Top Mass Reconstruction in Semi Electronic t Eventsparticles.ipm.ir/special seminar/materialDisplay-zeinali13bahman88... · Top Mass Reconstruction in Semi Electronic t t Events Maryam

Top MassReconstruction

inSemi Electronic tt̄

Events

Maryam Zeinali

Overview

Golden Channel

Event Selection

Software, Sample andSelection Cuts

25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance

Signal andBackgroundDistributions

Monitoring Variables

Training Variables

Testing the Method

How MVA Methodswork?

Top Mass Reconstructionin

Semi Electronic tt̄ Events

Maryam Zeinali

IPM Weekly Meeting

February 2 2010

1 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Outline

OverviewGolden Channel

Event SelectionSoftware, Sample and Selection Cuts25 GeV: Too Tight?

Jet-Parton MatchingAlgorithmPerformance

Signal and Background DistributionsMonitoring VariablesTraining VariablesTesting the MethodHow MVA Methods work?

2 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Outline





2 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Outline





2 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Outline





2 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview

I Goal? To measure the top quark mass

I How? Using tt̄ events, semi electronic decay channel

I Branching ratio? 19 ∗

69 ∗ 2 = 4

27 ≈ 15%

I Event signature? An energetic electron, four jets thattwo of them are b jets and missing transverse energy

I Backgrounds to suppress?? W+jets,? QCD,? single top,. . . but non of them are really matters!? The main background to top mass measurementcomes from the signal itself!

3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview

I Goal?

To measure the top quark mass



69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview


I How?

Using tt̄ events, semi electronic decay channel


69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview



I Branching ratio?

19 ∗

69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%

I Event signature?

An energetic electron, four jets thattwo of them are b jets and missing transverse energy


3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%


I Backgrounds to suppress?

? W+jets,? QCD,? single top,. . . but non of them are really matters!? The main background to top mass measurementcomes from the signal itself!

3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%


I Backgrounds to suppress?? W+jets,

? QCD,? single top,. . . but non of them are really matters!? The main background to top mass measurementcomes from the signal itself!

3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%


I Backgrounds to suppress?? W+jets,? QCD,

? single top,. . . but non of them are really matters!? The main background to top mass measurementcomes from the signal itself!

3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%


I Backgrounds to suppress?? W+jets,? QCD,? single top,

. . . but non of them are really matters!? The main background to top mass measurementcomes from the signal itself!

3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%


I Backgrounds to suppress?? W+jets,? QCD,? single top,. . . but non of them are really matters!

? The main background to top mass measurementcomes from the signal itself!

3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Overview




69 ∗ 2 = 4

27 ≈ 15%



3 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Golden Channel: Lepton + Jets Final State

I Leptonic side is used for triggering purposesI Four undistinguishable reconstructed jets at final state:

12 possible ways to reconstruct hadronic top 4-vector!4 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Software, Sample and Selection Cuts

I CMSSW 3 1 4 is usedI TTbar PYTHIA is skimmed at GenLevel to select only

semi electronic eventsI At least 4 jets are required to pass ET > 25GeV and|η| < 2.4

I Exactly one electron is asked to have these criteria:? pt > 20GeV and |η| < 2.4 excluding the gap? identified as RobustTight? reliso which is defined as the sum of all isolationvalues in a cone of 0.3 over electron ET should be lessthan 0.1

I Cut flow table:

Initial tt̄ events 485829Initial semi ele events 70925>= 4 Jet 46587== 1 Electron 21822

⇒ 66% pass cuts on jets. Cuts are abnormal?

5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Software, Sample and Selection CutsI CMSSW 3 1 4 is used

I TTbar PYTHIA is skimmed at GenLevel to select onlysemi electronic events

I At least 4 jets are required to pass ET > 25GeV and|η| < 2.4


I Cut flow table:



5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Software, Sample and Selection CutsI CMSSW 3 1 4 is usedI TTbar PYTHIA is skimmed at GenLevel to select only

semi electronic events

I At least 4 jets are required to pass ET > 25GeV and|η| < 2.4


I Cut flow table:



5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:



5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:



5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:



5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:

Initial tt̄ events 485829

Initial semi ele events 70925>= 4 Jet 46587== 1 Electron 21822


5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:

Initial tt̄ events 485829Initial semi ele events 70925

>= 4 Jet 46587== 1 Electron 21822


5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:

Initial tt̄ events 485829Initial semi ele events 70925>= 4 Jet 46587

== 1 Electron 21822


5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:



