Measurement of the Top Quark Mass in Dileptonic Top Quark Pair Decays with √

ATLAS-CONF-2013-077 18July2013

ATLAS NOTE

ATLAS-CONF-2013-077

July 16, 2013

Measurement of the Top Quark Mass in Dileptonic Top Quark Pair Decays with √

s = 7 TeV ATLAS Data

The ATLAS Collaboration

Abstract

This note presents a measurement of the top quark mass in dileptonic top quark pair decays using 4.7 fb

of

s=

7 TeV

collision data recorded by the ATLAS experiment at the Large Hadron Collider in 2011. This event topology is characterised by the presence of two charged leptons, at least two neutrinos and several jets, two of which originate from bottom quarks. Using the template method and the

observable, defined as the average invariant mass of the two lepton plus

to be 173.09

0.64 (stat)

1.50 (syst) GeV.

©Copyright 2013 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

The mass of the top quark (m

) is a fundamental parameter of the Standard Model (SM) of particle physics. The most recent combinations of the measurements performed at the Tevatron [1] and at the LHC [2], based on data luminosities of up to 8.7 fb

and 4.9 fb

, yield m

173.20

0.51 (stat)

0.71 (syst) GeV and m

173.3

0.5 (stat)

1.3 (syst) GeV, respectively. The most precise mea- surements of this type are performed with the production of top quark pairs (t¯ t) in the t¯ t

lepton+jets channel, i.e. the decay t¯ t

b`ν bq ¯ q ¯ with

e, µ, where one of the W bosons from the t¯ t decays into a charged lepton and a neutrino and the other into a quark-antiquark pair. The LHC at CERN serves as a top quark factory, and thanks to the large sample of t¯ t pairs collected by the ATLAS and CMS exper- iments, analyses exploiting the t¯ t dileptonic final state can also provide precision measurements of the top quark mass.

Compared to the previous preliminary ATLAS measurement in the eµ channel based on a calibration curve method using the mean of the m

estimator (the transverse top quark mass) [3], the result presented in this note uses the average invariant mass of the charged lepton plus b-jet systems, m

, as an estimator for m

and determines the top quark mass using the template method [4] which gives better statistical precision.

This note is organised as follows: after a short description of the ATLAS detector in Section 2, the data and Monte Carlo simulated samples are discussed in Section 3. Details of the object definition and event selection are given in Section 4 and the background estimation is explained in Section 5. The description of the reconstruction of the m

estimator is given in Section 6, and the template method is explained in Section 7. The evaluation of the systematic uncertainties is discussed in Section 8 and the result of the measurement is given in Section 9. A summary and conclusions are given in Section 10.

2 The ATLAS Detector

The ATLAS detector [5] at the LHC covers nearly the entire solid angle around the collision point

. It consists of an inner tracking detector surrounded by a thin superconducting solenoid, electromagnetic and hadronic calorimeters, and an external muon spectrometer incorporating three large superconducting toroid magnet assemblies.

The inner-detector system is immersed in a 2T axial magnetic field and provides charged particle tracking in the range

2.5. The high-granularity silicon pixel detector covers the vertex region and provides typically three measurements per track. It is followed by the silicon microstrip tracker which provides measurements from four double strip layers. These silicon detectors are complemented by the transition radiation tracker, which enables extended track reconstruction up to

2.0. By providing typically more than 30 straw-tube measurements per track, the transition radiation tracker improves the inner detector momentum resolution, and also provides electron identification information.

The calorimeter system covers the pseudorapidity range

4.9. Within the region

3.2, electromagnetic calorimetry is provided by barrel and end cap lead

liquid argon (LAr) electromagnetic calorimeters, with an additional thin LAr presampler covering

1.8 to correct for energy loss in material upstream of the calorimeters. Hadronic calorimetry is provided by the steel

scintillating-tile calorimeter, segmented into three barrel structures within

1.7, and two copper

LAr hadronic end- cap calorimeters. The solid angle coverage is completed with forward copper/LAr and tungsten/LAr

1ATLAS uses a right-handed coordinate system with its origin at the nominal interaction point (IP) in the centre of the detector and thez-axis along the beam pipe. Thex-axis points from the IP to the centre of the LHC ring, and theyaxis points upward. Cylindrical coordinates (r, φ) are used in the transverse plane,φbeing the azimuthal angle around the beam pipe. The pseudorapidity is defined in terms of the polar angleθasη=−ln tan(θ/2). Transverse momentum and energy are defined as pT=psinθandET=Esinθ, respectively.

calorimeter modules optimised for electromagnetic and hadronic measurements respectively.

The muon spectrometer comprises separate trigger and high-precision tracking chambers measuring the deflection of muons in a magnetic field with an integral up to 8 Tm in the central region. The precision chamber system covers the region

2.7 with three layers of monitored drift tubes, complemented by cathode strip chambers in the forward region. The muon trigger system covers the range

2.4 with resistive plate chambers in the barrel, and thin gap chambers in the endcap regions.

A three-level trigger system is used. The first level trigger is implemented in hardware and uses a subset of detector information to reduce the event rate to a design value of at most 75 kHz. This is followed by two software-based trigger levels, which together reduce the event rate to about 300 Hz.

3 Data and Monte Carlo Samples

Data from LHC proton-proton collisions are used, collected at a centre-of-mass energy of

s

7 TeV with the ATLAS detector during the year 2011 and corresponding to an integrated luminosity of 4.7 fb

with an uncertainty of 1.8% [6].

