# Presentation: 153458

## Top Quark Mass Measurement with Dynamical Likelihood Method at CDF RunII

**Top Quark Mass Measurement with Dynamical Likelihood Method ****at CDF RunII**

_**Kohei Yorita**_
**Kunitaka Kondo**
**Waseda University , Japan**
**For the CDF collaboration**
** ****~ FNAL Wine & Cheese Seminar ~**
**on June 11****th****, 2004**

## Outline of this talk

**Outline of this talk**

**Introduction**
**Data Sample & Event Selection**
**Dynamical Likelihood Method ****(DLM)**
**Signal Monte Carlo Studies**
**Background Effects**
**Current Results from RunII**
**Systematic Uncertainty**
**Various Checks **
**                   ****& Some Comparisons**
**9.    Conclusions**

**                   ****Ms. Particle**
**Q: How many particles in me?**

## Top quark production and decay

**Top quark production and decay**

** ****Dilepton (e,********) ****	****BR=5%**
** ****Lepton (e, ********) +jets****	****BR=30%**
** ****All jets****	****	****BR=44%**
**  ******** ****+ X ****	****	****             BR=21%**

_**Final states :**_

*** Higher statistics **
*** Lower background**

**Use this channel with**
**at least 1 bjet. **

**The Tevatron is the only**
**place which can produce**
**top quark until LHC runs!**

**qq , gg fractions **
**reversed at LHC**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              3/41  ***

_**Tree level :**_

****** ****= ****5.8 ~7.4 pb ****at 1.96TeV**
**(Cacciari et al.)**

##   Why is Top Mass interesting?

**  ****Why is Top Mass interesting?**

**Special Relation to Higgs mass, together with W boson mass.**

**(1)  Fundamental Standard Model parameter.**
**(2)  Top quark is heavy (~ 180 GeV)**
**        ****Yukawa coupling  ~ 1.****  **
**    **** ***** The mass is near the Electro-Weak Symmetry breaking scale.**
**     ***** If we can measure strength of this coupling (i.e.ttH), **
**        ****a test of the Higgs sector in the SM can be done.   **

**RunII Goal : 2 ~ 3 GeV! **

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              4/41  ***

**(4) More detailed studies of top events **
**     ****by using “M****top ****” can be performed.**
**     ****i.e. ttbar resonance, P/CP test, **
**     ****W helicity, new particle search etc. **

## Review of Run I Results

**Review of Run I Results**

**    ****New World Average (2004)  ****     *****M******t****** = 178.0 ************ 4.3 GeV***** *****(************2.7************3.3)***
**                                               *****hep-ex/0404010***

***     ******M******t****** = 174.3 ************ 5.1 GeV (************3.2************4.0)***
***                                      ******(Fermilab-TM-2084)***

**Old World Average (1999)**

**New D****Ø l+j measurement,**
**  ****(Nature 429, 638-642 (2004))**

**Standard Model Higgs Mass: **

**Most probable:         96 GeV  ******** 113 ********    GeV Upper limit****(95% CL)****:219 GeV  ******** 237 GeV**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              5/41  ***

**62 **
**42**

## RunII Data at CDF

**RunII Detector Upgrades**

**Record initial luminosity **
**        ****= 8.2 ******** 10****31**** sec****-1**** cm****-2**

**Data taking efficiency ~80-90%**

** ****New silicon tracker (7-8 layers) (|********|<2)**
** ****New central drift chamber**
** ****New time of flight detector**
** ****Extended muon coverage (|********|<1.5)**
** ****New DAQ**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              6/41  ***

** ****In this analysis,**
** ****We use **_**162 pb**__**-1**_** collected **
** ****until September 2003.**
** ****Cf) RunI ~110 pb****-1**

## Event Selection

**Observed events : **

- One lepton : central electron / muon
-        Et(Pt) > 20 GeV,  |eta| < ~1.0
- Met > 20 GeV
- 4 tight jets : Et > 15 GeV, |eta| < 2.0
- At least one SVX b-tagged jet

**Kinematical cuts for “lepton+jets”**

**SVX b jet tagging**

** ****Exactly 4 jets**

- We do not use the events
- with more than 4jets,
- to minimize the
- contaminations by initial
- and final state radiation.

