CDF Top Quark Mass Measurement with the Matrix Element …eddata.fnal.gov/lasso/summerstudents/papers/2016/Gabriele-Franciolini.pdf• Lepton + jets events: one W boson decay hadronically,

Gabriele Franciolini, University of Pisa (Supervisor: George Velev, FNAL)Fermilab Summer School - Final presentation22 September 2016

CDF Top Quark Mass Measurement with the Matrix Element Method

22 Sep 2016 Gabriele Franciolini | CDF Top mass measurement with matrix element method

Outline

• Top mass measurements

• Channel and Event Selection

• Matrix element method

• Study of the integration methods: pMC, qMC

• Analysis of the preliminary results with the new TF

• Study of the sensitivity to the

• Future development of the analysis

2

�JES


Tevatron Collider• Proton - Antiproton collider• Completed in 1983• Main achievement: Top quark discovery, 1995• Energy reached Run II:

3

• Lead in top physics:• Production properties

(cross sections, AFB)• Decay properties (width, BR)• Intrinsic properties (mass,

spin, charge)• Exotic searches involving

top quarks

ps = 1.96 TeV


Top Mass Measurement: Previous results

4

World comb. 2014 : Precision0.44%


Top Mass measurements: Advances in Precision

• D0 final measurement in lepton+jets:

( precision) PRL 113, 032002 (2014); PRD 91, 112003 (2015)

• CMS 7 + 8 TeV measurements in all channels: (Latest)

PRD 93, 072004 (2016)

( precision!)

• CDF latest measurement aim:

• Reach the highest possible precision From CDF Data.

• Examine tension between LHC and Tevatron Results

5

0, 43%

mt = 174.98± 0.58stat+JES ± 0.49syst GeV/c2 = 174.98± 0.76 GeV/c2

mt = 172.44± 0.13stat ± 0.44syst GeV/c2 = 172.44± 0.48 GeV/c2

0.28%


CDF Top Mass Measurement: Channels

• Top decay Branching Ratio:

• decay signatures: • Dilepton events: both W bosons decay into an or final state.

- Lowest branching ratio: ( including leptons) -Two undetected neutrinos: Unconstrained kinematics

• Hadronic events: both W bosons decay hadronically (6 jets)- Highest branching ratio:

- Large QCD multi-jet background

• Lepton + jets events: one W boson decay hadronically, the other into an or .-Characterised by an isolated lepton, four jets, missing transverse energy.

-Branching ratio: (𝝉 events included) events: if decays into or , it appears in the electron/muon+jets signal sample.

6

tt̄

e⌫ µ⌫

⇠ 7% ⌧

⇠ 55%

e⌫ µ⌫

⇠ 38%

⌧⌧ e µ

t ! Wb ⇠ 100%


CDF Top Mass Meas.: L+jets event selection / Background

• Lepton + jets: event signature:• High transverse momentum charged lepton;• Large missing transverse energy (escaping neutrino from W decay in the final state);• At least 4 jets;

• Tight or loose jets:• Tight jet: , • Loose jet: ,

• 5 subsamples based on the number of identified (tagged) b-jets (T or L):• 0-tag, 1-tagL, 1-tagT, 2-tagL, 2-tagT.

• Background: non- events that mimics the L+jets signature:• W+jets (W+ , W+ , W+ , W+LF) Included in the Likelihood • QCD (“fake” electrons, secondary electron): reduced by selection cuts.• other: (Single-top, Diboson (WW,WZ,ZZ), Z+jets)

7

pT/ET

ET > 20GeV |⌘| 6 2.0

|⌘| 6 2.4ET > 12GeV

tt̄

bb̄ cc̄ c


CDF Latest measurement: Improvement respect to past analysis• Increase of Integrated Luminosity: Exploiting the full CDF Run II Dataset.• from 5.6 fb-1 to 9.0 fb-1 : ~ 60% more data;

• Inclusion of new sample categories:• untagged category: 0-tag;• loose categories: 1-tagL, 2tagL;

• For the first time in CDF analysis the Background Matrix Element modelling of the likelihood is included;

• Inclusion and refinement of the quasi-MC method in the Integration code;

• Smaller systematic uncertainties on the final measurement by introducing several new signal and background modelling;