5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method





I Cut flow table:


⇒ 66% pass cuts on jets. Cuts are abnormal?5 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Distribution of Partons’pt in Semi ElectronicEvents

Leading jet pt Next leading jet pt

Next to next leading jet pt Next to next to next leading jet pt

6 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Jet-Parton Matching Algorithm

1. All events survived the selection cuts are fed to thejet-parton matching algorithm

2. Among four hard scattered partons, take the one withthe hardest pt .

3. Make a loop over all jets in the event. No cut is put onjets in the loop.

4. The jet with the minimum distance to the parton isflagged.

5. If ∆r < 0.3, jet is called as matched and removed fromthe list of jets.

6. Take the next leading parton and go to stp 2.

7 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method









7 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method









7 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method









7 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method









7 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method









7 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method









7 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Jet-Parton Matching Performance

I How the method works?

I Let’s define right and wrong jet combinations: Signaland Background? Take four leading jets in the event,? If all of them are matched to the partons, only oneamong 12 possible combinations contribute to signal.The other 11 possible ways take part in backgrounds.? If not all four leading jets matched to the partons,then all 12 combinations are considered as backgrounds.? For illustration: consider the number of initial eventsto be N and number of events with exactly 4 leadingjets have matched to the partons is S . Then thenumber of background contributions, B, can becalculated: B = S ∗ 11 + (N − S) ∗ 12.

I Now to see how good matching algorithm is, we cancompare Signal combination to the Gen Info.

8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method






8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method




I Let’s define right and wrong jet combinations: Signaland Background

? Take four leading jets in the event,? If all of them are matched to the partons, only oneamong 12 possible combinations contribute to signal.The other 11 possible ways take part in backgrounds.? If not all four leading jets matched to the partons,then all 12 combinations are considered as backgrounds.? For illustration: consider the number of initial eventsto be N and number of events with exactly 4 leadingjets have matched to the partons is S . Then thenumber of background contributions, B, can becalculated: B = S ∗ 11 + (N − S) ∗ 12.


8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method




I Let’s define right and wrong jet combinations: Signaland Background? Take four leading jets in the event,

? If all of them are matched to the partons, only oneamong 12 possible combinations contribute to signal.The other 11 possible ways take part in backgrounds.? If not all four leading jets matched to the partons,then all 12 combinations are considered as backgrounds.? For illustration: consider the number of initial eventsto be N and number of events with exactly 4 leadingjets have matched to the partons is S . Then thenumber of background contributions, B, can becalculated: B = S ∗ 11 + (N − S) ∗ 12.


8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method




I Let’s define right and wrong jet combinations: Signaland Background? Take four leading jets in the event,? If all of them are matched to the partons, only oneamong 12 possible combinations contribute to signal.The other 11 possible ways take part in backgrounds.

? If not all four leading jets matched to the partons,then all 12 combinations are considered as backgrounds.? For illustration: consider the number of initial eventsto be N and number of events with exactly 4 leadingjets have matched to the partons is S . Then thenumber of background contributions, B, can becalculated: B = S ∗ 11 + (N − S) ∗ 12.


8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method




I Let’s define right and wrong jet combinations: Signaland Background? Take four leading jets in the event,? If all of them are matched to the partons, only oneamong 12 possible combinations contribute to signal.The other 11 possible ways take part in backgrounds.? If not all four leading jets matched to the partons,then all 12 combinations are considered as backgrounds.

? For illustration: consider the number of initial eventsto be N and number of events with exactly 4 leadingjets have matched to the partons is S . Then thenumber of background contributions, B, can becalculated: B = S ∗ 11 + (N − S) ∗ 12.


8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method






8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method






8 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Mass of hadronic W− right jet combination

− Gen Info

9 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Mass of hadronic W: LOG scale− right jet combination

− Gen Info

10 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Pt of hadronic W− right jet combination

− Gen Info

11 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Mass of hadronic top− right jet combination

− Gen Info

12 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Mass of hadronic top: LOG scale− right jet combination

− Gen Info

13 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Pt of hadronic top− right jet combination

− Gen Info

14 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


∆φ(1st lightjet, 2nd lightjet)− right jet combination

− Gen Info

15 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


∑i p

lightjetit

− right jet combination

− Gen Info

16 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


∆φ(leptonicB , electron)− right jet combination

− Gen Info

17 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


∆φ(hadronicB , hadronicW )− right jet combination

− Gen Info

18 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


∆φ(leptonicB , hadronicW )− right jet combination

− Gen Info

19 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Monitoring variables that can discriminatebetween right and wrong jet combinations

