6.5 and ARIADNE 4.1, arXiv:hep-ph/0405247 [hep-ph].

[20] M. L. Mangano, M. Moretti, F. Piccinini, R. Pittau, and A. D. Polosa, ALPGEN, a generator for hard multiparton processes in hadronic collisions, JHEP

(2003) 001,

arXiv:hep-ph/0206293 [hep-ph].

[21] S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with Parton Shower simulations: the POWHEG method, JHEP

(2007) 070, arXiv:0709.2092 [hep-ph].

[22] T. Sjostrand, S. Mrenna, and P. Skands, PYTHIA 6.4 Physics and Manual, JHEP

(2006) 026, hep-ph/0603175 [hep-ph].

[23] ATLAS Collaboration, Electron performance measurements with the ATLAS detector using the 2010 LHC proton-proton collision data, Eur. Phys. J. C72 (2012) 1909, arXiv:1110.3174 [hep-ex].

[24] M. Cacciari, G. P. Salam, and G. Soyez, The Anti-k

jet clustering algorithm, JHEP

(2008) 063, arXiv:0802.1189 [hep-ph].

[25] ATLAS Collaboration, Jet energy measurement with the ATLAS detector in proton-proton collisions at

s

7 TeV, arXiv:1112.6426 [hep-ex].

[26] ATLAS Collaboration, Commissioning of the ATLAS high-performance b-tagging algorithms in the 7 TeV collision data, ATLAS-CONF-2011-102 ,

https://cdsweb.cern.ch/record/1394252/.

[27] ATLAS Collaboration, Measurement of the b-tag e

ciency in a sample of jets containing muons with 5 fb

of data from the ATLAS detector, ATLAS-CONF-2012-043 ,

https://cdsweb.cern.ch/record/1435197/.

[28] ATLAS Collaboration, Measurement of the mistag rate with 5 fb

of data collected by the ATLAS detector, ATLAS-CONF-2012-040 , https://cdsweb.cern.ch/record/1435194/.

[29] ATLAS Collaboration, Performance of Missing Transverse Momentum Reconstruction in Proton-Proton Collisions at 7 TeV with ATLAS, Eur. Phys. J. C72 (2012) 1844,

arXiv:1108.5602 [hep-ex].

[30] ATLAS Collaboration, Measurement of the charge asymmetry in top quark pair production in pp collisions at

s

7 TeV using the ATLAS detector, Eur. Phys. J. C72 (2012) 2039, arXiv:1203.4211 [hep-ex].

[31] ATLAS Collaboration, Measurement of the top quark-pair production cross section with ATLAS in pp collisions at

s

7 TeV, Eur. Phys. J. C71 (2011) 1577, arXiv:1012.1792 [hep-ex].

[32] ATLAS Collaboration, Measurement of the top quark mass with the template method in the t¯ t lepton

jets channel using ATLAS data, Eur. Phys. J. C72 (2012) 2046, arXiv:1203.5755 [hep-ex].

[33] ATLAS Collaboration, Measurement of the W boson polarization in top quark decays with the

ATLAS detector, JHEP

(2012) 088, arXiv:1205.2484 [hep-ex].

[34] ATLAS Collaboration, Measurement of t¯ t production with a veto on additional central jet activity in pp collisions at

s

7 TeV using the ATLAS detector, Eur. Phys. J. C72 (2012) 2043,

arXiv:1203.5015 [hep-ex].