# Presentation: 666294

## Juan Estrada - Fermilab
for the DØ Collaboration

W&C Seminar

April 25, 2003

- New preliminary measurement of the mass of the top quark at DØ using Run I data

**Juan Estrada - Fermilab**
**for the DØ Collaboration**
**W&C Seminar**
**April 25, 2003**

- Juan Cruz Estrada - Fermilab

## Overview

- The lepton+jets decays of the top quark
- Introduction to the measurement of Mt
- Method used for this re-analysis
- Testing the analysis in simulated samples
- New preliminary Run I Mt measurement
- The mass of the W boson in the same sample
- Systematic uncertainties (JES)
- Conclusion

- Juan Cruz Estrada - Fermilab

## Lepton + jets channel

***p***

***p***

- Jet 3

- Jet 2

- Jet 1

- Jet 4

- 30% of the total
- significantly less background that the all jets channel.

- NOT
- detected

***Signature :***
***1 charged lepton***
***4 jets ***
***Missing energy***

- Juan Cruz Estrada - Fermilab

## Lepton+jets channel

**D****Ø ****Statistics Run I : 125 pb****-1**
**Standard Selections**** :**
-  Lepton: Et>20 GeV,|e|<2,||<1.7
-  Jets: 4, ET>15 GeV, ||<2
-  Missing ET > 20 GeV
-  “ETW ’’> 60 GeV ; |W |<2 **	****	**
**	****	****	****	****	****91 events**
*	**	**Ref.  PRD 58 (1998), 052001:*
- 		After 2(77 events):  ~29 signal + ~48 backg.
- 		(0.8 *W+jets* and 0.2 QCD)
**Specific cuts for this analysis**:
** ****4 Jets only :   ****	****	****	****71 events **
** ****Background Prob. :  ****	****	**_**22 events**_** **

- Juan Cruz Estrada - Fermilab

## Top Mass 

- For those of you who did not try to measure Mt..., this is how the mass distributions looks like.
- It is a challenging problem and that is why we have been applying _**sophisticated methods**_ making good use all the information that we have.

- fitted mass

- DØ , *PRD 58 52001, (1998)*

- standard
- selection

- Juan Cruz Estrada - Fermilab

## Template method Previous DØ and CDF publications

- Data => ***M******t***~B

- _Reducing the dimensionality of the problem_
- A multidimensional (xi) template is obtained for each value of the input mass, and the data sample is then compared with those MC templates to find the most likely value for ***M******t***:

- Template(xi;***M******t***=B)

- Template(xi;***M******t***=A)

- Some limitations:
- _prescribed permutation_ is selected on basis of a kinematic fit.
- _few variables_, containing most of the information, are selected for the templates.
- _single template_ fits the whole sample.

- Sample probabilities

- Juan Cruz Estrada - Fermilab

## DØ measurement using templatesPRD 58 52001, (1998)

- 2D templates
- (NN, fitted mass)

- MC studies give
-  8 GeV resolution

- Fit to data sample

- 100            200       mfit (GeV)

- Discriminator

- Discriminator

- mfit (GeV)

- mfit (GeV)

- Juan Cruz Estrada - Fermilab

## Measurement of Mt, two alternatives

-  Maximize:

- using templates

- But, if possible, it will be better to calculate a probability for each individual event

- Simple case with several types of events, each type follows a Gaussian distribution with width σk and mean M0.

- event weight depends on *m**i** *

- correct weighted average!!

- Juan Cruz Estrada - Fermilab

## Measurement of Mt, two alternatives

- 	If you have to choose between templates and event probabilities, consider the following points:
- The _**the greater the variation between the events the greater the difference in the two methods**_
- For _**templates you could actually introduce larger fluctuation if you add to your sample low quality events**_ (large σk), this will never happen for the correctly weighted average.
- 	*..note that there is no reason why analysis of same sample with two different methods should give you the same result, because methods are not totally correlated.*

- Juan Cruz Estrada - Fermilab

## Measurement of Mt using event probability

- 	...ok, the event probabilities are better.
- 	How do we calculate the events probabilities?
- 	(for templates, we just use MC simulation of the detector)
- 	The standard model predicts these probabilities  (differential cross section) in terms of the parton level quantities (four-vectors of all partons involved), *but we do not have access to parton level quantities for events in our data sample.*
- 	We will use only LO calculations, and I will show how far we can get with that. I will also show some problems due to our LO approximation...

- Juan Cruz Estrada - Fermilab

## Measurement of Mt using event probability(before we get into de details)

- _The probability for each event being signal is calculated as a function of the top mass_. The probability for each event being background is also calculated. The results are combined in one likelihood for the sample. (Similar to the methods of Dalitz, Goldstein and Kondo, Mt measurement in the dilepton channel by DØ - PRD **60** 52001 (1999) and idea by Berends et al for W+W- production.)