• NLO signal MC: Reduction of uncertainty in Calibration Procedure

8


Matrix Element Technique

• Full kinematic and topological information in any event is considered.• Calculation of the Matrix element to find the probability for the event:• Integration over phase space

• 32 variables of integration: 19 variables of integration:

• Signal and Background: for different

• Likelihood:

• Calibration of Method: • Pseudo-experiment to correct biases and missing background modelling• A fast and reliable integration algorithm is essential

9

(mt,�JES)

d�(x) [tt̄ ! b(l⌫)b(qq0)]

constraints

Lev(y|mt,�JES) = a(fsig)Lsig(y|mt,�JES) + b(fbkg)Lbkg(y|�JES)

Ltot

(y|mt

,�JES

) =NY

i=1

Lev

(y|mt

,�JES

)


Validation of the integration method : Pull Distribution pMC• pMC integration: Random sequence of points with importance sampling;

• Relative error behaviour:

• Pull distribution: Mean:

Standard dev:

Pull variable:

10

�I/I ⇠ O(N�1/2)

�k,ij,l =Wk,ij,l� < Wk,ij >

�k,ij

< Wk,ij >=1

N

NX

l=1

Wk,ij,l

�k,ij =

vuut 1

N � 1

NX

l=1

(Wk,ij,l� < Wk,ij >)2

k = event

i, j = (�JES ,Mt) bins

l = integration


PullEntries 1.953521e+07Mean 10− 2.885eStd Dev 0.977Underflow 0Overflow 44Integral 1.954e+07Skewness 0.2166−

/ ndf 2χ 1.901e+05 / 823Prob 0Constant 2.207e+01± 8.112e+04 Mean 0.000229±0.001281 − Sigma 0.0001± 0.9514

Pull5− 4− 3− 2− 1− 0 1 2 3 4 5

Freq

uenc

y

0

10000

20000

30000

40000

50000

60000

70000

80000



Pull distribution

Validation of the integration method : Pull Distribution pMC

• Problem in the pull distribution: 2 events gave a spike

11

�k,ij,l 8(k, i, j, l) (l 2 [1, 22])

3− 2− 1− 0 1 2 3

160165

170175

1801850

0.005

0.01

0.015

0.02

0.025

0.03

Profile_1Profile_1

Entries 961Mean x 1.806− Mean y 177.6Std Dev x 1.174Std Dev y 7.849Integral 2.647Skewness x 1.353Skewness y 0.7309− 0 0 0 0 2 0 0 0 0

Profile_1

3− 2− 1− 0 1 2 3

160165

170175

1801850

0.02

0.04

0.06

0.08

0.19−10×

Profile_2Profile_2

Entries 14415Mean x 2.343− Mean y 185.7Std Dev x 0.91Std Dev y 2.059Integral 10− 7.017eSkewness x 2.3Skewness y 2.3− 0 0 0 0 0 0 0 0 0

Profile_2Entries 14415Mean x 2.343− Mean y 185.7Std Dev x 0.91Std Dev y 2.059Integral 10− 7.017eSkewness x 2.3Skewness y 2.3− 0 0 0 0 0 0 0 0 0

Profile_2

(�)

(�)(GeV/c2)

(GeV/c2)

22 Sep 2016 Gabriele Franciolini | CDF Top mass measurement with matrix element method12

Validation of the integration method : Pull Distribution pMC

�k,ij,l 8(k, i, j, l) {l 2 [1, 22] ^ k 6= (58, 330)}

• integrations with random seed of ~1000 events (MC, , , 1TagT)



Pull5− 4− 3− 2− 1− 0 1 2 3 4 5

Freq

uenc

y

0

10000

20000

30000

40000

50000

60000

70000

80000



Pull distribution

mt = 173 GeV/c2 �JES = 0 �

22


Validation of the integration method : Pull Distribution qMC

• qMC integration: sobol sequence of points instead of random sequence;

• Sobol sequence: LDS (Low-discrepancy sequence) (uniformly spread across the integration domain)

• Expected relative error:

• Introduction of random scrambling: Owen + Faure-Tezuka: random scrambling preserving LDS

• Importance sapling embedded in the code;

• Expected faster convergence of the integral.

13

�I/I ⇠ O(N�1+")



• Problem in the pull distribution: the same problematic events.

