# Presentation: 224072

## Optimal Use of Information for Measuring Top Mass in lepton+jets tt Events

** ****Breese Quinn, Fermilab**
- for the DØ Collaboration
- DPF2003

** ****General introduction**
** ****Explanation of the optimized method used in the new M****t**** measurement **
** ****Preliminary Run I measurement of ****M****t  ****using optimized method**
** ****Systematic errors**
** ****Conclusions**

**Notes:**

Explain plots more

More physics, less technical, esp after slide 25,26

Watch jargon

## Event topology and selections

**Standard Selection :**
- Lepton: ET>20 GeV,|e|<2,||<1.7
- Jets: 4, ET>15 GeV, ||<2
- Missing ET > 20 GeV
- “ETW ’’> 60 GeV ; |W|<2
**Gives 91 events**
*Ref.  PRD 58 (1998), 052001               ***M****t****= 173.3 ******** 5.6 (stat) ******** 5.5 (syst.) GeV****            **
- After 2  77 events
- 29 signal
- 48 backg. (80% *W+jets*, 20% QCD)
**Additional cuts for this analysis**:
**4 Jets only ******** 71 events **
**Background Prob. ******** 22 events**

_**D**__**Ø Statistics Run I (125 pb**__**-1**__**)**_

- B. Quinn FNAL

- DPF2003 April 5-8

## Published measurements of Mtat DØ and CDF

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

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

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

**A multidimensional (x****i****) 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*****: **

**A prescribed jet permutation is selected on the basis of a kinematic fit.**
**A few variables, containing most of the information, are selected for the templates.**
**The background is accounted for using a separate template. **
**A likelihood is built to select the templates closest to the data.**

- B. Quinn FNAL

- DPF2003 April 5-8

## Approach for new Mt measurement by DØ   

***Approach for new M******t****** measurement by D******Ø  ****** ***

**background- **
**like event**

**signal-like events**

****

****

****

*For each event, signal and background probabilities are added. The probabilities for individual events are then multiplied together.  All jet permutations are considered.*

**P****signal**

**P****background**

**m****t**

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

- 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 into one likelihood for the sample.

- Similar to the methods of Dalitz, Goldstein and Kondo, and Mt measurement in the dilepton channel by DØ - PRD **60** 52001 (1999).

- B. Quinn FNAL

- DPF2003 April 5-8

##  Three differences between the two approaches

_**Template Method**_

_**Optimized Method**_

- All the events are presented to the _**same template**_.
- The template corresponds to a probability distribution for the entire sample, using _**several variables**_ calculated from MC simulations.
- The features of individual events are integrated _**(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).
- The full information contained in each event is contributed to the probability: _**well-measured events contribute more than poorly-measured events.**_

- B. Quinn FNAL

- DPF2003 April 5-8

## The general method

**Detector and reconstruction effects (e.g. fiducial regions) are multiplicative and lead to acceptance corrections independent of the parameter to be estimated:**
**The probability ****P(x;α)**** can be calculated as:**

***The general method***

**x**** : the set of variables measured in the detector               ****y**** : the set of parton level variables **
**d****n****σ**** : the differential cross section                                      ****f(q)**** : the parton distribution functions **
**W(y,x)**** : transfer function, the probability that a parton level set of variables ****y**** will show up in the            **
**               ****detector as the set of variables ****x****  **

- B. Quinn FNAL

- DPF2003 April 5-8

## Transfer function W(x,y)

***Transfer function W(x,y)***

***W(x,y)*** : probability of measuring** ****x**** **when** ****y**** **was produced ** (*****x*** : measured 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. And 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*), the parameters were extracted from MC simulation.

- B. Quinn FNAL

- DPF2003 April 5-8

## Probability for tt 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
- These variables of integration were chosen because |M|2 is almost  negligible except near the four Breit-Wigners peaks within |M|2.