**P****signal**

**P****background**

**P(m****t****)**

**P****signal**

**M****t**

- Mt

- Mt

- Mt

- Mt

****

- Mt

- Mt

- Mt

- Mt

- P

- background event

- signal event

- Juan Cruz Estrada - Fermilab

##  Three differences between the two approaches

- Template Method

- This analysis

- All the events are presented to the _**same template**_. Average probability distribution.
- The template corresponds to a probability distribution for the entire sample, using _**selected variables**_ calculated from MC simulations.
- The _**features of individual events are averaged **_over the variables not considered in the template.

- Each event has its _**own probability distribution.**_
- The probability depends on _**all measured quantities**_ (except for unclustered energy).
- Each event contributes with its own  specific features to the probability, which _**depends how well is measured**_.

- Juan Cruz Estrada - Fermilab

## Calculation of signal probability

- 	If we could _**access all parton level quantities**_ in the events ( the four momentum for all final and initial state particles), then we would simply _**evaluate the differential cross section as a function of the mass of the top quark for these partons**_. This way we would be using our best knowledge of the physics involved.

*	*Since we do not have the parton level information for data, we use the differential cross section and _**integrate over everything we do not know**_*.*

- Juan Cruz Estrada - Fermilab

## Transfer function W(x,y)

***W(x,y)*** probability of measuring** x **when** y **was produced ** (*****x*** jet variables, ***y***** **parton variables):

- where
-            ***E******y******  ****  *      energy of the produced quarks
-           * ****E******x  ****   *      measured and corrected jet energy
-           * ****p******y******e       *****        **produced electron momenta
-            ***p******x******e******   *****  ****     **measured electron momenta
-            *********y****** ******j****** ************x******j***   produced and measured jet angles

- Energy of electrons is considered well measured, an extra integral is done for events with muons. Due to the excellent granularity  of the D calorimeter, angles are also considered as well measured. A sum of two Gaussians is used for the jet transfer function (*W**jet*), parameters extracted from MC simulation.

- Juan Cruz Estrada - Fermilab

##  Probability for tt events  (“d”)

-  2(in) + 18(final) = 20 degrees of freedom
-  3(e) + 8(1..4) + 3(Pin=Pfinal)+1(Ein=Efinal) = 15 constraints
- 20 – 15 = 5 integrals
- Sum over 24 combinations of jets, all values of the neutrino momentum are considered. Because it is L.O., we use only 4-jet events.
*********1******    *****        **momentum of one of the jets		***m******1******,m******2***         top mass in the event
***M******1******,M******2***     W mass in the event			***f(q******1******),f(q******2******)*** parton distribution functions (CTEQ4) for qq incident chann.
***q******1******,q******2***         initial parton momenta 			*********6******      ******  ******   *****  **six particle phase space
***W(x,y)***      probability of measuring x when y was produced in the collision
- We choose these variables of integration because |M|2 is almost  negligible,  except near the four peaks of the Breit-Wigners within |M|2.

- Juan Cruz Estrada - Fermilab

## Transfer function Wjet(x,y)

_**Models**_ the smearing in jet energies
- from effects of _**radiation, hadronization,**_*** ***measurement*** ***_**resolution**_ and jet*** ***_**reconstruction**__*** ***__**algorithm**_

- Correcting on average, and considering these distributions to be single Gaussians, can underestimate parton energies

- Use 2 Gaussians, one to account for the peak and the other to fit the asymmetric tails (light quarks and b quarks have separate parameters).

**asymmetries**

- Juan Cruz Estrada - Fermilab

## Transfer function in ttbar

**Solid Line:** Calculated by using the _**transfer function on partons**_
**Dashed: **Same as solid, but with a variant transfer function

**Top Mass**

- Juan Cruz Estrada - Fermilab

## Transfer Function in W+jets

**3 jets invariant mass**

- Invariant mass of three jets using W+4-jets events from VECBOS + ISAJET * (*Smooth curve, same as before). The shape is reproduced.... any bias introduced by non perfect agreement is calibrated using MC simulations.

- Juan Cruz Estrada - Fermilab

## Acceptance Corrections

- _Detector Acceptance_

- _Likelihood_

**Production probability***** ***

**Detector acceptance**

**Measured probability**

- where

- , Ngen(N) is number of generated(observed) events

- Juan Cruz Estrada - Fermilab

## Signal and Background

_**The background probability is defined only in terms of the main backgound**_ (W+jets, 80%)  which proves to be also  adequate for multijet background treatment in this analysis.
- The background probability for each event is calculated using _**VECBOS subroutines for W+jets**_.
- The values of _**c**__**1**__** and c**__**2**__** are optimized**_, and the likelihood is normalized automatically at each value of .

