Experimental aspects of top Experimental aspects of top quark physics quark physics

Lecture #2Lecture #2

Regina Demina

University of Rochester

Topical Seminar on Frontier of Particle Physics

Beijing, China08/15/05

08/15/05 Regina Demina, Lecture #2 2

OutlineOutline

• Invariant mass

• Template method to measure top mass

• Matrix element method– Jet energy scale calibration on W-boson

• Combined result– Constraint on Higgs mass

• Control questions

08/15/05 Regina Demina, Lecture #2 3

Invariant massInvariant mass

• Top quark decays so fast there is no time to put it on a bathroom scale

• We measure its mass through energy and momentum of its products:

• tbW, Wqq’

• E(t)=E(b)+E(q)+E(q’)

• P(t)=P(b)+p(q)+p(q’)

• M2(t) = E2(t)-p2(t)

• M, E, p in GeV

08/15/05 Regina Demina, Lecture #2 4

Challenges of MChallenges of Mtoptop Measurement MeasurementLepton+Jets Channel

bbqqltt

Observed Final state

Complicated final state to reconstruct Mtop

4jetsEl T

Leading 4 jets combinations• 12 possible jet-parton

assignments• 6 with 1 b-tag (b-tag helps)• 2 with 2 b-tags

Poor jet energy scale and resolution• Hard to find the correct

combination

Good b-tagging and jet energy scale and resolution

and good algorithm to reconstruct Mtop

08/15/05 Regina Demina, Lecture #2 5

Wbb MCData

tt MC

Datasets

Result Likelihood fit:

Best signal + bkgd templates to fit datawith constraint on background normalization

Likelihoodfit

Massfitter

Signals/background templates

Data

2 mass fitter:•Finds top mass that fits event best•One number per event•Additional selection cut on resulting 2

Template methodTemplate method

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1. Try all jet-parton assignments with kinematic constraints, but assign b-tagged jets to b-partons

2. Select the rec. mass Mt from the choice of lowest 2

3. Badly reconstructed Mt (2 > 9 ) is removed

Top mass isfree parameter

All jets are allowed to be float according to their resolutions to satisfy that M(W+)=M(W-)=80.4 GeV, M(t)=M(t)

Mass Fitter (event by event)Mass Fitter (event by event)

08/15/05 Regina Demina, Lecture #2 7

More correct combination

with b-tag

Mt(GeV/c2) Mt(GeV/c2)

Mt(GeV/c2) Mt(GeV/c2) Bkgd is large in the 0-tag

Templates for different number of tagsTemplates for different number of tags

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Samples: Herwig with Mtop = [130 to 230] GeV Get analytical functions (2 Gaussian + gamma)

of reconstructed mass, Mt

as a function of true mass, Mtop Fit parameters: linear depend.

on Mtop

Smooth PDFs(Mt | true Mtop)Mt(GeV/c2)

Signal templates for different masses Signal templates for different masses

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Comb. –Log Likelihood

2. 7 GeV/c)(4.3)stat(2.31M 9.282top syst

Expected error

Result on MtopResult on Mtop

08/15/05 Regina Demina, Lecture #2 10

Top mass using matrix element Top mass using matrix element method in Run Imethod in Run I

• Method developed by DØ (F. Canelli, J. Estrada, G. Gutierrez) in Run I

Systematic error dominated by JES 3.3 GeV/c2

With more statistics it is possible to use additional constraint on JES based on hadronic W mass in top events – in situ calibration

Single most precise measurement of top mass in Run IMt =180.1±3.6(stat) ±4.0(syst) GeV/c2

08/15/05 Regina Demina, Lecture #2 11

Matrix element methodMatrix element method

• Goal: measure top quark mass• Observables: measured momenta of jets and leptons • Question: for an observed set of kinematic variables x what

is the most probable top mass • Method: start with an observed set of events of given

kinematics and find maximum of the likelihood, which provides the best measurement of top quark mass

