1

Precision measurement of the top quark

mass in events with two leptons

Yuriy Ilchenko

(Southern Methodist University)

Thesis Defense for Ph.D.

in Experimental High Energy Physics

12/07/2012

Standard Model of elementary particles

2

Interaction particles – gauge bosons (integer spin):

mediators of the following interactions

Weak

Electromagnetic

Strong - SU(3)

Standard Model (SM) is the theoretical

framework to describe elementary particles

Matter particles – fermions (half-integer

spin): leptons ( e, μ, τ, νe , νμ , ντ ) and

quarks ( u, d, c, s, t, b )

Elementary Particles in the

Standard Model

Electroweak - SU(2)L x U(1)Y

Fundamental Interactions

Fermions acquire mass by interacting with Higgs field through

their Yukawa coupling

Excitation of the Higgs field is the Higgs boson

Standard Model of elementary particles

3

To generate masses for W, and Z bosons

Electroweak gauge symmetry is broken by introducing Higgs field

Higgs mechanism eliminates Goldstone Boson and produces mass

SU(2)L x U(1)Y → U(1)Q

Leads to massive bosons

Lagrangian with Higgs doublet

The top quark

4

Top quark properties:

Fermion, spin sz=1/2

Heaviest known elementary particle –

about 175 GeV

short lifetime – τ t ≈ (3.3+1.3-0.9) x 10-25 s

τ t < τ had (5.23 x 10-25 s), decays

before hadronizing

the only quark whose properties

can be studied in isolation

Top quark history:

Predicted by the theory (SM) – Γb(Z→bb) consistent with b weak isospin

partner

Observed in 1995 at by D0 and CDF

Completed the existence of 3rd

generation of quarks

Fermions in the Standard Model (SM)

Top quark is the heaviest

elementary particle known

5

The top quark in the Standard Model

Mass of the top quark mt is free

parameter in the SM

Top quark role in the SM :

o Yukawa coupling to Higgs is

close to 1 (0.994 ± 0.007) –

indicate a potential fundamental

role of top in EWSB

o sets an indirect constraint on the

Higgs mass and other particles

through radiative loop

corrections:

Feynman diagrams for radiative corrections

=> Important to measure mt precisely!

Constraints on mt and mW @ 68% CL

(2009). Shaded region – range of Higgs

mass.

6

Top quark production

At hadron collider two production ways:

In pairs (tt) via strong interaction

Single quark via electroweak interaction

Single top leading order diagrams Double top leading order diagrams

tt pair Single t

Single top:

• σ ≈ 3.4 pb @ 2 TeV

• large background

Double top

• σ ≈ 7.0 pb @ 2 TV

• low background

qq annihilation gluon fusion

(quark-antiquark annihilation -85%,

gluon fusion 15%)

=> The analysis is performed on top pair events

First evidence by D0 in 2006 and CDF in 2009

7

Top quark decay

In the Standard Model top quark decays

through electroweak interaction:

In 99.8% cases: to W and b-quark

(t→W+b )

Other cases < 0.02%: W and s or

even d quarks

Top pair decay products

b-quark hadronizes into a jet

W that decays further

two light quarks that hadronize into

two jets, or lepton + neutrino

Top quark decay mode

Top pair final states are dictated by possible decay modes of W boson:

Dilepton (WW → llvv)

Lepton + jets (WW → lvqq)

All jets (WW → qqqq)

8

Top pair final states

Dilepton channel (WW → llvv):

• Distinct signal signature – two

leptons, two jets, two neutrinos

• Low background

• Low statistics – 9% of ttbar

events

• Lepton + jets channel (WW → lvqq)

• Modest background

• Large statistics – 45% of ttbar

events

• All jets channel (WW → qqqq)

• Large background

• Large statistics– 46% of ttbar

events

e,μ e,μ

b-jet

ν ν

b-jet b-jet b-jet

ν e,μ

jet

jet

Dilepton mode Lepton +jets mode

ttbar branching ratios

Tevatron

9

Proton-antiproton collider

2 km in diameter

Located at Fermilab near

Chicago

Center-of-momentum energy

is 1.96 TeV

Has two experiments: CDF

and D0

Delivered about 12 fb-1 of data

Each experiment

recorded about 10 fb-1

It was shut down in Sep 2011

Downtown Chicago Fermilab

CDF D0 Tevatron

10

The D0 detector

Multi-purpose detector at one of

the ppbar collision points:

Central Tracking (Silicon

Microstrips and Fiber tracker)

Determine particle

momentum

Vertex, charge, particle ID

Ur/Liquid Argon Calorimeter

Measure energy of

photons, electrons, jets

Muon Spectrometer (Drift

Tubes, Scintillators, and Toroid)

Identify muons

Complement the tracker in

muon momenta

measurement

Schematic view of the D0 detector

Central Tracking System

Spherical (r, θ, φ) or cylindrical (ρ, θ, φ)

coordinate systems are used,

where θ → η

(pseudorapidity)

11

Data Quality Monitoring

Data Quality Monitoring (DQM) is an important and integral part of the data taking

process.