Monte Carlo simulated events are used to model the t¯ t signal and most of the background contribu- tions. Production of t¯ t events is simulated using the next-to-leading order (NLO) Monte Carlo program P

-hvq [7] with the NLO parton density function set CT10 [8]. Parton showering, hadronisation and underlying event (i.e. aspects of a hadronic interaction attributed not to the hard scattering process, but rather to the accompanying interactions of the rest of the proton) are modelled using the Pythia [9]

program with the P

2011C tune [10]. Single top quark production in the s and Wt-channels is also generated with P

-hvq and P

using the same configuration, while single top quark production in the t-channel is simulated using the AcerMC generator [11] interfaced to Pythia. For this analy- sis, the t¯ t and single top quark production samples are generated using seven values of m

at 2.5 GeV intervals from 165 GeV to 180 GeV, with the largest samples at m

172.5 GeV. All t¯ t simulation samples are normalised to the predicted t¯ t cross-section which for pp collisions at a centre-of-mass energy of

s

7 TeV is 177

pb for a top quark mass of 172.5 GeV. It is calculated at next-to- next-to-leading order (NNLO) in QCD including resummation of next-to-next-to-leading logarithmic (NNLL) soft gluon terms with Top++2.0 [12–17]. The PDF+

uncertainties are calculated using the PDF4LHC prescription [18] with the MSTW2008 68% CL NNLO [19, 20], CT10 NNLO [8, 21] and NNPDF2.3 5f FFN [22] PDF sets, added in quadrature to the scale uncertainty. The NNLO

NNLL value, as implemented in Hathor 1.5 [23], is about 3% larger than the plain NNLO prediction. The single top quark production cross sections are normalised to the approximate next-to-next-to-leading order pre- dictions of 64.6 pb [24], 4.6 pb [25] and 15.7 pb [26] for the t, s and Wt-production channels respectively.

The production of W or Z bosons in association with jets is simulated using the Alpgen generator [27]

interfaced to the H

[28] and J

[29] packages. Diboson production processes (WW , WZ and ZZ) are simulated using the H

generator.

Multiple soft proton-proton interactions are added to all simulated samples. The events are re- weighted such that the distribution of the number of interactions per bunch crossing (pile-up

) in the simulated samples matches that in the data. The mean number of interactions per bunch crossing for the data of this analysis is about 8.7. The samples are then processed through the GEANT4 simula- tion [30, 31] and the reconstruction software used for ATLAS data.

2Pile-up is the term given to the extra signal produced in the detector byppinteractions other than the one producing the hard scattering event under study.

4 Event Selection

The event selection is based on the following reconstructed objects in the detector: electrons, muons, jets and missing transverse momentum (E

). An electron candidate is defined as an energy deposit in the electromagnetic calorimeter with an associated well-reconstructed track [32]. Electron candidates are required to have transverse energy E

25 GeV and

2.47, where

is the pseudorapidity of the electromagnetic cluster associated with the electron. Candidates in the transition region between the barrel and end-cap calorimeter, i.e. candidates fulfilling 1.37

1.52, are excluded. Muon candidates are reconstructed from track segments in di

erent layers of the muon chambers. These seg- ments are combined starting from the outermost layer, with a procedure that takes material e

ects into account, and matched with tracks found in the inner detector. The final candidates are refitted using the complete track information, and are required to satisfy p

20 GeV and

2.5. Isolation criteria, with upper limits on the amount of energy deposited near the candidates, are applied to both electron and muon candidates to reduce the background from hadrons mimicking lepton signatures and backgrounds from heavy flavour decays inside jets. For electrons, the energy not associated to the electron cluster and contained in a cone of

R

q∆φ²+ ∆η² =

0.2 must not exceed an

dependent threshold with a value between 1.4 and 3.7 GeV, after correcting for energy deposits from pile-up, which are of the order of 0.5 GeV. In addition, the total transverse momentum of the tracks contained in a cone of

R

0.3 must not exceed 1 GeV. For muons, the sum of track transverse momenta in a cone of

R

0.3 around the muon is required to be less than 2.5 GeV, and the total energy deposited in a cone of

R

0.2 around the muon is required to be less than 4 GeV. The longitudinal impact parameter of each lepton along the beam axis with respect to the reconstructed primary vertex is required to be less than 2 mm. The primary vertex is defined as the reconstructed vertex with the largest sum of the squares of transverse momenta of the tracks assigned to it.

Jets are built with the anti-k

algorithm [33] with a radius parameter R

0.4, starting from energy clusters of adjacent calorimeter cells called topological clusters [34]. These jets are calibrated first by correcting the jet energy using the scale established for electromagnetic objects (EM scale), then per- forming a further correction to the hadronic energy scale using calibration factors, that depend on energy and

data and Monte Carlo simulation [35, 36]. Jet quality criteria are applied to identify and reject jets re- constructed from energy deposits in the calorimeters originating from particles not emerging from the hard scattering vertex [37]. To avoid selecting jets from additional pp interactions, a fraction (JVF) of the sum of the p

of tracks associated with a jet is required to be from the p

of tracks compatible with the selected primary vertex:

0.75. Jets with no associated tracks are also accepted.

The reconstruction of E

is based upon the vector sum of calorimeter energy deposits projected onto the transverse plane. It is reconstructed from topological clusters, calibrated at the EM scale and corrected according to the type of the associated physics object. Contributions from muons are included by using their momentum measured from the track and muon spectrometer systems in the E

recon- struction.

Overlaps between di

erent types of objects are removed. Muons reconstructed within a

R

0.4 cone of a jet are removed to reduce the contamination caused by muons from hadron decays within jets.

Electrons are rejected if their distance to the closest jet is smaller than

R

0.4.

To identify jets originating from the hadronisation of b-quarks an algorithm based on a neural-net

relying on topological properties such as the vertex decay length significance, is applied [38]. The chosen

working point of this “MV1” algorithm corresponds to a b-tagging efficiency of 70% for jets originating

from b-quarks in simulated t¯ t events and a light quark jet rejection factor of about 130. To better model

the b-tagging performance in the data, p

and

dependent scale factors obtained from di-jet events are

applied to Monte Carlo jets, depending on their original flavour [38–40]. They are calculated per jet and

finally multiplied to obtain an event weight applied to any final state distribution. Irrespective of their origin, jets tagged by this algorithm are called b-tagged jets in the following. Whether they are tagged or not, jets originating from b-quarks are called b-jets in the following.