- Juan Cruz Estrada - Fermilab

## Background Probability

- We extracted from VECBOS events simulator the subroutines that calculate the matrix element for W+4 jets events. W. Giele helped showing us the way to use these subroutines.  For this probability we use MC integration:

- We integrate until we ensure the convergence.

- Juan Cruz Estrada - Fermilab

## Background Probability

- We extracted from VECBOS events simulator the subroutines that calculate the matrix element for W+4 jets events. W. Giele helped showing us the way to use these subroutines.  For this probability we use MC integration:

- We integrate until we ensure the convergence.

- Juan Cruz Estrada - Fermilab

## Testing this in Run I DØ using full MC

- Examples of product likelihood functions. _**Each example corresponds to one experiment with the statistics that D**__**Ø collected during **_
_**Run I.**_
- The signal(HERWIG) and background (VECBOS) events were run through the full DØ Run I simulation.

- Juan Cruz Estrada - Fermilab

## Blind Analysis

- This analysis was defined by MC studies, without looking at the data sample. One of the checks indicated that there could be a shift introduced by background contamination.

- Juan Cruz Estrada - Fermilab

## Extra selection in Pbkg

**In order to increase the purity of signal, another selection is applied on P****bkg****, with efficiencies:  ***********signal****** ******=0.70,  ************W+jets****** ******=0.30, ***
***                         ************multijets****** ******=0.23***

**P****bkg****<1E-11**

**ttbar@175GeV**

**W+jets**

- Juan Cruz Estrada - Fermilab

## Blind Analysis, purified sample

- This analysis was defined by MC studies, without looking at the data sample. One of the checks indicated that there could be a shift introduced by background contamination.

- ~0.5 GeV shift

- Juan Cruz Estrada - Fermilab

## Crosscheck of linearity of response

**Test of linearity of response with MC samples containing large numbers of events.**

- Juan Cruz Estrada - Fermilab

## Probabilities in Data

**Comparison of (****16  signal**** + ****55 background****) MC and data sample before the background probability selection. **

- Background probability

- Discriminator

- Juan Cruz Estrada - Fermilab

## Top probability in the background region

***-ln(P******tt******) as a function of M******t******  ***
*** ******for 10******-9******<P******bkg****** <10******-8******  ***

- Juan Cruz Estrada - Fermilab

## Top probability for signal region

***-ln(P******tt******) as a function of M******t******  ***
*** ******for 10******-12******<P******bkg****** <10******-11******  ***

- Juan Cruz Estrada - Fermilab

## New Preliminary Result

**M****t****= 180.1 ******** 3.6 GeV ******** SYST  - preliminary**
**This new technique improves the statistical error on M****t**** from 5.6 GeV [****PRD 58 52001, (1998)****] to 3.6 GeV. **_**This is equivalent to a factor of  2.4 in the number of events.**_**  ****22 events pass our cuts, from fit: (12 s + 10 b)**
**(0.5 GeV shift has been applied, from MC studies)**

- Juan Cruz Estrada - Fermilab

## MC studies with 12s+10b

- The MC simulations show that the results obtained are consistent with expectations.

- Juan Cruz Estrada - Fermilab

## Varying the background probability selection

- The result is very stable with respect to the selection on background probability.

- Juan Cruz Estrada - Fermilab

## Comparing results in data and MC

- mass

- stat.err.

- uncertainty from JES

- PRD** 58 52001, (1998)**

- (new)

- [GeV]

| 173.3 | 5.6 | (NN)      (LB)
8.0      8.7  | 4.0
 |
| --- | --- | --- | --- |
| 180.1 | 3.6 | (12s+10b) 
5.4 | 3.3 |

- data

-   expected

- PRD** 58 52001, (1998) : 71 events **
**NN  =  24 ± 8**
**LB  =  29 ± 8**

- New** : 22 events **
**n****S****  =  12 ± 4 (measured sample)**
- corrections:0.70(4 jets)x0.71 (Pb)
**N****S**** =  25 ± 7 (in the 1998 sample)**

- Number of top decays

- Juan Cruz Estrada - Fermilab

## Compatibility between 1998 and 2003

- Assume there is _**no systematic difference between the two methods**_
- and that both methods give an unbiased measurement of Mt .
- 		1998  (24 events)	          	(173.3 ± 5.6) GeV
- 		2003  (12 ev. subsample)	(180.1 ± 3.6) GeV
- If the methods were the same and _**all the events had the same**_
_**resolution**_: σ24=5.6  σ12=7.9, the fluctuations is 24 events when you
- vary only 12 is σ12/24=7.9/2=4.0  the difference is therefore 1.7 σ
- 2.  Both methods are not the
- same (see introduction), and
- all the events have their own
- width, no reason to expect the
- same result... even with the same
- sample.  Simple case, σ12/24=5.0,
-  the difference is 1.4 σ