20 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method



21 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method



22 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Correlation of variables for right jet combinations

23 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Correlation of variables for wrong jetcombinations

24 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Training Variables with TMVA: LikelihoodMethod

25 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Testing of the MVA Method: Likelihood

26 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Testing of the MVA Method: Likelihood

26 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Evaluation of the Results: Likelihood Method

27 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Evaluation of the Results: PEDRS Method

28 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Background Rejection Vs Signal Efficiency:Comparing Likelihood and PEDRS Methods

29 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Likelihood Method

Projective likelihood estimator (PDE approach)

I Builds a model out of probability density functions

I Reproduces the input variables for signal and background

I For a given event, the likelihood for being of signal type is

obtained by multiplying the signal probability densities of all

input variables, which are assumed to be independent, and

normalising this by the sum of the signal and background

likelihoods

I Because correlations among the variables are ignored, this

PDE approach is also called naive Bayes estimator

Classifier

I The likelihood ratio for event i , yL(i), is defined by:

yL(i) = LS (i)LS (i)+LB (i) where LS(B)(i) =

∏nvark=1 pS(B),k(xk(i))

? nvar is the number of input variables used

30 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Likelihood Method

Projective likelihood estimator (PDE approach)

I Builds a model out of probability density functions

I Reproduces the input variables for signal and background

I For a given event, the likelihood for being of signal type is

obtained by multiplying the signal probability densities of all

input variables, which are assumed to be independent, and

normalising this by the sum of the signal and background

likelihoods

I Because correlations among the variables are ignored, this

PDE approach is also called naive Bayes estimator

Classifier

I The likelihood ratio for event i , yL(i), is defined by:

yL(i) = LS (i)LS (i)+LB (i) where LS(B)(i) =

∏nvark=1 pS(B),k(xk(i))

? nvar is the number of input variables used

30 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


PDERS MethodMultidimensional likelihood estimator (PDE range-search approach)

I A generalization of the projective likelihood classifer to nvardimensions

I If the multidimensional PDF for signal and background were

known, this classifer would exploit the full information

contained in the input variables, and would hence be optimalI The PDE for a given test event (discriminant) is obtained by

counting the (normalised) number of training events that

occur in the ”vicinity” of the test eventI The classifcation of the test event may then be conducted on

the basis of the majority of the nearest training events

Classifier

I PDERS method takes the ratio yPDERS(i ,V ) =nS (i,V )

NSnS (i,V )

NS+

nB (i,V )

NB

as the estimator by defining a volume V around the test

event, i , and by counting the number of signal, nS(i ,V ) and

background events nB(i ,V ) obtained from the training

sample in that volume while NS(B) is the total number of

signal (background) events in the training sample

31 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


PDERS MethodMultidimensional likelihood estimator (PDE range-search approach)

I A generalization of the projective likelihood classifer to nvardimensions

I If the multidimensional PDF for signal and background were

known, this classifer would exploit the full information

contained in the input variables, and would hence be optimalI The PDE for a given test event (discriminant) is obtained by

counting the (normalised) number of training events that

occur in the ”vicinity” of the test eventI The classifcation of the test event may then be conducted on

the basis of the majority of the nearest training events

Classifier

I PDERS method takes the ratio yPDERS(i ,V ) =nS (i,V )

NSnS (i,V )

NS+

nB (i,V )

NB

as the estimator by defining a volume V around the test

event, i , and by counting the number of signal, nS(i ,V ) and

background events nB(i ,V ) obtained from the training

sample in that volume while NS(B) is the total number of

signal (background) events in the training sample

31 / 32



Events

Maryam Zeinali

Overview

Golden Channel

Event Selection


25 GeV: Too Tight?

Jet-PartonMatching

Algorithm

Performance



Training Variables

Testing the Method


Outlook and To Do List

I Although by applying event selection cuts thebackgrounds to the signal can be suppressed, top massreconstruction is suffering from a huge contribution ofcombinatorial backgrounds.

I The results reported are obtained by running TMVApackage based on ROOT. There is anotherimplimintaion of MVA methods based on CMSSWenvironment.

I The final analysis has to be moved to CMSSW framework sooner or later. Then it needs to synchronize thecode accordingly.

32 / 32

Documents

Top Mass Reconstruction in Semi Electronic t Eventsparticles.ipm.ir/special seminar/materialDisplay-zeinali13bahman88... · Top Mass Reconstruction in Semi Electronic t t Events Maryam