The t¯ t events in the dileptonic final state are characterised by the presence of two isolated leptons with relatively high p

, E

arising from the two neutrinos from the leptonic W boson decays, and two b-jets. The selection of events consists of a series of requirements on the general event quality and on the reconstructed objects, designed to select events consistent with this topology. The following event selection is applied:

•

to suppress non-collision background, events are required to have at least one good primary vertex candidate with at least five associated tracks;

•

the event must contain exactly two opposite sign leptons with E

25 GeV for electrons and p

20 GeV for muons, at least one of which should have fired a single lepton trigger with threshold at least 2 GeV lower;

•

For the e

e

and

channels E

60 GeV is required. In the eµ channel H

130 GeV is required, where H

is the scalar sum of p

of the two selected leptons and the jets;

•

in the e

e

and

channels m(e

e

)

15 GeV is required, to reduce background from low mass resonances like mesons decaying to lepton anti-lepton pairs. To reduce the Z

ground, values of the invariant mass of the lepton-lepton system compatible with the Z mass are vetoed by requiring

e

)

91 GeV

10 GeV;

•

the event is required to have

2 jets with p

25 GeV and

2.5. It is also required that exactly two of these jets are b-tagged.

For the Monte Carlo simulated samples an additional requirement is imposed. The events are required to contain two true leptons (e or

W- or Z-boson decays or from a

decay and both selected leptons are required to match these true leptons. The contribution of events with two such “real” leptons are evaluated with the simulated samples, while events with one or more “fake” leptons are evaluated with a data-driven approach (see Section 5).

5 Background Estimation

Physics background processes with two charged leptons from W or Z decay in the final state, which are similar to t¯ t dilepton events, are dominated by single top quark production in the Wt-channel. Addi- tional contributions come from Drell-Yan processes and diboson production with additional jets. These contributions are estimated directly from the MC simulation normalised to the relevant cross sections.

Events may also be wrongly reconstructed as dileptonic t¯ t due to the presence of misidentified, or

“fake”, leptons together with b-tagged jets and E

. The term fake lepton is used to indicate jets

wrongly reconstructed as electrons or non-prompt leptons arising from heavy quark decays. The fake

lepton background is estimated using a data-driven matrix method [41]. It has two ingredients: an

estimation of the number of fake leptons in a background enhanced control region with low E

, and

a region around the Z peak where true leptons can easily be identified. From these, the probability for a

reconstructed lepton to be a fake is derived as a function of the lepton

and p

, which is then used to

estimate the expected events with fake leptons in the data sample. Thanks to the strict event selection

requirements this background is very low. The matrix method estimate is

4

7 events, where the

uncertainty is statistical and systematic, consistent with zero and much smaller than the dominant single

top background. Consequently, this source of background is neglected in the m

measurement.

All channels

t¯ t signal 2400

400

Fake leptons -4

7

Single top quark 73

15

Drell-Yan 3.1

1.3

Diboson 0.75

0.29

Total expected 2500

400 Total observed 2913

Table 1: The observed numbers of events in 4.7 fb

of

s

7 TeV data after the final event selection, for the combination of the e

e

, eµ and

channels. The relative fractions of events in data for the different channels are 9%, 67% and 24% for the e

e

, eµ and

channels respectively. In addition, the expected numbers of signal and background events corresponding to the integrated luminosity of the data are given. The Monte Carlo estimates assume SM cross sections. The background with fake leptons is estimated from data. The uncertainties for the estimates include the components detailed in the text.

The observed numbers of events in the data after the event selection, together with the expected numbers of signal and background events corresponding to the integrated luminosity of 4.7 fb

are given in Table 1. The uncertainty on the t¯ t signal MC is calculated as the quadratic sum of the symmetrised uncertainties from luminosity of 1.8% and cross section calculation of 5.9%, as well as the systematic uncertainties from the jet energy scale, b-jet energy scale and b-tagging scale factor that will be discussed in Section 8. The single top quark cross section uncertainty is taken as 20%. In the Drell-Yan and diboson cases every event is assigned a base uncertainty of 4% and 5% respectively and an additional uncertainty of 24% per jet is added in quadrature [42]. Assuming a top quark mass of m

172.5 GeV, the number of events observed in data is about 16% higher than the prediction, but consistent within uncertainties.

The template method implemented here depends on the shape of the distributions only, and does not rely on the normalisation of the signal plus background prediction. Consequently, shape comparisons of the relevant kinematic observables between data and the predictions are shown in Figure 1. In this figure the sum of the predictions is normalised to the number of events observed in data. In all figures the shape of the data can be properly accounted for by the sum of signal and background predictions.

6 The m

Estimator

The m

estimator definition is based on the invariant mass of the charged lepton plus b-jet systems.

Selected events contain two charged leptons and two b-tagged jets. There are two possible assignments of the two b-tagged jets to the two charged leptons, each leading to two values for the corresponding pair of invariant masses. For each assignment the average of the two invariant masses is calculated.

Finally, the lowest average mass is taken as the m

estimator for the event. The width of the m

distribution depends on the correct assignment of b-quarks to b-tagged jets. Wrong assignments tend to make the distribution wider. The chosen algorithm gives correct assignments in 77% of the cases. The corresponding result can be seen in Figure 2 (a) which shows the observed distribution in data together with the prediction assuming m

172.5 GeV.

7 Template Fits and Closure Tests

In the template method, simulated distributions are constructed for a chosen quantity sensitive to the

parameter under study, known as the ’physics parameter’, using a number of discrete values of that

[GeV]

lepton pT

0 50 100 150 200

entries / 5 GeV

0 100 200 300 400 500 600 700 800

900 s=7 TeV data

=172.5 GeV , mtop

t t

background uncertainty ATLAS Preliminary

Ldt=4.7 fb-1

∫

(a)

[GeV]

b-tagged jet pT

0 50 100 150 200

entries / 5 GeV

0 100 200 300 400

500 s=7 TeV data

=172.5 GeV , mtop

t t

background uncertainty ATLAS Preliminary

Ldt=4.7 fb-1

∫

(b)

η lepton

-3 -2 -1 0 1 2 3

entries / 0.25

0 100 200 300 400 500 600 700 800 900

=7 TeV data s

=172.5 GeV , mtop

t t

background uncertainty ATLAS Preliminary

Ldt=4.7 fb-1

∫

(c)

η b-tagged jet

-3 -2 -1 0 1 2 3

entries / 0.25

0 100 200 300 400 500 600 700

800 s=7 TeV data

=172.5 GeV , mtop

t t

background uncertainty ATLAS Preliminary

Ldt=4.7 fb-1

∫

(d)

Njets

2 3 4 5 6 7

events

0 200 400 600 800 1000 1200 1400 1600 1800 2000

2200 s=7 TeV data

=172.5 GeV , mtop

t t

background uncertainty ATLAS Preliminary

Ldt=4.7 fb-1

∫

(e)

Figure 1: Distributions after applying all selection requirements for data (points with error bars), the sum

of signal and background (black line) and for background alone (grey histogram). The signal plus back-

ground prediction is normalised to the number of events observed in data. The uncertainties shown for

data are statistical only. The hatched band indicates the shape uncertainty of the signal and background

contributions due to the jet energy scale, b-jet energy scale and b-tagging scale factor uncertainties. Sub-

figures show the p

of leptons and b-tagged jets (a, b) and the pseudo-rapidity of leptons and b-tagged

jets (c, d). Subfigure (e) shows the number of jets in the selected events. The rightmost bin in subfig-

ures (a, b) contains the overflow.