• Our sample is a mixture of signal and background

)()1(),(),( sgn xPfmxPfmxP bkgtopttoptevt

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Matrix Element MethodMatrix Element Method

Normalization depends on mt

Includes acceptance effects

probability to observe a set of kinematic variables x for a given top mass

Integrate over unknown q1,q2, y

f(q) is the probability distribution than a parton will have a momentum q

dnσ is the differential cross sectionContains matrix element squared

t

t

W(x,y) is the probability that a parton level set of variables y will be measured as a set of variables x

bq’

q

),()()();()(

1);( 2121sgn yxWqfqfdqdqmyd

mmxP t

n

tt

08/15/05 Regina Demina, Lecture #2 13

Transfer functions (partonTransfer functions (partonjet)jet)

• Partons (quarks produced as a result of hard collision) realize themselves as jets seen by detectors– Due to strong interaction partons turn into

parton jets– Each quark hardonizes into particles (mostly

and K’s)– Energy of these particles is absorbed by

calorimeter – Clustered into calorimeter jet using cone

algorithm• Jet energy is not exactly equal to parton

energy– Particles can get out of cone– Some energy due to underlying event (and

detector noise) can get added– Detector response has its resolution

• Transfer functions W(x,y) are used to relate parton energy y to observed jet energy x

08/15/05 Regina Demina, Lecture #2 14

Top ID in “lepton+jets” channelTop ID in “lepton+jets” channel

• 2 b-jets • Lepton: electron or muon• Neutrino (from energy

imbalance)• 2 q’s – transform to jets of

particles• Note that these two jets come

from a decay of a particle with well measured mass – W-boson – built-in thermometer for jet energies

lWorqqW

bWt

ttpp

'

08/15/05 Regina Demina, Lecture #2 15

• All jets are corrected by standard DØ Jet energy scale (pT, )

• Overall JES is a free parameter in the fit – it is constrained in situ by mass of W decaying hadronically

• JES enters into transfer functions:

JES in Matrix ElementJES in Matrix Element

JES

EJES

EW

JESEEWp

j

pj

),(),,(

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Signal IntegrationSignal Integration• Set of observables – momenta of jets and leptons: x• Integrate over unknown

– Kinematic variables of initial (q1,q2) and final state partons (y: 6 x3 p) = 20 variables

– Integral contains 15 (14) -functions for e()+jets• total energy-momentum conservation: 4• angles are considered to be measured perfectly: 2x4 jet +2 lepton • Electron momentum is also considered perfectly measured, not true for muon

momentum: 1(0)– 5(6) dimensional integration is carried out by Vegas– The correspondence between parton level variables and jets is established by

transfer functions W(x,y) derived on MC• for light jets (from hadronic W decay)• for b-jets with b-hadron decaying semi-muonically• for other b-jets

• Approximations– LO matrix element– qqtt process only (no gluon fusion – 15%)

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Background integrationBackground integration

• W+jets is the dominant background process

• Kinematics of W+jets is used as a representation for overall background (admixture of multijet background is a source of systematic uncertainty)– Contribution of a large number of diagrams makes

analytical calculation prohibitively complex– Use Vecbos

• Evaluate MEwjjjj in N points selected according to the transfer functions over phase space

• Pbkg- average over points

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Sample compositionSample compositionLepton+jets sample

– Isolated e (PT>20GeV/c, ||<1.1)

– Isolated (PT>20GeV/c, ||<2.0) – Missing ET>20 GeV– Exactly four jets PT>20GeV/c, ||<2.5

(jet energies corrected to particle level)

Use “low-bias” discriminant to fit sample composition – Used for ensemble testing and

normalization of the background probability.