- Juan Cruz Estrada - Fermilab

## Check of Mw with DØ Run I Data

- 80.9 ± 2.6 GeV

**Can **_**help reduce the uncertainty in the jet energy scale (JES**_**)**** see:**_[http://dpf2002.velopers.net/talks_pdf/120talk.pdf](http://dpf2002.velopers.net/talks_pdf/120talk.pdf)_** (DPF2002 proceedings)**
**1.5 GeV shift is applied and 20% increase in the error, from MC studies. We associate this shift to effects from our L.O. approximation.**

- Juan Cruz Estrada - Fermilab

## Number of events for signal and backg(something to consider in the future)

- Number of events for signal and backg(something to consider in the future)

**Because of radiation, ~20% of the signal events look more like background than signal. When only events with good jet-parton matching are used, this is resolved (better treatment of higher order effects will help).**

- Juan Cruz Estrada - Fermilab

## MW, MC studies

- We see that the signal events that are reconstructed as background are responsible for the 1.5 GeV shift in MW.
- This will have to be solved if we want high precision top physics (~1 GeV). Higher order corrections will have to be included.

- Juan Cruz Estrada - Fermilab

## Jet Energy Scale (main systematic effect)

- We use a _**Monte Carlo simulation of the detector to build the transfer function**_ (or the templates in our previous analysis).
-  It is essential to _**check that the energy scale in the MC simulation is representative of that in the detector**_. This can be done for the electromagnetic showers using Ze+e- decays. It is _**not so easy to do for hadronic showers**_.
- Our _****__**+jet sample gives 2.5% uncertainty in JES.**_  In 1998 this translated to 4.0 GeV in Mt.

- Juan Cruz Estrada - Fermilab

## Systematic Uncertainty JES(presented HCP2002)

_**Using a sample of **__****__**+jet**_ [PRD 58 52001, (1998)] we got a function that matches the JES in MC and data with 2.5%+0.5 GeV uncertainty per jet.
- For the result presented in HCP2002 (analysis tools session),_** we did the analysis of data with and without this correction**_.
- This was a _**very conservative approach**_, because we just wanted to demonstrate the statistical power of the analysis.

- Et  (GeV)

-           1                            2    *η*

- Juan Cruz Estrada - Fermilab

## Systematic error due to JES

- For the result presented here, we are using the previous calibration and its uncertainty for each jet: ±(2.5%+0.5 GeV).
******JES****=3.3 GeV**

- Consistent with MC expectations

- Juan Cruz Estrada - Fermilab

## Systematic uncertainty due to top-production model

**u: fraction of events in the experiment where all the jets can be matched with partons from top quark decays. Increasing the fraction u, effectively turns on radiation and hadronization effects.  The systematic uncertainty is:**
**	********=1.5 GeV**
**(Each point corresponds to the maximum of a likelihood for a large event sample).**
** **

**Herwig MC with official D****Ø simulation**

- Juan Cruz Estrada - Fermilab

## Total Uncertainty

- I. Determined from MC studies with large  event samples:

| Signal model | 1.5 GeV |
| --- | --- |
| Background model | 1.0 GeV |
| Noise and multiple interactions PRD 58 52001, (1998) | 1.3 GeV |

- II. Determined from data:

**                            ****Total systematic:****	****4.0 GeV**
**         ****M****t**** = 180.1 ****±**** 5.4 GeV  (preliminary)**

| Jet Energy Scale | 3.3 GeV |
| --- | --- |
| Parton Distribution Function | 0.2 GeV |
| Acceptance Correction | 0.5 GeV |

- Juan Cruz Estrada - Fermilab

## New [preliminary] Result

- _The relative error in this result is 3%_, compare to 2.9% from the previous CDF and DØ combined average for all channels.

- Juan Cruz Estrada - Fermilab

## Conclusions 

** ****	****Using LO approximation (and parameterized showering) we calculated the event probabilities, and measured:       **
**M****t****=180.1 ******** 3.6 (stat) ******** 4.0 (syst) GeV   preliminary**
**	****Significant improvement to our previous analysis****, ****is ****equivalent to 2.4 times more data****:**
- Correct permutation is always considered (along with the other eleven)
- All features of individual events are included, thereby well measured events contribute more information than poorly measured events.
- To consider for the future:
- The possibility of checking the value of the *W* mass in the hadronic branch on the same events provides a **new handle on controlling the largest systematic error**, namely, the jet energy scale.
- A very general method (application to W boson helicity, Higgs searches, .... )

- Juan Cruz Estrada - Fermilab