[GeV]

mlb

50 100 150

events / 6 GeV

0 100 200 300 400

500 s=7 TeV data

=172.5 GeV , mtop

t t

background uncertainty ATLAS Preliminary

Ldt=4.7 fb-1

∫

(a)

[GeV]

mlb

50 100 150

normalised events / 5 GeV

0 0.02 0.04 0.06 0.08 0.1 0.12

mtop

165.0 GeV 172.5 GeV 180.0 GeV ATLAS Simulation

Preliminary

(b)

Figure 2: Distributions of m

after applying all selection requirements for data (points with error bars), the sum of signal and background (black line) and for background alone (grey histogram), assuming m

172.5 GeV (a). The signal plus background prediction is normalised to the number of events observed in data. The uncertainties shown for data are statistical only. The hatched band indicates the shape uncertainty of the signal and background contributions due to the jet energy scale, b-jet energy scale and b-tagging scale factor uncertainties. The rightmost bin contains the overflow. Dependence of the m

distribution on m

for t¯ t Monte Carlo samples generated with di

erent input top quark masses (b), together with the signal probability density functions obtained from the combined fit to all templates described in Section 7.

parameter. These templates are then fitted to functions that interpolate between di

erent input values of the physics parameter, fixing all other parameters of the functions. In the final step a likelihood fit of these functions to the observed data distribution is used to obtain the value for the physics parameter that best describes the data. In this procedure, the experimental distributions are constructed such that they are unbiased estimators of the physics parameter used as input in the signal Monte Carlo samples.

Consequently, the top quark mass determined this way from data corresponds to the mass definition used in the Monte Carlo. It is expected that the error introduced by equating this mass definition and the pole mass is of order 1 GeV [43].

Signal and background templates for m

are constructed as a function of the top quark mass used in the Monte Carlo generation in the range 165–180 GeV, using separate samples for each of the seven different mass points. The t¯ t signal templates for the m

distributions are fitted to the sum of a Gaussian and a Landau function, while for the background the m

distributions are fitted to a Landau function.

Background templates are dominated by the top quark mass dependent single top quark production. In Figure 2 (b) the sensitivity of the m

observable to the input value of the top quark mass is shown by the superposition of the signal templates and their fits for three input values. The parameters of the fitting functions of m

depend linearly on m

for both the signal and background templates. This allows signal and background probability density functions for the m

estimator to be built that depend only on m

. These functions are then used in an unbinned likelihood fit to the data for all events, i

1, . . . N. The likelihood function maximised is:

L

(m

r)

N

Y

i=1

h

(1

r)

P

(m

)

r

P

(m

)

,

(1)

where P

and P

are the signal and background probability density functions and r is the relative

normalisation of the background contribution. The value of r is small, r

0.03

0.01, and a fixed

r

0.03 is used in the likelihood fit.

Using pseudo-experiments on large Monte Carlo samples, a good linearity is found between the input top quark mass used to perform the pseudo-experiments, and the results of the fits. Within their statistical uncertainties, the mean values and widths of the pull distributions are consistent with the expectations of zero and one, respectively. Finally, the expected statistical uncertainty on m

obtained from pseudo- experiments for an input top quark mass of m

172.5 GeV, and for a luminosity of 4.7 fb

, is 0.64 GeV.

8 Systematic Uncertainties

The systematic uncertainties are estimated by varying the respective uncertainty source and determin- ing the impact on the mass measurement via pseudo-experiments. Except where stated otherwise this is based solely on MC samples. Wherever applicable the uncertainty sources are varied by one stan- dard deviation (±1σ) with respect to the default value. The resulting average value of the fitted m

in the pseudo-experiments

is compared to the corresponding value without variation and the differ- ence is used to determine the systematic uncertainty. The MC samples used in the determination of the systematic uncertainties correspond to an integrated luminosity of about 100 fb

each, contain events generated using the CT10 PDFs and use the setup described in Ref. [44]. The statistical uncertainty on m

obtained from each of the MC samples is about 0.2 GeV. For most of the uncertainty sources the same sample is used, but with a changed parameter, such that the observed m

values for the central and the changed sample are highly correlated. In all cases the actual observed difference is quoted as the systematic uncertainty on the corresponding source, even if it is smaller than the statistical precision of the di

erence, following Ref. [45]. The total uncertainty is calculated as the quadratic sum of the individual contributions, i.e. neglecting possible correlations. The sources and systematic uncertainties investigated are listed in Table 2 and their evaluation is explained in the following.

Method calibration: The method has been shown to be unbiased within the statistical precision of the Monte Carlo samples. Any residual mass di

erence between the fitted and the input top quark mass for a given Monte Carlo sample is taken into account by this uncertainty. Consequently, the maximum of the average absolute mass deviation

and its statistical uncertainty observed in the top quark mass variation samples is assigned as the uncertainty from this source.

Signal MC generator: The systematic uncertainty due to the choice of the t¯ t signal generator program is studied by comparing the results of pseudo-experiments performed with samples generated by either the MC@NLO [46, 47] or the Powheg [7] packages both generated with m

172.5 GeV and using the H

[28] program to perform the hadronisation. The full difference in the fitted m

is

m

0.14 GeV. As a complementary determination, NLO generator scale variation e

ects are studied by comparing the results of pseudo-experiments performed with two dedicated MC samples generated using MC@NLO interfaced to Herwig with m

172.5 GeV, where the renormalisation and factorisation scales are simultaneously varied up by a factor 2, or down by a factor 1

2. The full di

erence in the fitted mass between the two samples is taken as the uncertainty from the scale variation. This is evaluated to be

m

0.20 GeV. The larger of the two numbers is quoted as the uncertainty accounting for both e

ects.