- B hadrons are
- long-lived.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              7/41  ***

- Identify by Vertex
- of displaced tracks

**Total ****22**** events ; electrons 12,  muons 10**

## DLM Introduction

**DLM Introduction**

**- Originally proposed in 1988 by K. Kondo.(J.Phys. Soc. 57, 4126)**

**The Method  :**

**- Basic idea is to use matrix elements convoluted likelihood.**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              8/41  ***

## Likelihood Definition in DLM

**Likelihood Definition in DLM**

_***For i-th event,***_*** likelihood is defined as,***

*M* : Matrix element of tt process,

*F* : Parton distribution function for (za,zb) and Pt of tt system

*w* : Transfer function,   x ; partons             y ; observables

** ****M****top**** = M****top *****min.***

_***Two Summations and one integration :***_
*I**t *: Possible combination(Jets to partons) ,       *I**s *: Two z solutions,
- In practice, integration of x, sw made by Monte Carlo Method.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              9/41  ***

_***Extract top mass by maximum likelihood method,***_

- Sw=(l+)2

## Performance :

- Mtop (GeV)

- 165

- 185

**10 events likelihood distributions: L(M)**

_***For ppt user!***_

_***Demonstration!!!***_

***Performance :***

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              10/41  ***

## Transfer Functions ; w~ Jets to Partons ~

**Transfer Functions *****; w******~ Jets to Partons ~***

**Jet Measurement and Energy Scale Correction at CDF**

- Transferred variable =

**Transfer function **
**    ****-  To Go back to partons from jets, it is necessary.**

- We start with jets corrected by,
- (1) Calorimeter non-uniformity
- (2) Calorimeter Scale
- (3) Jets to hadrons

- All jets are formed by dR=0.4 cone cluster algorithm.

-  At present, we ignore the difference of directions between parton & jets.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              11/41  ***

## Transfer Functions ; w~ Jets to Partons ~

**Transfer Functions *****; w******~ Jets to Partons ~***

_***b jets***_

_***b jets***_

_***w jets***_

_***w jets***_

**Et bin : 9 bins**
**15-25-35-45-55-65-75-85-95-<**

**Eta bin : 3 bins**
**Central  < 0.7**
**Wall       0.7~1.32**
**Plug       > 1.32**

**Strong Et dependence **

- is asymmetric and depends on Et &of the jets.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              12/41  ***

- 30 histograms for each b/w jet.
- We do not fit them, but random
- generation along the shape to get
- parton momenta.

## Transfer Function performance

**Transfer Function performance**

|  | W mass <RMS> (GeV) | Top mass  <RMS> (GeV) |
| --- | --- | --- |
| Before TF | 71.4 <12.8> | 152.1 <20.4> |
| After TF | 80.9 <12.2> | 174.8 <19.1> |

**2jets W mass**

**3jets Top mass**

****** ****dependence**

**Pt dependence**

_***CDF sim.***_

_***CDF sim.+TF. ***_

**Comparisons between (CDF sim.)  and (CDF sim.+Transfer function)**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              13/41  ***

**Means are back to inputs and RMS gets better after TF.**

**Input W : 80.4 GeV**

**Input top : 175 GeV**

_***CDF sim.***_

_***CDF sim.+TF. ***_

**M****top**

**M****w**

**M****top**

**M****w**

## Transfer function Top Mass dependence

**Transfer function ****Top Mass dependence**

**bjet has the top mass dependence.**

_***b jets***_

_***w jets***_

**We use the transfer function obtained from M****top****=175 GeV .**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              14/41  ***

- Plots: Mean of

- as a function of Et of jets.

## Monte Carlo signal studies

**Monte Carlo signal studies**

- _22 events Pseudo expts using M__top__ = 175 GeV sample_

- _Different Mass sample_

- Center of pull is consistent with 0.

- Width is consistent with 1.0.

- _Default Slope : 0.83_

- Slope : 0.98

- Transfer function from 175 GeV.

- Use Transfer function at each mass.
- ex) 160 GeV sample        160 GeV TF.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              15/41  ***

- Due to mass dependence of TF.
- Use this slope to get input mass.
-           Signal only mapping slope !

- Q: Is this really coming from only TF?

- _A: Yes, checked,_

## Pull distributions(signal only)

**Pull distributions(signal only)**

**Center of Pull**

**Width of Pull**

**Outputs from 1000 sets of 22 signal events pseudo expts.**
**after the correction to each set.**

- By taking into account the slope as a mapping function,
- top mass can be reconstructed correctly, no input mass
- bias for the center and width.     In fact,.........Go next slide.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              16/41  ***

## Test Using Blind Samples madeby CDF top mass group

-  Six top mass samples: generated with randomly selected top masses
-     using  Herwig or Pythia. (200k events each).
-  For users: unknown ( top mass, Herwig or Pythia)
-                       known (no backgrounds,  masses are in reasonable range)

**A**

**B**

**C**

**D**

**E**

**F**

**DLM promises no biases and good performance(<1.0 GeV)!**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              17/41  ***

**Error stat only**

## So far, We have studied Signal Monte Carlo and got reasonable results without bias by correcting transfer function mass dependence.