It is performed

online throughout the data acquisition

offline processing at computer tiers

during production of simulated data

D0 and ATLAS many similarities in DQM

Online monitoring

Incoming data comes in histograms

DQM Framework executes algorithms

to check quality of the data

DQM Display is a platform to monitor results, debug problems, etc.

I have worked on Online DQM at ATLAS detector – in particular, DQM Display

Online Monitoring Data Flow at ATLAS

12

DQM Display (DQMD) DQM Display serves as visualization tool of the automatic data quality assessment

Main features

Shifters can validate the quality of the incoming data

Be warned about the problems related to data quality

Can see relevant information about the origins of problems

Provides graphical representation of the detector with navigation functionality

Main Panel of DQMD Detailed Panel of DQMD

Y. Ilchenko et al` `Data quality monitoring display for ATLAS experiment at the LHC,'‘ J.Phys.Conf.Ser. 219, 022035 (2010)

13

Mass measurement in dilepton channel

Statistical Uncertainty is expected to be low

Emphasis on improving Systematical Uncertainty

Standard Jet Energy Calibration is the main contribution to

Systematical Uncertainty

Improve Jet Energy Calibration

Neutrino Weighting (NuWT) method is used to measure mt in dilepton channel –

Based on MC templates

Use Likelihood approach – gives central value and stat. uncertainty

Choose best

discriminating

variables xi

Form signal and

background MC

templates of xi

Perform likelihood

fit between data

and templates

Method Calibration

(mt,σstat)

14

Justifying templates (Bayes’ theorem)

Weight produced by NuWT indicates how probable the event to be from ttbar

event of a certain mass mt

P({o}|mt) – probability to observe final state {o} given top quark mass mt

Bayes’ theorem relates P({o}|mt) and P(mt|{o})

P(mt|{o}) – probability measure top quark mass mt given ttbar decayed to

observed final state {o}

Assuming no prior knowledge about P(mt):

or

It allows

to form templates W({o}|mt) from MC for different mt hypotheses

use Likelihood to extract mt and stat. uncertainty when analyzing data

15

Kinematic reconstruction and weight

Kinematic parameters of leptons and b-jets

measured directly, neutrinos leave

undetected

Assuming neutrinos η and mt, event can be

fully kinematically reconstructed

Assign weight − W(η1,η2|mt) − how

consistent an event with top-quark mass

equal to assumed mt and particular choice

of neutrino rapididities η1,η2

Dilepton (eμ) event

Each neutrino - 2 solutions

from quadratic equations.

Additionally, two-fold ambiguity

in lepton-jet pairing.

Results in Nsoln <=8

σx,,σy – missing energy resolution

16

Neutrino rapidity distribution

MC neutrino rapidity distribution

The total event weight with assumed mt

obtained by

• integrating over η1,η2

• ρ(η1) and ρ(η2) – probability

distribution functions from MC

simulation

ρ(η)

where {o} is observed final state

Width of rapidity distribution vs

assumed top quark mass

Neutrino rapidity distribution

simulated for different masses of the

top quark, fit to Gaussian

dependence of the Gaussian width on

mt is fit to a straight line

17

NuWT: neutrino rapidity distribution

Schematical example of an event weight

distribution

μ

σ

Scanning over different mt values

produce weight distribution for each

event

𝑊(𝑚𝑡)

𝑚𝑡

Average event weight distribution

has broader peak due to resolution

effects and jet permutations

ISR/FSR shift mean value and add

high-mass tail

Every weight distribution and so every

event is characterized by moments - mean

value μ and - width σ

Average event weight distribution

18

Maximum Likelihood: templates

Construct probability density histograms –

“templates” - from moments

signal template (hs): moments, input top

quark mass

background template (hb): moments

For every MC event (either signal or

background) – produce weight distribution

Signal: put (μ, σ) in 3D histo at mt

Background: put (μ, σ) in 2D histo

Normalize templates

hs

hb

Slice of the signal template at

at mt=170 GeV

Background template

eμ

eμ

19

Maximum Likelihood: likelihood function

Likelihood function is given as

where

xi=(μ, σ) – weight distribution moments

ns – expected number of signal events

nb – expected number of background

events

Negative log likelihood with fit

(from previous analysis iteration)

t̂

tm̂

Fit –log(L(mt )) with parabola

Based on the assumption of the Gaussian shape of L(mt )