Hadronisation: Signal samples for m

172.5 GeV from the P

event generator are produced

performing the parton showering and the hadronisation with either P

with the P2011C tune

or Herwig and Jimmy with the ATLAS AUET2 tune [48]. Pseudo-experiments are performed for

each sample, and the full difference of the average results, 0.44 GeV, is quoted as the systematic

uncertainty.

Underlying Event: This systematic uncertainty is estimated using samples simulated with P

-hvq and P

. The uncertainty is obtained by comparing a sample with the P

2011 tune to a sample with the Perugia 2011

tune [10]. Both tunes use the CTEQ5L PDF [49] for parton shower and hadronisation. The same matrix element level P

-hvq events generated with CT10 PDF are used for both samples. The full di

erence in the fitted mass between the two models is taken as the systematic uncertainty for this source. The Perugia 2011

tune is a variation of the P

2011 tune with more semi-hard Multiple Parton Interactions. The colour reconnection parameters are kept fixed to the P

2011 tune values. The P

2011

H

tune gives similar predictions to Perugia 2011 for transverse activity against lead-track p

, an observable sensitive to underlying event activity in inclusive proton proton collisions [50]. The samples used for colour reconnection uncertainties yield notably di

erent predictions for these observables.

Colour Reconnection: The impact of di

erent models of Colour Reconnection (CR) of the partons en- tering the hadronisation is assessed by comparing samples simulated with Powheg-hvq and Pythia based on the P

2011 tune and the P

2011

CR tune [10] for parton shower and hadronisation. As for the underlying event systematics, the same matrix element level P

- hvq events generated with CT10 PDF are used for both samples. Compared to the standard Perugia 2011 tune the P

2011

CR tune leads to significantly less activity in the transverse region with respect to the leading charged particle as measured in Ref. [50]. In addition to the e

ect of colour reconnection this tune is therefore also used to estimate the systematic uncertainty associ- ated with the particle spectra in the underlying event. The full difference in the fitted mass between the two assumptions on the size of colour reconnection is taken as the systematic uncertainty for this source.

Initial and final state QCD radiation (ISR

FSR): The uncertainty caused by di

erent amounts of QCD gluon radiation in the initial state (ISR) and final state (FSR) is determined by comparing two dedicated signal samples generated with A

MC in combination with P

P2011C for hadro- nisation and parton showering. In these samples some P

P2011C parameters that control the showering are varied in ranges that are compatible with a study of additional jets in t¯ t events [51].

Half of the difference is assigned as the uncertainty.

Proton PDF: The signal samples are generated using the CT10 proton parton distribution functions.

These PDFs, obtained from experimental data, have an uncertainty that is reflected in 26 pairs of additional PDF sets provided by the CTEQ [52] group. To evaluate the impact of the PDF uncertainty on the signal templates, the events, from a sample generated using MC@NLO with H

fragmentation, are re-weighted with the corresponding ratio of PDFs, and 26 pairs of additional signal templates are constructed. Using these templates, 1000 pseudo-experiments are performed per variation pair, using the same events for the up and down variations within each pair to suppress statistical fluctuations. The uncertainty is calculated as half the quadratic sum of di

erences of the 26 pairs. In addition, the signal samples are also re-weighted to match the central PDF set for either the MSTW2008 [19] or the NNPDF23 [22] PDF set. The corresponding two differences with respect to the central CT10 PDF set are smaller than the uncertainty from the CT10 variations discussed above, which are therefore quoted as the final uncertainty.

Background: The background fraction has an overall uncertainty of about 28% due to the di

erent

components described in Section 5. To estimate its impact pseudo-experiments are performed

with the background contribution shifted by

mass deviation

to the one observed with the central background value is assigned as

a systematic uncertainty due to the background normalisation.

Jet energy scale (JES): The JES is a factor to correct the jet energy measured in the calorimeters for energy loss in the inert material, particle leakage and signal ine

ciency. The JES is derived using information from test-beam data, LHC collision data and simulation and its uncertainty increases with

and decreases with the p

of the jet. It amounts to about 1% in the central region for 55

p

500 GeV and goes up to 6% for low p

jets in the forward region [36]. The JES uncer- tainty has various components originating from the calibration method, the calorimeter response, the detector simulation, and the specific choice of parameters in the physics model employed in the MC event generator. A parameterisation with 21 uncorrelated components (20 for the JES uncertainty plus the bJES uncertainty discussed below) is used, as described in Ref. [36]. The JES is independently varied for each of the components by

with respect to the default value, de- pending on jet p

and

E

is adjusted accordingly. For each component, the top quark mass is fitted for the up and down variation, and half the difference is taken as the uncertainty due to this component. Finally, to obtain the total uncertainty on m

due to the JES uncertainties, the 20 individual JES uncertainties are summed quadratically. The uncertainties for the individual components and their sum are given in Table 3 in Appendix A.

Relative b-jet energy scale (bJES): This uncertainty is uncorrelated with the JES uncertainty and ac- counts for the remaining differences between jets originating from light quarks and those originat- ing from b-quarks after the global JES has been determined. The bJES uncertainty is about 1.8%

for low p

jets and smaller than 0.7% for jets with p

200 GeV. For the uncertainty estimation the bJES is shifted by

in every

p

bin and the E

is adjusted accordingly. The maximum mass di

erence with respect to the default sample is taken as the symmetric uncertainty from this source.

b-tagging e

ciency and mistag rate: The b-tagging scale factors account for di

erences in the e

- ciency and mistag rate of the b-tagging algorithm between data and MC [38–40]. They are derived for a given b-tagging working point together with their uncertainties for every jet according to its p

and

b-tagging scale factors are varied within their uncertainties. The maximum dif- ference to the default sample is taken as the uncertainty. Various assumptions on the correlations between the b-tagging scale factors uncertainties as a function of p

have been studied and found to result in similar uncertainties on m

.

Jet energy resolution: To assess the impact of this uncertainty, before performing the event selection, the energy of each reconstructed jet in the simulation is additionally smeared by a Gaussian func- tion such that the width of the resulting Gaussian distribution corresponds to the one including the uncertainty on the jet energy resolution [53]. The mass di

erence with respect to the unsmeared case is taken as the uncertainty.