Let’s move to a treatment of the backgrounds.
  We need to understand the background effects on signal likelihood distribution.

**Let’s move to a treatment of the backgrounds.**
**  ****We need to understand the background effects on signal likelihood distribution.**

**Very Short Summary on the way...**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              18/41  ***

## Background Estimate

**Background Estimate**

|  | Expected Number of events |
| --- | --- |
| W+light flavor | 1.2 ± 0.37 |
| Wbb | 0.7 ± 0.29 |
| Wcc | 0.3 ± 0.12 |
| Wc | 0.2 ± 0.12 |
| Single top | 0.17 ± 0.03 |
| WW | 0.08 ± 0.05 |
| QCD | 1.6 ± 0.38 |
| Bkg total | 4.2 ± 0.71 |
|  N observed | 22 |
| tt (6.7pb) | 20.9 |

**The background fraction **
**is estimated to be 19 ******** 5 ****%**

**Counting Method**

**Publication of this result **
**coming soon.**

**In the method, first, all events**
**are assumed to be signal. **
**Need correct background effect. **

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              19/41  ***

## Understanding of background ~ Likelihood Distributions ~

**Understanding of background ****~ Likelihood Distributions ~**

**We expect the background makes likelihood peak down ****when it is multiplied to signal events. **

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              20/41  ***

- CDF simulation

- Parton Level

- Typical –2ln(likelihood)
- distributions for signal
- and backgrounds.

**Signal**

**background**

**Signal:175GeV**

**background**

- Backgrounds : lower mass
- Signal            : input mass

- Peak :

- Absolute value of
- likelihood in signal
- is much larger than
- that in background

## Background Effects Details

**Background Effects Details**

- Reconstructed Mass Shift due to
- each background source.

- Reconstructed mass from 22
- events Pseudo expts. by varying
- background fraction.

- Mt=175 signal sample is used and Background Numbers are Poisson fluctuated.

- The size of shift is different in each source. But W+LF(mistag), QCD and Wbb(>80%) have similar behavior.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              21/41  ***

- Mass is shifted lower by background increase.
- Resolution also gets worse.

## The Mapping Function

**The Mapping Function**

- Parameterization of the slope and the constant of the fit

_***Slope***_

_***Constant***_

- The mapping function is obtained
- from 2000 sets of 22 events(fixed)
- pseudo experiments in each point,
- by varying the background fraction
- with Poisson distributed.

- Mass dependent correction factor.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              22/41  ***

- The background estimate in our
- sample is 19%.

## How to apply the mapping function?

**How to apply the mapping function?**

- Input :    (1) Reconstructed Mass & Error from the sample
-               (2) Background fraction in the sample

- Example

- Extract the top mass

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              23/41  ***

- * Statistical errors are also
-   scaled by the slope properly.

- (1)

- (2)

## Pull distribution ofS:17.8ev + B:4.2ev = 22 events

**Pull distribution of****S:17.8ev + B:4.2ev = 22 events**

- Plots after applying the
- mapping function of 19%
- background to each output
- mass .

- No bias ! Even if the sample includes backgrounds.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              24/41  ***

**Center of Pull**

**Width of Pull**

## Extracted top mass from RunII

**Extracted top mass from RunII**

** ****Observed  :Total ****22**** events; electrons 12, Muons 10**

**Correct background-pulling**
**4.2 events expected.**

- Fit : Two 2nd order polynomials for positive/negative errors.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              25/41  ***

## Expected statistical uncertainties

**Expected statistical uncertainties**

**Before Mapping function applied**

**After Mapping function applied**

- Black arrows : Data  + 3.4,  – 3.8 GeV

- Black arrows : Data  + 4.5,  – 5.0 GeV

**Stat. error is scaled by ~30% ,**
**due to the mapping slope.**

**Mean : + 4.2,  ****– ****3.8 ****GeV**
**MPV  : + 3.5,  ****–**** 3.2 GeV**

**Mean : + 5.4,  ****– 5.0 GeV**
**MPV  : + 4.5,  ****– 4.1 GeV**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              26/41  ***

## Systematic uncertainty

## Jet Energy uncertainty

**Jet Energy uncertainty**

| Description | Mtop GeV |
| --- | --- |
| Calorimeter non-uniformity | 2.6 ± 0.1 |
| Central Calorimeter Response | 4.2 ± 0.2 |
| Corrections to Hadrons | 2.0 ± 0.1 |
| Total | 5.3 ± 0.3 |