14

�k,ij,l 8(k, i, j, l) (l 2 [1, 22])

3− 2− 1− 0 1 2 3

160165

170175

1801850

0.005

0.01

0.015

0.02

0.025

0.03

Profile_1Profile_1

Entries 961Mean x 1.806− Mean y 177.6Std Dev x 1.174Std Dev y 7.849Integral 2.647Skewness x 1.353Skewness y 0.7309− 0 0 0 0 2 0 0 0 0

Profile_1

3− 2− 1− 0 1 2 3

160165

170175

1801850

0.02

0.04

0.06

0.08

0.19−10×

Profile_2Profile_2

Entries 14415Mean x 2.343− Mean y 185.7Std Dev x 0.91Std Dev y 2.059Integral 10− 7.017eSkewness x 2.3Skewness y 2.3− 0 0 0 0 0 0 0 0 0

Profile_2Entries 14415Mean x 2.343− Mean y 185.7Std Dev x 0.91Std Dev y 2.059Integral 10− 7.017eSkewness x 2.3Skewness y 2.3− 0 0 0 0 0 0 0 0 0

Profile_2


/ ndf 2χ 1.01e+05 / 830Prob 0Constant 1.98e+01± 6.28e+04 Mean 0.00026± 0.00407 Sigma 0.0002± 0.9619

Pull5− 4− 3− 2− 1− 0 1 2 3 4 5

Freq

uenc

y PullEntries 1.524338e+07Mean 10− 9.001eStd Dev 0.977Underflow 0Overflow 0Integral 1.524e+07Skewness 0.2098−


Pull distribution

(�)

(�)(GeV/c2)

(GeV/c2)



• integrations with random seed of ~1000 events (MC, , , 1TagT)

15

22

mt = 173 GeV/c2 �JES = 0 �

�k,ij,l 8(k, i, j, l) {l 2 [1, 22] ^ k 6= (58, 330)}



Pull5− 4− 3− 2− 1− 0 1 2 3 4 5

Freq

uenc

y

0

10000

20000

30000

40000

50000

60000



Pull distribution


q-MC vs p-MC: estimation of precision

Given same termination parameters: (time, max n points, precision) Compare the histograms of:

More quantitative testing needed: time and convergence.

16

qMCEntries 690959Mean 0.09363Std Dev 0.07291Underflow 0Overflow 1091Integral 6.899e+05Skewness 5.177

µ/σ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N

0

2000

4000

6000

8000

10000

12000

qMCEntries 690959Mean 0.09363Std Dev 0.07291Underflow 0Overflow 1091Integral 6.899e+05Skewness 5.177

qMCpMC

Entries 887964Mean 0.1144Std Dev 0.07336Underflow 0Overflow 1982Integral 8.86e+05Skewness 4.798

µ/σ0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

N0

2000

4000

6000

8000

10000

12000

pMCEntries 887964Mean 0.1144Std Dev 0.07336Underflow 0Overflow 1982Integral 8.86e+05Skewness 4.798

pMC

rk,ij =�k,ij

< Wk,ij >8 k, i, j

< rk,ij >= 0.094 < rk,ij >= 0.11


New Transfer Functions

• Transfer Functions. Probability density relating:

measured quantities parton-level quantities (observed in detectors) (used for ME calculation)

• TF can be factorised in:

• New TF derived from MC simulations including loose categories ( ):• 1TagL• 2TagL

• For event with only tight categories old/new should produce the same results

17

T (x|y,�JES)

Et > 12GeV

T (x|y,�JES) = Ta(⌘jet,�jet|⌘part,�part)Tm(pt,jet|pt,part)

⌘jet,�jet, pt,jet ⌘part,�part, pt,part


MC Generated: PYTHIA, , , 0Tag category.

Old TF New TF

18

Comparison between New/Old TF: Single event

Event Ntight NLoose nbtags missingEt ev.lpt jet1pt jet2pt jet3pt jet4pt

7 4 0 0 49.4882 52.4504 64.0641 70.1314 40.4148 28.5606

Mt = 170GeV/c2 �JES = 0�

(�)(�)(GeV/c2)

(GeV/c2)


1000 ev MC Generated: PYTHIA, , ,1TagT.