Minimum of parabola defines top quark mass

estimate mt

Half width where –log(L) rises to 0.5 unit above its

minimum defines statistical uncertainty

20

The NuWT Method calibration

Our method is based on number of assumptions

Likelihood function L(mt ) is Gaussian

Neutrino rapidities are distributed according to SM expectations

Additionally background shifts mt from its true value

NuWT calibration is needed

verify method performance and precision

accounts for possible residual effects

Gives more accurate central value and stat. uncertainty

NuWT is tested with pseudoexperiment technique (ensemble testing)

Based on events from MC

Each pseudoexperiment is similar to data events within

fluctuations

21

Ensemble testing

Ensemble testing - running many pseudo-

experiments

For each mt hypothesis, measurement is

performed in 1000 pseudo-experiments

for pseudo-experiment choose events randomly

from the signal (S) and background (B) MC

samples

• Number of S and B events are obtained from

Poisson distribution

• Mean of the Poisson is random from

Gaussian

• Mean and Width of Gaussian – expected

yield and uncertainty

• the average event numbers match the

expected yield

• Select ones where total number of events

equals those in data

Background MC Sample

Signal MC Sample

…

Pse

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Ensemble testing: calibration curve

The relationship between fitted top quark mass and the actual

input top quark mass is fitted to a line.

Linear fit is used as a calibration tool on the results from data.

Calibration points and fit:

ee eμ μμ

Calibrated cent. value and stat.

uncertainty:

α β

High χ2 of calibration curve

Pseudo-experiment (PE) studies to

calibrate the measurement show

calibration curve high χ2

high χ2 main sources

signal template statistics

background oversampling

non-unitary ALPGEN weights

Dominating contribution is found to be

due to template statistics

23

Calibration curve for eμ channel

High χ2

Template statistics effect on

calibration curve

To estimate the template statistics effect

varied templates within uncertainties for

each pseudoexperiment

produce fitted mass distribution for

each pseudoexperiment

plot RMS of those distributions

average RMS is 0.3 GeV

24

Template statistics contributes additional uncertainty of 0.3 GeV added in

quadrature with statistical uncertainty at every input mass point

Calibration curve for eμ channel with template statistics uncertainty

Good χ2

25

ee eµ µµ combined

without template stat. 170.2 ± 6.5 174.2 ± 3.2 183.5 ± 17.5 173.7 ± 2.8

with template stat. 170.3 ± 6.4 174.2 ± 3.2 183.8 ± 18.0 173.7 ± 2.8

Calibrated results

=> Template statistics has no or negligible effect on the

measurement

Template statistics effect on

measurement in data

26

Ensemble testing: stat. uncertainty

To test calibrated statistical uncertainty, ensemble testing technique is used

Pull variable evaluates correctness of calibrated statistical uncertainty

Pull points and fit:

ee eμ μμ

Pull corrected calibrated stat.

uncertainty:

λ

27

Event Yields and Data Sample

Apply kinematic and topological cuts – best signal to background ratio

Two isolated leptons with opposite charge

leptons Pt > 15 GeV

Two jets inclusive.

Jets Pt > 20 GeV

Topological cuts

ee: METsig>5.0;

eµ: Ht>120 GeV;

µµ: METsig>5.0, MET>40 Gev

Ht cut is effective against Z->tau tau and diboson that are largest in eμ

METSig cut rejects events with MET from resolution fluctuation

MET cut is powerful against for Z->ll background

σ is variance of prob. distr.

p(MET). σ and p(MET) are

computed from object momentum

resolutions.

28

32.95

8.1

2.21 0

ee

138.7

10.6 5.6

8.95 eμ

44.6 24.5

3.2

4.5 μμ

-Z->ll -Diboson -ttbar -Instrum.