Jet reconstruction e

ciency: The jet reconstruction e

ciency for data and the Monte Carlo simulation are found to be in agreement with an accuracy of better than 2% [35]. To account for the remaining uncertainty, 2% of the jets are randomly removed from the events. The event selection and the fit are repeated on the changed sample. The e

ect on the measured top quark mass is negligible.

Missing transverse momentum: The impact of a possible miscalibration of the E

is assessed by changing the energy scale and resolution of the soft calorimeter energy deposits within their un- certainties. These energy deposits, which are not included in the reconstructed jets and leptons, only contribute to E

.

Pile-up: To investigate the uncertainty due to the presence of additional proton-proton interactions in the

event, the fit is repeated in data and simulation at m

172.5 GeV as a function of the number

of reconstructed vertices n

and the average number of interactions per bunch crossing

Description Value [GeV]

Measured value 173.09

Statistical uncertainty 0.64

Method calibration 0.07

Signal MC generator 0.20

Hadronisation 0.44

Underlying event 0.42

Colour reconnection 0.29

ISR/FSR 0.37

Proton PDF 0.12

Background 0.14

Jet energy scale 0.89

b-jet energy scale 0.71

b-tagging efficiency and mistag rate 0.46

Jet energy resolution 0.21

Missing transverse momentum 0.05

Pile-up 0.01

Electron uncertainties 0.11

Muon uncertainties 0.05

Total systematic uncertainty 1.50

Total uncertainty 1.63

Table 2: The measured value of m

and the contributions of the various sources detailed in the text to the total systematic uncertainty.

sample is divided in three parts corresponding to different n

and

and the mass is measured for each of those partitions. In both cases the change of m

in data is reproduced by MC within statistical uncertainties. However, a possible residual e

ect on m

is assessed by computing the sum of the differences of a linear interpolation of the fitted masses to the full sample in every n

and

bin in simulation, weighted either with the relative frequency of observing a given n

and

in data, or with the corresponding frequencies in simulation. The di

erence of the sums in data and simulation is taken as the uncertainty from this source.

Electron and muon uncertainties: This category takes into account the uncertainties in the e

ciency of the trigger, in the identification and reconstruction of electrons and muons, as well as residual uncertainties due to a possible miscalibration of the lepton energy scales. The number quoted is the quadratic sum of all the studied components and is dominated by the uncertainty on the lepton energy scales.

9 Results

The result of the fit to 2011 ATLAS data in the dileptonic t¯ t decay channel is:

m

173.09

0.64 (stat)

1.50 (syst) GeV

Figure 3 shows the m

distribution in data together with the corresponding fitted probability density functions for signal plus background and for the background contribution alone. The inset shows the

−2 lnL

profile as a function of the fitted top quark mass. The vertical lines correspond to

of the

[GeV]

mlb

40 60 80 100 120 140 160

events / 5 GeV

0 100 200 300 400

=7 TeV data s

3% background

0.64 GeV

± = 173.09 best fit: mtop

[GeV]

mtop

172 173 174

-2lnL

0 0.5 1 1.5 2

ATLAS Preliminary

Ldt=4.7 fb-1

∫

Figure 3: Fitted m

distribution in data. The fitted probability density functions for the signal plus background and for the background contribution alone are also shown. The inset shows the

profile as a function of the fitted top quark mass.

statistical uncertainty. The result has a total uncertainty similar to that of the ATLAS m

measurement in the l

scale, the systematic uncertainty on m

is dominated by the uncertainties stemming from the imperfect knowledge of the jet energy calibration.

Compared to the previous ATLAS result in the eµ channel based on the mean of the m

estimator [3], a number of improvements have been made to reduce both the statistical and systematic uncertainties.

For this analysis the e

e

and

channels are also used. Due to the better understanding of systematic effects some phase space restrictions were removed, for example reducing the p

cut on jets and muons. The expected statistical precision of the template method for the m

and the m

estimators is very similar, however the template method o

ers better precision than using the mean of the distribution. As a consequence the statistical precision on the same data sample is significantly improved. The choice of the m

estimator, i.e. not requiring a full event reconstruction, reduces the sensitivity of the measurement to some systematic e

ects, most notably to initial and final state QCD radiation and the energy scales.

The improved understanding of the final state distributions in t¯ t events helps to reduce the magnitude of the variations performed in the Monte Carlo simulations for evaluating the systematic uncertainties.

Based on a measurement of the jet multiplicity distributions in t¯ t events [51], the ISR and FSR variations

could be reduced, mainly for the ISR part. In addition, a better understanding of the detector together

with changes in the JES calibration procedure, now using in-situ techniques, leads to a relative reduction

of the bJES uncertainty [55] by about 40%, which in turn reduces the bJES uncertainty on m

. On

the m

analysis side, the default signal Monte Carlo has been changed from MC@NLO with H

to P

with P

using the P

2011C tune, because it provides an improved description of

some observed quantities [56]. Due to this change, the systematic uncertainties stemming from the

underlying event and colour reconnection are now evaluated with the P

generator with P

for

the parton shower and hadronisation, and using the P

2011C tune, consistently with the default

signal MC samples. To suppress statistical effects, the sample size in the Monte Carlo comparisons

[GeV]

m

160 170 180 190

0.5 9

0.00

± 0.00

± 0.00

Tevatron Combination 2013

173.20 ± 0.51 ± 0.71

arXiv:1305.3929

dilepton

D0 5.3 fb-1

174.00 ± 2.36 ± 1.44

Phys. Rev. D86 (2012) 051103

dilepton

CDF 5.6 fb-1

170.28 ± 1.95 ± 3.09

Phys. Rev. D83 (2011) 111101

dilepton

CMS 5.0 fb-1

172.50 ± 0.43 ± 1.48

Eur. Phys. J. C72 (2012) 2202

dilepton mlb

ATLAS 4.7 fb-1

173.09 ± 0.64 ± 1.50

ATLAS-CONF-2013-077

mT2

µ

-1 e

ATLAS 4.7 fb

175.2 ± 1.6 ±

ATLAS-CONF-2012-082

l+jets (3d)

ATLAS 4.7 fb-1

172.31 ± 0.75 ± 1.35

ATLAS-CONF-2013-046

ATLAS Preliminary July 2013

(stat) (syst)

Figure 4: The present result is compared to a number of other measurements, see text for details. The data points show the measured values with their statistical uncertainty (red) and the total uncertainty including systematics (blue).

has been increased and identical 4-vectors for the hard matrix element calculation have been used. The estimated colour reconnection uncertainty on m

is now much smaller.