19

Comparison between New/Old TF

LogL

400

600

800

1000

1200

1400

1600

1800

LogL

JES∆

3− 2− 1− 0 1 2 3

tM

160

165

170

175

180

185 LogL

400

600

800

1000

1200

1400

1600

1800

LogL

LogL

5400

5600

5800

6000

6200

6400

6600

LogL

JES∆

3− 2− 1− 0 1 2 3

tM

160

165

170

175

180

185 LogL

5400

5600

5800

6000

6200

6400

6600

LogL

Mt = 170GeV/c2 �JES = 0�

(�)(�)

(GeV

/c2)

(GeV

/c2)


Study of the sensitivity on Djes

• Analysis of 3 MC samples with different parameters:• signal events, , , 1TagT & 2TagT categories; • 10000 events for every sample.

• Calculate total : ;

• Create 1D histogram of profiled likelihood: , ; (using the profiled likelihood method)

• Extract , (assuming gaussian behaviour of the likelihood in the limit of large statistics);

• Plot the dependency , to the input ;

• Expected linear dependency to be corrected with calibration.

20

Mt = 172.5GeV/c2

log(L)

logL(Mt) logL(�JES)

�JESMt

Mt �JES

�JES,MC = {�1, 0,+1}

�JES,MC



21

�JES,MC = �1�

tM160 165 170 175 180 185

LogL

13000

14000

15000

16000

17000

18000

LogLLogL

JES∆3− 2− 1− 0 1 2 3

LogL

13000

14000

15000

16000

17000

18000

LogLLogL

JES∆2− 1.9− 1.8− 1.7− 1.6− 1.5−

tM

171

171.5

172

172.5

173

173.5

LogL

(�)

(�)

(GeV

/c2)

(GeV/c2)



22

�JES,MC = 0�

JES∆3− 2− 1− 0 1 2 3

LogL

15000

15500

16000

16500

17000

17500

18000

18500

19000

LogLLogL

tM160 165 170 175 180 185

LogL

13000

14000

15000

16000

17000

18000

19000

LogLLogL

JES∆1.6− 1.5− 1.4− 1.3− 1.2− 1.1− 1−

tM

170

170.5

171

171.5

172

LogL

(�)

(�)

(GeV

/c2)

(GeV/c2)



23

JES∆3− 2− 1− 0 1 2 3

LogL

18000

18500

19000

19500

20000

20500

LogLLogL

tM160 165 170 175 180 185

LogL

15000

16000

17000

18000

19000

20000

21000

LogLLogL

�JES,MC = 1�

JES∆1.1− 1− 0.9− 0.8− 0.7−

tM

168.5

169

169.5

170

170.5

171

LogL

(�)

(�)

(GeV

/c2)

(GeV/c2)



Linear dependence: expected to be corrected with calibration!

24

SampleJES∆1− 0.5− 0 0.5 1

JES

∆

1.8−

1.6−

1.4−

1.2−

1−

0.8− / ndf 2χ 30 / 1− 4.93eProb 1p0 0.02696±1.32 − p1 0.03179± 0.42

/ ndf 2χ 30 / 1− 4.93eProb 1p0 0.02696±1.32 − p1 0.03179± 0.42

Sample)JES∆ (JES∆

SampleJES∆

1− 0.5− 0 0.5 1

M_t

169.5

170

170.5

171

171.5

172

172.5

/ ndf 2χ 0.375 / 1Prob 0.5403p0 0.1155± 171 p1 0.1414±1.25 −

/ ndf 2χ 0.375 / 1Prob 0.5403p0 0.1155± 171 p1 0.1414±1.25 −

Sample) JES∆M_t (

(�)(�)

(�)

(GeV

/c2)


Future development of the analysis

• Further understand of qMC integration and implement error estimation;

• Include total cross section and acceptance as normalisation of the weights;

• Study the sensitivity on and with the complete weight definition;

• Debug the new TF;

• Test the methods for loose categories;

• Combine signal and background likelihood;

• Final calibration (pseudo-experiments);

25

Mt�JES


Backup Slides

26


Matrix Element Method: Motivation

• Provides superior Statistical sensitivity in the extraction of SM parameters;

• Completeness of information exploited in each event:• The superior sensitivity is achieved by taking into account the full topological and

kinematic information in a given event;

• Can be used to determine several parameters:• Theoretical parameters describing the physics of the processes measured;• Experimental parameters: describing the detector response;

• Theoretical assumption about the process under study (PDF, ME, TF) are used in the most efficient manner:• In the limit which all the event probabilities are known, by the Neyman-Pearson Lemma,

the likelihood is an optimal test statistic.