_**Jet Energy Scale**_

**Shift for one of part of JES.**
****** ****uncertainty**

_**Transfer Function**_

**“****Jets             Parton Probability density”**

-  Took out-of-cone corrections uncertainty for fragmentations,  _**1.6 GeV**_
-  Hadronization model is already included in generator systematics.
-  Correlated ISR/FSR, jet smearing 15%.
-  It is very hard to validate whether the shape of transfer function in MC
-   can represent that of data correctly.  We will continue the works by doing,
-                   (1) hadronic W mass,  (2) Z           bb,   (3) bjet-gamma balance e.t.c
-          For now, we take 2.0 GeV error to be conservative.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              28/41  ***

## ISR/FSR uncertainty

**ISR/FSR uncertainty**

**We have now the following two samples set the parameters range by **
**comparing with Drell-Yan data.**

| Description |  Mtop = M - Mdefault |
| --- | --- |
| ISR less | – 0.2 ± 0.2 GeV |
|   ISR more | + 0.3 ± 0.2 GeV |

**ISR systematic : 0.5 GeV**

**More ISR  : ********QCD**** = 384, K = 0.5**
**Less  ISR  : ********QCD**** = 100,  K = 2.0**
**    ****Run I: no ISR: K = infinite**

| Description |  Mtop = M - Mdefault |
| --- | --- |
| FSR Less | –  0.4 ± 0.2 GeV |
|  FSR More | +  0.5 ± 0.2 GeV |

**FSR systematic : 0.5  GeV**

**More FSR  :  ********QCD**** = 384, K = 0.5**
**Less FSR  :  ********QCD**** = 100,  K = 2.0**

_**ISR (Initial State Radiation)**_

_**FSR (Final State Radiation)**_

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              29/41  ***

**We checked several ways such as On/Off, diff ********s ****, RunI like.**

## Parton Distribution Function

**Parton Distribution Function**

| Sources |  Mtop GeV |
| --- | --- |
| (1)  | 1.4 ± 0.4 |
| (2) | 0.6 ± 0.2 |
| (3)  | 1.1 ± 0.3 |
| Total | 1.9 ± 0.5  |

**PDF systematic : 2.0 GeV**

**Add in quadrature the following,**
**(1) CTEQ6M 20 pairs of eigenvectors**
**(2) Two different ********s**** with MRST**
**(3) CTEQ5L vs MRST**

_**PDF General**_

_**NLO vs LO PDF**_

**PDF**** :gg 15%(NLO), 5%(LO) **

**NLO PDF effect : 0.4 ****±**** 0.2 GeV**

**We reweight gg contribution to 15%(NLO) from 5%(LO).**
**This makes a difference of 0.4 GeV.**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              30/41  ***

## Other Systematic uncertainties 

**Other Systematic uncertainties **

_**Generator**_

**Pythia and Herwig**

_**0.6 **__**±**__** 0.2 GeV**_

**(also checked Grappa,  0.6 GeV)**

_**Spin correlations (Herwig)**_

**We ignore spin corr.matrix **
**element in the likelihood.**
**On/Off difference is 0.7 GeV**

_**0.4 **__**±**__** 0.2 GeV**_

_**Additional jet smearing**_

_**0.6 **__**±**__** 0.2 GeV**_

_**Unclustered Energy**_

_**0.1 **__**±**__** 0.2 GeV**_

_**Background Modeling**_

_**Background Fraction**_

_**0.5 GeV**_

_**0.5 GeV**_

**Error due to 19****±5%**

**Resolution underestimated in our MC**
**Additional 15% gives**

**The effect of difference for**
**Unclustered calorimeter energy**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              31/41  ***

## Systematics Summary

**Systematics Summary**

| Sources | Mtop(GeV/c2)   |
| --- | --- |
| Jet Energy Scale | 5.3 |
| ISR | 0.5 |
| FSR | 0.5 |
| PDF | 2.0  |
| Generator | 0.6  |
| Spin correlation | 0.4  |
| NLO effect | 0.4 |
| Bkg fraction(±5%) | 0.5 |
| Bkg Modeling | 0.5 |
| MC Modeling(jet,UE) | 0.5 |
| Transfer function | 2.0  |
| Total | 6.2  |