The result for m

is shown in Figure 4, together with a number of other measurements. These results include: the ATLAS m

measurement in the l

ment in the eµ channel [3], the most precise determinations of m

in in the t¯ t dileptonic decay channel by CMS [57], CDF [58] and D0 [59], and the latest Tevatron combined value [1] based on twelve mea- surements in all t¯ t decay channels.

10 Summary and Conclusion

The top quark mass has been measured using the m

estimator with the template method in the dilepton t¯ t decay channel, based on

s

7 TeV proton-proton collision data collected by ATLAS at the LHC in 2011 and corresponding to an integrated luminosity of about 4.7 fb

. The measured value of m

is:

m

173.09

0.64 (stat)

1.50 (syst) GeV

This measurement supersedes the previous ATLAS result in the eµ channel [3]. The total uncertainty is competitive with the latest ATLAS result in the l

e

ects, with the largest contribution coming from jet and b-jet energy scale uncertainties.

References

[1] CDF and D0 Collaborations, T. Aaltonen et al., Combination of CDF and D0 results on the mass

of the top quark using up to 8.7 fb

at the Tevatron, CDF Note 10976, D0 Note 6381, arXiv:1305.3929.

[2] ATLAS and CMS Collaborations, Combination of ATLAS and CMS results on the mass of the top quark using up to 4.9 f b

of data, ATLAS-CONF-2012-095,

http://cds.cern.ch/record/1460441.

[3] ATLAS Collaboration, Top quark mass measurement in the eµ channel using the m

variable at ATLAS, ATLAS-CONF-2012-082, http://cds.cern.ch/record/1460394.

[4] 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.

[5] ATLAS Collaboration, The ATLAS Experiment at the CERN Large Hadron Collider, JINST 3 (2008) S08003.

[6] ATLAS Collaboration, Improved luminosity determination in pp collisions at

s

7 T eV using the ATLAS detector at the LHC, CERN-PH-EP-2013-026,

http://cds.cern.ch/record/1517411.

[7] S. Frixione, P. Nason and C. Oleari, Matching NLO QCD computations with parton shower simulations: the POWHEG method, JHEP 11 (2007) 070.

[8] H.-L. Lai et al., New parton distributions for collider physics, Phys. Rev. D82 (2010) 074024.

[9] T. Sj¨ostrand, S. Mrenna and P. Skands, PYTHIA 6.4 physics and manual, JHEP 05 (2006) 026.

[10] P. Z. Skands, Tuning Monte Carlo generators: The Perugia tunes, Phys. Rev. D82 (2010) 074018.

[11] B.P. Kersevan and E. Richter-Wa¸s, The Monte Carlo Event Generator AcerMC versions 2.0 to 3.8 with interfaces to PYTHIA 6.4, HERWIG 6.5 and ARIADNE 4.1, arXiv:hep-ph/0405247.

[12] M. Cacciari et al., Top-pair production at hadron colliders with next-to-next-to-leading logarithmic soft-gluon resummation, Phys. Lett. B710 (2012) 612.

[13] P. B¨arnreuther, M. Czakon, A. Mitov, Percent-Level-Precision Physics at the Tevatron:

Next-to-Next-to-Leading Order QCD Corrections to q q ¯

t¯ t

X, Phys. Rev. Lett. 109 (2012) 132001.

[14] M. Czakon, A. Mitov, NNLO corrections to top-pair production at hadron colliders: the all-fermionic scattering channels, JHEP 12 (2012) 054.

[15] M. Czakon, A. Mitov, NNLO corrections to top pair production at hadron colliders: the quark-gluon reaction, JHEP 01 (2013) 080.

[16] M. Czakon, P. Fiedler, A. Mitov, The total top quark pair production cross-section at hadron colliders through

), arXiv:1303.6254.

[17] M. Czakon and A. Mitov, Top

: a program for the calculation of the top-pair cross-section at hadron colliders, arXiv:1112.5675.

[18] M. Botje et al., The PDF4LHC Working Group Interim Recommendations, arXiv:1101.0538.

[19] A.D. Martin et al., Parton distributions for the LHC, Eur. Phys. J. C63 (2009) 189.

[20] A.D. Martin et al., Uncertainties on

in global PDF analyses and implications for predicted hadronic cross sections, Eur. Phys. J. C64 (2009) 653.

[21] J. Gao et al., The CT10 NNLO Global Analysis of QCD, arXiv:1302.6246.

[22] R.D. Ball et al., Parton distributions with LHC data, Nucl. Phys. B867 (2013) 244.

[23] M. Aliev et al., HATHOR – HAdronic Top and Heavy quarks crOss section calculatoR, Comput.

Phys. Commun. 182 (2011) 1034.

[24] N. Kidonakis, Next-to-next-to-leading-order collinear and soft gluon corrections for t-channel single top quark production, Phys. Rev. D83 (2011) 091503(R).

[25] N. Kidonakis, Next-to-next-to-leading logarithm resummation for s-channel single top quark production, Phys. Rev. D81 (2010) 054028.

[26] N. Kidonakis, Two-loop soft anomalous dimensions for single top quark associated production with a W

or H

, Phys. Rev. D82 (2010) 054018.

[27] M. L. Mangano et al., ALPGEN, a generator for hard multiparton processes in hadronic collisions, JHEP 07 (2003) 001.

[28] G. Corcella et al., HERWIG 6: An event generator for hadron emission reactions with interfering gluons (including supersymmetric processes), JHEP 01 (2001) 010.

[29] J. M. Butterworth, J. R. Forshaw, and M. H. Seymour, Multiparton interactions in photoproduction at HERA, Z. Phys. C72 (1996) 637.

[30] S. Agostinelli et al., GEANT4 – a simulation toolkit, Nucl. Instrum. Meth. A506 (2003) 250.