27

22 Sep 2016 Gabriele Franciolini | CDF Matrix element measurement of Top quark mass

Validation of the integration method : Pull Distribution qMC• qMC integration: sobol sequence of points instead of random sequence;

• Sobol sequence: LDS (Low-discrepancy sequence)

• Koksma–Hlawka inequality:

• Expected relative error: (faster convergence)

• Owen + Faure-Tezuka scrambling preserving LDS

• Importance sapling embedded in the code.28

��1

N

NX

i=1

f(xi)�Z

Is

f(u)du

�� V (f)D⇤N (x1, ..., xn)

�I/I ⇠ O(N�1+")

D⇤N (PN ) = Supa2A

��#{PN 2 A}

N� �(A)

�� , A =dY

i=1

[0, bi) 8bi s.t. 0 bi < 1


Integration Framework: Fermigrid

Director Libraries, paths …

Master Events

Workers: 1 2 3 4 5 6 …

• Program installation;• Learn job submission procedure;• Learn program errors handling;

• Learn to analyse data format consistent with ME analysis code

29

Local Machine

FermiGrid


Signal and Background : Monte Carlo Samples / Validation

• Signal:• signal: Powheg + Phytia S.Frixione et al., JHEP07 (2007)

• Background:• W/Z + jets: Alpgen+Pythia M.L. Mangano et al. JHEP0307:001 (2003)• Diboson: Pythia 6 T. Sjöstrand et al., JHEP06, 026 (2006)• Single top: Madgraph 4 + Pythia J. Alwall et al., JHEP09, 028 (2007) • QCD: Data with lepton failing one of the “good lepton” criteria

• Validation of Samples:• Validation plots : C. Tosciri-Laurea-University of Pisa• Compare quantity of interest between data and MC events of the samples

30

tt̄


Signal and Background: MC samples - Validation Plots

31


Backup Slides: Systematic Uncertainties

32

Bkg in Lev

New sgn MC

Remove overlap


Backup Slides: Expected and Observed Sample composition

Expected and Observed Sample composition

33


Backup slides: Selection requirements for event-category

Selection requirements for event-category

34


Matrix Element Technique 2

• Determines from:• Vector of observed data: event kinematics • Vector of model parameters: ,

• Probability: Integration over all phase space

• 32 variables of integration: 19 variables of integration:2 initial particles (8 var.) constraints 6 final particles (24 var.)

• Signal and Background for different

• Likelihood:

35

a

y

�! mt �JES

(mt,�JES)

d�(x) [tt̄ ! b(l⌫)b(qq0)]

� = lnpqpq0

, ~pT (tt̄), m1...4, ⌘1...4, �1...4

M2t,lep, M2

t,had, M2W,lep, M2

W,had

Pev(y|mt,�JES) = A(y)[fPsig(y|mt,�JES) + (1� f)PW+jets(y|�JES)]

L(y|mt,�JES) =NY

i=1

Pev(y|mt,�JES)

Pev(y|a)�!


Comparison between New/Old TF

100 ev MC Generated: PYTHIA, , , 0Tag.

Old TF New TF

36

LogL

60

80

100

120

140

LogL

JES∆

3− 2− 1− 0 1 2 3

tM

160

165

170

175

180

185 LogL

60

80

100

120

140

LogL

LogL

460

480

500

520

540

560

580

600

620

LogL

JES∆

3− 2− 1− 0 1 2 3

tM

160

165

170

175

180

185 LogL

460

480

500

520

540

560

580

600

620

LogLMt = 170GeV/c2 �JES = 0�

(�)(�)

(GeV

/c2)

(GeV

/c2)

CDF Top Quark Mass Measurement with the Matrix Element …eddata.fnal.gov/lasso/summerstudents/papers/2016/Gabriele-Franciolini.pdf• Lepton + jets events: one W boson decay hadronically,

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