**Dominated by **
**Jet Energy Scale.**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              32/41  ***

**More understanding of**
**transfer function will **
**reduce the error.**

**Avoid both under/over**
**estimate.(correlations)**

**Improvements by a better understanding of our simulation i.e. calorimeter response will be coming very soon.**

## CDF RunII Preliminary Results Summary

**CDF RunII Preliminary Results Summary**

|  | TemplateMethod | Multivariate Method | DynamicalLikelihoodMethod |  TemplateMethod
(125pb-1) |
| --- | --- | --- | --- | --- |
| Expected    Statistical Uncertainty | 7.3 | 6.4 | + 5.4 (4.5)
– 5.0 (4.1) | 13.9 |
| Results |  |  |  |  |
| Total Measured Uncertainty | +   9.6– 10.1 | + 9.3
– 9.3 | + 7.7– 8.0 | + 19.2– 18.9 |

**174.9       ****±6.5**

**+7.1**
**–****7.7**

**179.6       ****±6.8**

**+6.4**
**–****6.3**

**177.8       ****±6.2**

**+4.5**
**–****5.0**

**175         ****± 8.4**

**+17.4**
**–****1****6.9**

- : Monte Carlo

- : Data

**Lepton+jets (btag)**

**Dilepton**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              33/41  ***

- Currently DLM is the most precise
- measurement in RunII.

## More checks of MC vs Data (1)

**More checks of MC vs Data (1)**

- For i-th event,

- An event has one likelihood.

- _Event likelihood_

- More likely to be background

- Although absolute value
- does not have any meaning,
- we can compare Monte
- Carlo with Data directly.

- Agreement is quite good !

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              34/41  ***

## More checks of MC vs Data (2)

**More checks of MC vs Data (2)**

- Maximum Likelihood mass
- in each event from MC .

- How about Maximum likelihood mass in each event?
- (gives us shape information!)

- Signal RMS :  ~22 GeV
- cf) Template: ~30 GeV

- Comparison between
- MC and Data.

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              35/41  ***

## Conclusions and Plans

**Conclusions and Plans**

** ****From 22 events with 4.2 event background**
**  ****(162 pb-1),  We measured top mass by DLM to be,**

**M****top**** = 177.8 ****±****     (stat.) ****±**** 6.2 (syst.)GeV/c****2**

**4.5**
**5.0**

_**Top Mass Results**_

_**Things to do**_

**-- Hadronic W mass measurement in this channel.**

** ****Currently, this is the most precise measurement using**
**  ****RunII data.**

**Total:         GeV/c****2**

**+7.7**
**–****8.0**

**Cf) world average :**
**178********4.3 (********2.7********3.3)**** GeV/c****2**

**-- Reduce systematics (JES!) **

**-- Get more data.**

**DLM is a very powerful method which can test both the**
**Standard model and beyond.**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              36/41  ***

## Backup slides

**Backup slides**

## More comments on DLM

**More comments on DLM**

**d******** : assume that each final state parton occupies **
**      ****a unit phase volume in each event.**

**1. Normalization, **

**2. Phase space,**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              38/41  ***

**N(y) gives no effect on top mass measurement.           constant**

- (1)

- (1)

- In principle,

## Comparisons between   DLM and DOM(RunI)

**Comparisons between   DLM and DOM(RunI)**

**~ These two Method look very similar, but Not identical! ~**

|  | DLM(RunII) | DOM(RunI) |
| --- | --- | --- |
| Event | b-tagged ,only 4jets (22)
No more.. | Non-btag, only 4jets (71)
Background likelihood cut (22) |
| Background

Treatment | 4.2 events (~20%)
(QCD Fake 40%)
Mapping  | 10 events (~50%) 
(W+jets 85%)
In the likelihood |
| Likelihood | Signal likelihood only | Signal and background likelihood |
| Others | - | Normalization & acc correction |

**DLM :**

**DOM :**

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              39/41  ***

## More on backgrounds

**More on backgrounds**

- Single top

- Mistag

- Wcc

| source | Joint likelihood |
| --- | --- |
| Mistag | ~162 GeV |
| Wbb | ~162 GeV |
| Wcc | ~157 GeV  |
| Wc | ~158 GeV |
| nonW | ~161 GeV |
| Single top | ~170 GeV |
| WW | ~160 GeV |

**5 events pseudo experiment using only each background source**

- (Wbb/nonW)

- (Wc/WW)

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              40/41  ***

**Max. likelihood mass in each event**

**Mapping slope**

## How Likelihood looks like?

**How Likelihood looks like?**

- Signal example: - log(likelihood)

- Blue : all added up
- Red  : right comb.
- Black : wrong comb.

- Blue : all added up
- Black : each comb.

- Peak around 175 GeV

- Likelihood tends to be higher in
- lower mass region.

- Range[155-195]GeV

- Bkg example: - log(likelihood)

_**25 events examples using generator level input**_

***   ******June 11******th****** , 2004                            FNAL W&C Seminar -  Kohei Yorita                                              41/41  ***