- 5 integrals
- 20 degrees of freedom: 2(in) + 18(final)
- 15 constraints: 3 (e) + 8 (1..4) + 3 (Pin=Pfinal) + 1 (Ein=Efinal)
- Sum over the 12 jet permutations
- All values of the neutrino momentum are considered

- B. Quinn FNAL

- DPF2003 April 5-8

## Signal and Background

***Signal and Background***

**The background probability is defined only in terms of the main background **
**W+jets (80%)**
**An adequate representation for the QCD multijet background (20%).**
**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 ********.**

- B. Quinn FNAL

- DPF2003 April 5-8

## Extra selection in Pbkg

***Extra selection in P******bkg***

**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***

**ttbar@175GeV**

**W+jets**

**PRD 58, 52001 (1998)**

**D=P****sig****/(P****sig****+P****bkg****)**

- B. Quinn FNAL

- DPF2003 April 5-8

## Signal and background probabilities: a MC vs. data comparison

- Background probability comparison between data (dots) and MC (histogram).  Background (signal) MC events are shown in blue (red).  The MC S/B ratio was set to the measured ratio S/B=12/10 for Pbkg<10-11 .

- Signal probability comparison between data (dots) and MC (histogram) in the form of a discriminant D=Psig/(Psig+Pbkg).  The signal probability was taken at it’s maximum value. The MC S/B ratio was set to the measured ratio S/B=12/10 for Pbkg<10-11 .

- B. Quinn FNAL

- DPF2003 April 5-8

## Top probability for data events

***Top probability ******for data events***

**Right plots show  -ln(P****tt****) as a function of M****t**** for  10****-9****<P****bkg**** <10****-8****  (red arrows in lower figure).**

- B. Quinn FNAL

- DPF2003 April 5-8

## Top probability for data events

***Top probability ******for data events***

**Right plots show  -ln(P****tt****) as a function of M****t**** for  9.7x10****-13 ****<P****bkg**** < 9.0x10****-12****   (red arrows in lower figure).**

- B. Quinn FNAL

- DPF2003 April 5-8

## Varying the background probability cut

***Varying the background probability cut***

- The top plot shows Mt as a function of the cut in the background probability (Pbkg).  Mt is very stable over a change in the number of events (N) of more that a factor of 2, and a change in Pbkg of more that a factor of 10.
- The plots on the right show –ln(L) as a function of Mt for each of the points in the plot above.  The background enters mainly as a tail at low masses.

- B. Quinn FNAL

- DPF2003 April 5-8

## Preliminary Result with DØ Run I data

***Preliminary Result with D******Ø Run I data***

**M****t****= 179.9 ******** 3.6 GeV ******** SYST**
**This optimized method 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.**_** **
**Out of 22 events which pass the cuts, the analysis gives a total of 12.5 ± 3.0 t-tbar events.  **

**D****Ø Preliminary**

**D****Ø Preliminary**

- B. Quinn FNAL

- DPF2003 April 5-8

## Total Uncertainty

**Determined from MC studies with large event samples:**
**Determined from data:**

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

**Total systematic:****	****6.0 GeV**
**Total:****	****	****	****7.0 GeV**

_**D**__**Ø Preliminary**_

| Jet Energy Scale | 5.6 GeV |
| --- | --- |
| Parton Distribution Function | 0.2 GeV |
| Acceptance Correction | 0.5 GeV |

**This error will be significantly reduced in the final result. **

- B. Quinn FNAL

- DPF2003 April 5-8

## Tevatron Top quark mass measurements

***Tevatron Top quark mass measurements***

- B. Quinn FNAL

- DPF2003 April 5-8

## Check of Mw: Future handle on Jet Energy Scale

**D****Ø Preliminary**

**D****Ø Preliminary**

**M****w**** can be measured in the same events where M****t**** is measured**
**This can be very helpful for reducing the uncertainty in the jet energy scale**
**DØ is currently studying this option for Run II.  See the Proceedings of DPF2002 (Top quark physics) **_**[http://dpf2002.velopers.net/talks_pdf/120talk.pdf](http://dpf2002.velopers.net/talks_pdf/120talk.pdf)**__**.  **_