Event Yields and Data Sample Integrated luminosity is 4.3 fb-1 of Run II

MC and data samples for modeling

Expected yields in MC and number of events in data after kinematic reconstruction

Data: 49 Data: 190 Data: 80

29

Calibrated result:

Data Measurement

mt(combined)= 173.7 ± 2.8 (stat.) GeV

Negative log likelihood (before calibration)

Combined likelihood is

obtained multiplying

likelihoods of all channels

ee eμ

μμ combined

mt(ee)= 170.3 ± 6.4 (stat.) GeV mt(eμ)= 174.2 ± 3.2 (stat.) GeV

mt(μμ)= 183.8 ± 18.0 (stat.) GeV

30

Expected statistical uncertainties

Distributions of pull-corrected calibrated statistical uncertainties

ee eμ

μμ combined

Good agreement for ee, eμ, and combined. μμ-channel is consistent with

expectation at probability level of 7%

31

Systematic uncertainties

Statistical uncertainty is calculated with Likelihood

Systematic uncertainty is due to systematic effects - due to inaccurate

equipment, assumptions, imperfect calibration

cannot be eliminated by using bigger statistics

some are of comparable scale to the statistical uncertainty

Systematic uncertainties are divided in four categories

Jet Energy Calibration

effects of overall energy scale

residual biases from jet Pt and η dependences

data to MC jet response differences

QCD interactions modeling

ISR/FSR, b-fragmentation etc.

Object reconstruction and identification

Resolutions of jets and leptons, ID efficiencies etc.

Systematics of the method

uncertainty from calibration, limited statistics for templates etc.

Replaces the standard

Jet Energy Calibration

32

Standard Jet Energy Scale

Standard JES systematic is the dominating uncertainty in previous iteration of

the analysis

Standard JES

reconstruct energy back to particle jet

includes number of corrections

Parton evolution in calorimeter

Eoffset – energy in calorimeter from

underlying event

Fη – correct for calorimeter non-uniformity

R – absolute jet response

S – correct for losses due to showering

33

Jet Energy Scale: response calculation

JES correction is dominated by error on absolute Response => needed to be

measured accurately with robust and reliable method

Missing Energy Projection factor (MPF) – method to measure absolute Response

Use back-to-back photon + jet events in CC

Employs momentum conservation

Missing Energy Projection factor

Independent of Eoffset, S effects

Does not depend on jet reconstruction algorithm

34

Jet Energy Scale: sample purity

Jet may have leading π0→γγ, thus misidentified as a photon

Photon + jet events suffer from contamination of events with two jets

(dijet)

needed to be taken into account for R calculation

Purity variable is introduced

S – number of photon + jet events

B – number of dijet events

To estimate purity

Simple event counting: MC

Hollow Cone Method (HC07): Data Example of MC based and

HC07 purity

35

Jet Energy Scale: HC07 method

Hollow Cone Method

HC07 variable discriminates a photon against a jet

HC07 – scalar Pt of track in hollow cone 0.05 < ΔR < 0.7

Fit normalized MC templates (photon+jet, dijet) to data

Purity for tight photon definition (HC07 <1.0 GeV) estimated from medium

HC07 distribution Purity in central region

36

Standard JES

Derived from γ+jet events, systematic

limited (2% averaged over top jets)

l + jets channel

extract additional JES (kJES ) using

constraint of dijet mass from W→qq’ decay

simultaneously measure kJES and mt

dilepton channel

no W→qq’

Replace standard JES with l+jets result

• 2.5x smaller uncertainty

• small systematic for scale of b-jets in dilepton vs. l+jets events

• residual systematic uncertainty to encompass Pt and η

dependence of JES in dilepton

Jet energy scale (JES)

from l+jets channel

Precise measurement of the top-quark mass from lepton+jets events at D0

Phys. Rev. D 84, 032004 (2011)

Likelihood L(mt, kjes) in l+jets with

contours of equal probability

37

Adopting the l+jets channel JES

Event topology in l + jets differs from that in dilepton channel

Higher jet multiplicity affects reconstruction and so jet energies

Hadrons can be misrecognized by algorithm as belonging to an

incorrect jet

Different color flow scenarios l + jets and dilepton have an impact

on reconstructed jet energy

in l+jets, singlet W boson produces two quarks forming a color

dipole

color dipole produces more radiation in the region between

the quarks

The difference between two channels can be evaluated using the

following response double ratio b-jet responses in l+jets and

dilepton in MC and Data

38

Double ratio shows that

the response for the b-

quarks in dilepton channel

and l + jets channel are

very close

Asymptotic value is

shifted by 0.3% from

unity

b-jets responses in

l+jets and dilepton are

almost same

Double ratio

If the event topologies for both channels were equal, the double ratio would

equal unity

Double ration for b-jets as function of jet pt

39

Double ratio

Small variation of the double ratio from one can be a result of different jet

particle multiplicity

Average number of particles in a jet in l+jets and dilepton channels

Particle multiplicity in l+jets few percent higher than that in the

dilepton sample

Enough to produce observed shift in the double ratio up to 0.3%

=> error on l+jets jes is 0.3%, added as systematic uncertainty

40

Residual systematic

Arises from the dependence of kJES on

Pt and η

Estimated from shape of 𝜎𝐽𝐸𝑆

𝐽𝐸𝑆 in

photon+jet sample

Shift jet energy by the correction

factor from distribution minus

correction average (up and

down)