– Final fraction of ttbar events is fit together with masse+jets +jets

# of events 70 80

Signal fraction 45±12% 29±10%

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Calibration on Full MClepton+jets

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calibrated calibrated

expected: 36.4%

DØ RunII Preliminary

Mt=169.5±4.4 GeV/c2

JES=1.034±0.034

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Systematics summarySystematics summary

Source of uncertainty Effect on top mass (GeV/c2)

B-jet energy scale +1.32-1.25

Signal modeling (gluons rad)

0.34

Background modeling 0.32

Signal fraction +0.5-0.17

QCD contribution 0.67

MC calibration 0.38

trigger 0.08

PDF’s 0.07

Total +1.7-1.6

08/15/05 Regina Demina, Lecture #2 22

B-jet energy scale● Relative data/MC b/light jet energy scale ratio

•fragmentation: +-0.71 GeV/c2

different amounts of 0, different + momentum spectrum fragmentation uncertainties lead to uncertainty in b/light JES ratio

compare MC samples with different fragmentation models: Peterson fragmentation with eb=0.00191 Bowler fragmentation with rt=0.69

•calorimeter response: +0.85 -0.75 GeV/c2

uncertainties in the h/e response ratio + charged hadron energy fraction of b jets > that of light jets corresponding uncertainty in the b/light JES ratio

•Difference in pT spectrum of b-jets and jets from W-decay: 0.7 GeV/c2

08/15/05 Regina Demina, Lecture #2 23

Gluon radiationGluon radiation

Extra jets from initial/final state gluons

80% of the time, leading 4 jets correspond to 4 partons (qqbb)

• Final effect on top mass 0.34 GeV/c2

qq

e

08/15/05 Regina Demina, Lecture #2 24

Result and cross checksResult and cross checks

• Run II top quark mass based on lepton+jets sample: Mt=169.5 ±4.4(stat+JES) +1.7

-1.6 (syst) GeV/c2

• JES contribution to (stat+JES) 3.3 GeV/c2

• Break down by lepton flavor– Mt(e+jets)=168.8 ±6.0(stat+JES) GeV/c2

– Mt(+jets)=172.3 ±9.6(stat+JES)GeV/c2

• Cross check W-mass

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Summary of DØ MSummary of DØ Mtt measurements measurements

• Statistical uncertainties are partially correlated for all l+jets Run II results

DØ Run II preliminary

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Combination of Tevatron resultsCombination of Tevatron results

JES is treated as a part of systematic uncertainty, taken out of stat error

08/15/05 Regina Demina, Lecture #2 27

CombinationCombination

• Mt=172.7±2.9 GeV/c2

• Stat uncertainty: 1.7GeV/c2

• Syst uncertainty: 2.4GeV/c2

• hep-ex/0507091

• Top quark Yukawa coupling to Higgs boson

• gt=Mt√2/vev=0.993±0.017

08/15/05 Regina Demina, Lecture #2 28

Top Quark Mass: Motivation

• Fundamental parameter of the Standard Model.

• Important ingredient for EW precision analyses at the quantum level:

which were initially used to indirectly determine mt.

After the top quark discovery, use precision measurements of MW and mt to constrain MH.

W Wt

b

W W

H

MW mt2 MW ln(MH)

CDF&D0RUNII

08/15/05 Regina Demina, Lecture #2 29

What does it do to Higgs?What does it do to Higgs?

• MH=91+45-32GeV/c2

• MH<186 GeV/c2 @95%CL

MH,GeV/c2 Mt,GeV/c2

MW

,GeV

/c2

68% CL

08/15/05 Regina Demina, Lecture #2 30

Projection for uncertainty on top Projection for uncertainty on top quark massquark mass

Assumptions:• only lepton+jets channel considered • statistical uncertainty normalized at L=318

pb-1 to performance of current analyses. • dominant JES systematic is handled

ONLY via in-situ calibration making use of MW in ttbar events.

• remaining systematic uncertainties: include b-JES, signal and background modeling, etc (fully correlated between experiments) Normalized to 1.7 GeV at L=318 pb-1.

• Since most of these systematic uncertainties are of theoretical nature, assume that we can use the large data sets to constrain some of the model parameters and ultimately reduce it to 1 GeV after 8

fb-1.

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High statistics (LHC) approachHigh statistics (LHC) approachIn 100fb-1 about 1000 signal events is expected

No jes systematics !!!