- B. Quinn FNAL

- DPF2003 April 5-8

## Conclusions 

***Conclusions ***

**M****t**** = 179.9 ******** 3.6 (stat) ******** 6.0 (syst.) GeV **

**Significant improvement to the previous D****Ø ****measurement ****[M****t****= 173.3 ******** 5.6 (stat) ******** 5.5 (syst.) GeV (LB analysis in PRD)]**** - equivalent to 2.4 times more data:**
**Correct permutation is always considered (along with the other 11) **
**All features of the individual events are included, meaning well measured events contribute more information than poorly measured events.**
**The possibility of checking the value of the *****W***** mass in the hadronic branch on the same events provides a new handle in Run II for controlling the largest systematic error, the jet energy scale. **

_**D**__**Ø Preliminary**_

- B. Quinn FNAL

- DPF2003 April 5-8

## Two and three jet invariant masses

- Two (left plot) and three (right plot) jet invariant mass distributions.  The error bars correspond to t-tbar MC events for which the jets were matched to partons.  The curves correspond to our calculations for two different transfer functions Wjet(x,y).  The dashed-dotted line corresponds to the transfer function used in the final analysis.

**FWHM = 40 GeV**

- B. Quinn FNAL

- DPF2003 April 5-8

## Matrix Element

***Matrix Element***

-        no ttbar spin correlation included
-        ***s******qt*** : sine of angle between q and t in the q q CM
-        ****** : top quark's velocity in the q q CM
-        ***g******s*** : strong coupling constant

**Leptonic decay:**

**Hadronic decay:**

***M******t,**** ****M******W*** : pole mass of  top and W
***m******t****** ***: top mass in any event
***m******e************ ******,m******du*** : invariant mass of the e and du (or cs) system
*********t****** ,************W***  : width of top and W
***g******W*** : weak coupling constant
*********(cos **********eb,db******)*** : angular distribution of the W decay

- B. Quinn FNAL

- DPF2003 April 5-8

## Acceptance Corrections

_**Detector Acceptance:**_

_**Likelihood:**_

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

**Detector acceptance**

**Measured probability**

- ,   and  Ngen(N) is the number of generated(accepted) events

- B. Quinn FNAL

- DPF2003 April 5-8

## Crosschecks on Ensemble Tests (12 signal+10 background)

**From the ensemble tests we estimate a 0.5 GeV bias in the peak with respect to the generated value**

- B. Quinn FNAL

- DPF2003 April 5-8

## Crosschecks on Ensemble Tests (12 signal+10 background)

**The most probable result of these experiments is M****t****=174.7 GeV **
**top generated at M****t****=175.0 GeV**

- B. Quinn FNAL

- DPF2003 April 5-8

## Crosscheck of linearity of response

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

- B. Quinn FNAL

- DPF2003 April 5-8

## Systematic error due to tt model

***Systematic error due to tt model***

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

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

**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**

- B. Quinn FNAL

- DPF2003 April 5-8

## Systematic error due to background model

***Systematic error due to background model***

**Results for different VECBOS **
**flavors: Q****2**** scale of either <p****t****jet****>****2**** or **
**M****2****W**** ,and with either HERWIG or **
**ISAJET fragmentation.**
**From left to right: **
**M****2****W**** and IS**
**M****2****W**** and HW**
**<p****t****jet****>****2**** and HW.**
**The points with large error bars **
**were calculated with 250s+500b **
**events, and the ones with small error **
**bars with 400s+800b events.  The **
**number of events is specified before **
**the cut in P****bkg**** .**
**The assigned systematic uncertainty **
**is:  ********=1.0 GeV **

- B. Quinn FNAL

- DPF2003 April 5-8

## Extra selection in Pbkg

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

- B. Quinn FNAL

- DPF2003 April 5-8