[31] ATLAS Collaboration, The ATLAS Simulation Infrastructure, Eur. Phys. J. C70 (2010) 823.

[32] ATLAS Collaboration, Electron performance measurements with the ATLAS detector using the 2010 LHC proton-proton collision data, Eur. Phys. J. C72 (2012) 1909.

[33] M. Cacciari, G.P. Salam and G. Soyez, The anti-k

jet clustering algorithm, JHEP 04 (2008) 063.

[34] W. Lampl et al., Calorimeter Clustering Algorithms: Description and Performance, ATL-LARG-PUB-2008-002, http://cds.cern.ch/record/1099735.

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

s

7 TeV , Eur. Phys. J. C73 (2013) 2304.

[36] ATLAS Collaboration, Jet energy scale and its systematic uncertainty in proton-proton collisions at

s

7 TeV with ATLAS 2011 data, ATLAS-CONF-2013-004, http://cds.cern.ch/record/1509552.

[37] ATLAS Collaboration, Selection of jets produced in proton-proton collisions with the ATLAS detector using 2011 data, ATLAS-CONF-2012-020, http://cds.cern.ch/record/1430034.

[38] ATLAS Collaboration, Measurement of the Mistag Rate of b-tagging algorithms with 5 fb

of Data Collected by the ATLAS Detector, ATLAS-CONF-2012-040,

http://cds.cern.ch/record/1435194.

[39] ATLAS Collaboration, b-jet tagging calibration on c-jets containing D

mesons,

ATLAS-CONF-2012-039, http://cds.cern.ch/record/1435193.

[40] 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,

http://cds.cern.ch/record/1435197.

[41] 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.

[42] J. Alwall et al., Comparative study of various algorithms for the merging of parton showers and matrix elements in hadronic collisions, Eur. Phys. J. C53 (2008) 473.

[43] A. Buckley et al., General-purpose event generators for LHC physics, Phys. Rept. 504 (2011) 145.

[44] ATLAS Collaboration, Monte Carlo generator comparisons to ATLAS measurements constraining QCD radiation in top anti-top final states, ATL-PHYS-PUB-2013-005,

http://cds.cern.ch/record/1532067.

[45] R. Barlow, Systematic Errors: Facts and Fictions, arXiv:hep-ex/0207026.

[46] S. Frixione and B.R. Webber, Matching NLO QCD computations and parton shower simulations, JHEP 06 (2002) 029.

[47] S. Frixione, P. Nason and B.R. Webber, Matching NLO QCD and parton showers in heavy flavour production, JHEP 08 (2003) 007.

[48] ATLAS Collaboration, New ATLAS event generator tunes to 2010 data, ATL-PHYS-PUB-2011-008, http://cds.cern.ch/record/1345343.

[49] H. L. Lai et al., Global QCD analysis of parton structure of the nucleon: CTEQ5 parton distributions, Eur. Phys. J. C12 (200) 375.

[50] ATLAS Collaboration, ATLAS tunes of PYTHIA6 and Pythia 8 for MC11, ATL-PHYS-PUB-2011-009, http://cds.cern.ch/record/1363300.

[51] 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.

[52] J. Pumplin et al., New generation of parton distributions with uncertainties from global QCD analysis, JHEP 07 (2002) 012.

[53] ATLAS Collaboration, Jet energy resolution in proton-proton collisions at

s

7 TeV recorded in 2010 with the ATLAS detector, Eur. Phys. J. C73 (2013) 2306.

[54] ATLAS Collaboration, Measurement of the Top Quark Mass from

s

7 TeV ATLAS Data using a 3-dimensional Template Fit, ATLAS-CONF-2013-046,

http://cds.cern.ch/record/1547327.

[55] ATLAS Collaboration, Jet energy measurement and systematic uncertainties using tracks for jets and for b-quark jets produced in proton-proton collisions at

s

7 TeV in the ATLAS detector, ATLAS-CONF-2013-002, http://cds.cern.ch/record/1445265.

[56] ATLAS Collaboration, Measurement of the jet multiplicity in top–anti-top final states produced in 7 TeV proton-proton collisions with the ATLAS detector, ATLAS-CONF-2012-155,

http://cds.cern.ch/record/1493494.

[57] CMS Collaboration, Measurement of the top-quark mass in t¯ t events with dilepton final states in pp collisions at

s

7 TeV, Eur. Phys. J. C72 (2012) 2202.

[58] CDF Collaboration, Top quark mass measurement using the template method at CDF, Phys. Rev.

D83 (2011) 111101(R).

[59] D0 Collaboration, Measurement of the top-quark mass in p p collisions using events with two ¯

leptons, Phys. Rev. D86 (2012) 051103(R).

A Jet Energy Scale Uncertainty: Detailed Components

The relative JES uncertainty varies between about 1% and 3% depending on jet properties as given in Ref. [36]. For a better mapping of uncertainty categories between experiments, in view of future combinations, the total JES uncertainty has been split into 21 components, which vary as a function of jet p

and

and are considered uncorrelated. Their separate e

ects on the fitted top quark mass are summed quadratically to determine the total jet energy scale uncertainty given in Table 2. The results for the individual components and the sum are given in Table 3. For further details on each component, see Ref. [36].

Component Uncertainty

[GeV]

Statistical 0.15

Statistical NP1 0.05

Statistical NP2 0.04

Statistical NP3 0.11

Eta intercalibration (statistical) 0.08

Modelling 0.50

Modelling NP1 0.25

Modelling NP2 0.13

Modelling NP3 0.14

Modelling NP4 0.03

Eta intercalibration (modelling) 0.39

Detector 0.45

Detector NP1 0.45

Detector NP2 0.03

Mixed 0.06

Mixed NP1 0.04

Mixed NP2 0.04

Single particle high p

0.01 Relative non-closure MC 0.06

Pile-up o

set 0.49

Pile-up o

set (NPV term) 0.12 Pile-up o

set (µ term) 0.47

Close-by jets 0.26

Flavour 0.02

Flavour composition 0.02

Flavour response 0.01

bJES uncertainty 0.71

Total (without bJES uncertainty) 0.89

Table 3: The individual components of the JES uncertainty together with the corresponding uncertain-

ties on m

according to Ref. [36]. Some components are calculated as the quadratic sum of several

subcomponents, displayed in italics in the table.