𝜎𝐽𝐸𝑆

𝐽𝐸𝑆 by jet pt in η: [0,0.5]

correction average over all jets’ pt in all

η regions

To estimate residual uncertainty

New MC samples are produced

JES in the samples are shifted up

and down

41

Jet specific correction for light quarks, gluons

and heavy quarks

Jets initiated from different flavors of

partons

different kinematic

characteristics

different particles compositions

=> b and light jets have different

response

=> can result in a systematic shift on mt

Jet multiplicity for gluon and quark jets Previous iteration of this analysis

standard JES calibration to b

jets caused 1.8% shift in jet pt

42

Discrepancy in energy between Data and MC

Define correction factor for jet of flavor β

flavor-averaged in γ+jets events

Ei, Ri – single particle

energy and response

Systematical uncertainty is significantly reduced!

(Fcorr-1) for light jets in |η|<1.4 Correct jet energies based on their flavor

Jet specific correction for light quarks, gluons

and heavy quarks

New approach

• Correct b and light jet response in MC independently

• based on Single Particle responses (separately done on MC and Data)

• b/light systematic has been replaced by sample dependent systematic

(analogous to lepton+jets channel)

43

Systematic uncertainties

Major improvement –

lepton+ jets calibration

reduces standard JES

systematic that was 1.5

GeV

Major systematic effects

are coming from theoretical

modeling and systematic of

the method

Total combined systematic

uncertainty is 1.5 GeV

44

Major modeling uncertainties

Higher order effects – [0.6 GeV]

Default samples – ALPGEN+PYTHIA (no such higher-order effects as

gg initial state, additional radiation of hard jets)

Compared to MC@NLO+HERWIG

Color reconnection – [0.5 GeV]

Color reconnection – strong interaction between underlying event and

hard-scattering process

Sample with and without explicit color reconnection in PYTHIA are

compared

PDF uncertainty – [0.5 GeV]

Default samples – use set of PDF from CTEQ6L1

Compared to reweighted sample that matches CTEQ6M set of PDFs

Template Statistics – [0.5 GeV]

Arise from limited MC statistics

Bins in templates are varied within their uncertainties

New measurements performed 1000 times

45

Conclusion (I)

In 4.3 fb-1 the top quark mass estimate:

Combining with previous measurement 1 fb-1

(total of 5.3 fb-1) using BLUE method (Best

Linear Unbiased Estimator)

=> error on top quark mass is 1.6%

mt = 174.0 ± 2.4 (stat.) ± 1.4 (syst.) GeV

mt = 174.0 ± 2.8 (stat.+ syst.) GeV

mt = 173.7 ± 2.8 (stat.) ± 1.5 (syst.) GeV

Most precise measurement in dilepton

channel

First time JES systematics done to take

advantage of l+jets scale

Published in PRD (RC) 86, 051103 (2012)

Current D0 top quark mass average

Top quark mass measurement with

neutrino weighting method

46

Conclusion (II)

Constraints on mt and mW @ 68% CL

(2012).

Δχ2 of a global fit to electroweak data as a

function on the Higgs mass (2012).

mH = 94 +29 -24 GeV

Tevatron (World) average top quark mass

Contributions

47

D0 experiment

Top quark mass measurement (PRD (RC) 86, 051103 (2012))

γ+jet purity estimation (D0 internal Note 6327)

P20/p17 MC verification

ATLAS experiment

LAr Panel and commissioning

DQM Display - Y. Ilchenko et al` `Data quality monitoring display for ATLAS

experiment at the LHC,'‘ J.Phys.Conf.Ser. 219, 022035 (2010)

48

Back-up slides

49

Oversampling

Number of pseudoexperimnents (PE) is large

• Events are selected in ensembles more

than once

• A correction for correlation among

ensembles is performed

The uncertainty on average top quark mass

is corrected by following facor

• Nsig - # of signal events in PE

• Npe - # of PEs tried

• NMC - # of events in MC sample after

selection

The uncertainty on pulls are corrected with

Background MC Sample

Signal MC Sample

same event

…

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DQMD – Graphical View

50 DQMD Detailed Panel

DQMD – Graphical View

51 Graphical representation of Muon Spectrometer of ATLAS in DQMD